In the preceding section of Steady State, 1-D
heat conduction analysis, we considered
conduction problems for which the
temperature distribution in a medium was
determined solely by conditions at the
boundaries of the medium
To demonstrate the relationship between power input and surface temperature i...Salman Jailani
This experiment aims to demonstrate the relationship between power input and surface temperature under forced convection conditions. The experiment uses a heat exchanger placed in a duct with a fan and heater. The fan speed is varied from 0.5 m/s to 1.5 m/s while the heater power is held constant. Observations show that as fan speed, and therefore forced convection, increases, the difference between the heated plate temperature and ambient air temperature decreases.
This document discusses vapor/liquid equilibrium (VLE) and provides models for predicting VLE using simple models like Raoult's law and Henry's law. It defines key terms like mass fraction, mole fraction, molar concentration. Duhem's theorem is introduced which states that the equilibrium state is determined by fixing any two independent variables for a closed system. Simple calculations are shown for using Raoult's law to determine the bubble point and dew point temperatures and pressures of a binary system from its phase compositions or known temperature. P-x-y and T-x-y diagrams are used to illustrate the VLE behavior between the phases.
This document summarizes a laboratory experiment on the Joule-Thomson effect. The experiment measured the temperature change of carbon dioxide gas as it underwent adiabatic expansion from high to low pressures. The measured experimental Joule-Thomson coefficient for CO2 was 0.0074 K/kPa, with a 7.76% error compared to the theoretical coefficient calculated from gas properties. The results confirmed that temperature decreases with decreasing pressure during Joule-Thomson expansion of real gases.
This document contains chapter 1 of lecture notes on engineering thermodynamics. It introduces thermodynamics as the study of energy and its transformation between different forms, as well as the transfer of energy across system boundaries. It discusses the macroscopic and microscopic approaches to thermodynamics, defining key concepts like systems, properties, states, and processes. The chapter also outlines common units and properties measured in thermodynamics like pressure, temperature, and fluid behavior.
This document reports on two experiments conducted to determine thermodynamic properties of air. Experiment A involved simulating an adiabatic expansion of air in a vessel to calculate the adiabatic index. The average value obtained was 1.7, close to the expected value of 1.4. Experiment B used an isothermal expansion process to determine the ratio of volumes between two vessels, obtaining a value near the actual ratio of 2.43. Sources of error are discussed, and improvements like automated data logging are suggested to increase accuracy and consistency.
• Consulted on the heat transfer coefficients on two different materials, concrete and aluminum.
• Generated plotted graphs of the temperature loss per time using two different methods, the Heisler Method and Newtonian Cooling Method, all while performing error analysis.
1) Heat transfer by conduction occurs due to random molecular motion within a material. The rate of heat transfer by conduction is proportional to the temperature gradient and the thermal conductivity of the material.
2) Fourier's law of heat conduction describes conduction in Cartesian, cylindrical, and spherical coordinate systems. It relates the heat flux to the temperature gradient through the thermal conductivity.
3) The heat equation can be derived by applying the law of conservation of energy combined with Fourier's law. It describes the distribution of temperature as a function of time and space within a body undergoing transient or steady-state heat conduction.
This document describes a numerical method for solving the 2D steady-state heat equation for rectangular and T-shaped plates. For the rectangular plate, MATLAB is used to discretize the heat equation and implement an iterative solver to determine the temperature distribution. Contour and surface plots of the results are generated. For the T-shaped plate, the same approach is taken but the geometry is separated into two blocks that are solved together, with boundary conditions set at the interface.
To demonstrate the relationship between power input and surface temperature i...Salman Jailani
This experiment aims to demonstrate the relationship between power input and surface temperature under forced convection conditions. The experiment uses a heat exchanger placed in a duct with a fan and heater. The fan speed is varied from 0.5 m/s to 1.5 m/s while the heater power is held constant. Observations show that as fan speed, and therefore forced convection, increases, the difference between the heated plate temperature and ambient air temperature decreases.
This document discusses vapor/liquid equilibrium (VLE) and provides models for predicting VLE using simple models like Raoult's law and Henry's law. It defines key terms like mass fraction, mole fraction, molar concentration. Duhem's theorem is introduced which states that the equilibrium state is determined by fixing any two independent variables for a closed system. Simple calculations are shown for using Raoult's law to determine the bubble point and dew point temperatures and pressures of a binary system from its phase compositions or known temperature. P-x-y and T-x-y diagrams are used to illustrate the VLE behavior between the phases.
This document summarizes a laboratory experiment on the Joule-Thomson effect. The experiment measured the temperature change of carbon dioxide gas as it underwent adiabatic expansion from high to low pressures. The measured experimental Joule-Thomson coefficient for CO2 was 0.0074 K/kPa, with a 7.76% error compared to the theoretical coefficient calculated from gas properties. The results confirmed that temperature decreases with decreasing pressure during Joule-Thomson expansion of real gases.
This document contains chapter 1 of lecture notes on engineering thermodynamics. It introduces thermodynamics as the study of energy and its transformation between different forms, as well as the transfer of energy across system boundaries. It discusses the macroscopic and microscopic approaches to thermodynamics, defining key concepts like systems, properties, states, and processes. The chapter also outlines common units and properties measured in thermodynamics like pressure, temperature, and fluid behavior.
This document reports on two experiments conducted to determine thermodynamic properties of air. Experiment A involved simulating an adiabatic expansion of air in a vessel to calculate the adiabatic index. The average value obtained was 1.7, close to the expected value of 1.4. Experiment B used an isothermal expansion process to determine the ratio of volumes between two vessels, obtaining a value near the actual ratio of 2.43. Sources of error are discussed, and improvements like automated data logging are suggested to increase accuracy and consistency.
• Consulted on the heat transfer coefficients on two different materials, concrete and aluminum.
• Generated plotted graphs of the temperature loss per time using two different methods, the Heisler Method and Newtonian Cooling Method, all while performing error analysis.
1) Heat transfer by conduction occurs due to random molecular motion within a material. The rate of heat transfer by conduction is proportional to the temperature gradient and the thermal conductivity of the material.
2) Fourier's law of heat conduction describes conduction in Cartesian, cylindrical, and spherical coordinate systems. It relates the heat flux to the temperature gradient through the thermal conductivity.
3) The heat equation can be derived by applying the law of conservation of energy combined with Fourier's law. It describes the distribution of temperature as a function of time and space within a body undergoing transient or steady-state heat conduction.
This document describes a numerical method for solving the 2D steady-state heat equation for rectangular and T-shaped plates. For the rectangular plate, MATLAB is used to discretize the heat equation and implement an iterative solver to determine the temperature distribution. Contour and surface plots of the results are generated. For the T-shaped plate, the same approach is taken but the geometry is separated into two blocks that are solved together, with boundary conditions set at the interface.
1. Mass transfer is the movement of a component from one location to another where the concentration is different. It occurs through molecular diffusion and eddy diffusion.
2. Molecular diffusion is the random movement of molecules due to thermal motion. Eddy diffusion is the random macroscopic fluid motion in turbulent flows.
3. Fick's first law states that the rate of molecular diffusion is proportional to the concentration gradient. The rate of mass transfer stops when concentrations are uniform.
This file contains slides on Transient Heat conduction: Part-II
The slides were prepared while teaching Heat Transfer course to the M.Tech. students in the year 2010.
Contents: Semi-infinite solids with different BC’s - Problems - Product solution for multi-dimension systems -
Summary of Basic relations for transient conduction
This document defines key concepts related to set convergence, including:
1) The inner and outer limits of a sequence of sets in topological and normed spaces, which describe the limit inferior and limit superior of the sets.
2) Properties of set convergence like the limit inferior and limit superior being characterized as intersections and unions of the sets over cofinal subsets of the natural numbers.
3) Characterizations of the inner and outer limits of sets in terms of open neighborhoods in topological spaces and open balls in normed spaces.
4) The inner limit of a sequence of sets in a normed space being the points for which the distance to the sets goes to zero as the index increases.
chapter 4 first law of thermodynamics thermodynamics 1abfisho
This document discusses the first law of thermodynamics for closed systems. It begins by defining the first law as the law of conservation of energy, where energy cannot be created or destroyed, only transformed between states. The energy balance is then analyzed for closed systems, where the internal energy, kinetic energy, potential energy, work and heat transfer across boundaries are considered. Several examples are provided to demonstrate applying the first law to calculate changes in internal energy, work, heat transfer and other properties for closed thermodynamic systems undergoing various processes like constant volume, constant pressure and others.
Fluid Mechanics Chapter 4. Differential relations for a fluid flowAddisu Dagne Zegeye
Introduction, Acceleration field, Conservation of mass equation, Linear momentum equation, Energy equation, Boundary condition, Stream function, Vorticity and Irrotationality
This experiment aims to determine the relationship between the saturated temperature and pressure of steam in equilibrium with water between 0 and 14 bars using a Marcet boiler. The measured slope of the temperature-pressure graph is compared to theoretical values from steam tables. Results show a direct proportional relationship between temperature and pressure, with the experimental slope deviating slightly from the theoretical slope due to measurement errors ranging from 0.3-44%. The Marcet boiler can be used to study this relationship and various thermodynamic applications that involve changes in steam properties with pressure and temperature.
application of first order ordinary Differential equationsEmdadul Haque Milon
The document provides information about Group D's presentation which includes 10 members. It lists the members' names and student IDs. It then outlines 3 topics that will be covered: 1) Applications of first order ordinary differential equations, 2) Orthogonal trajectories, and 3) Oblique trajectories. For the first topic, it provides examples of applications in fields like physics, statistics, chemistry, and engineering. It also shows sample problems and solutions related to population growth, curve determination, cooling/warming, carbon dating, and radioactive decay. For the second topic, it defines orthogonal trajectories and provides an example of finding the orthogonal trajectories of a family of parabolas.
Advanced Engineering Mathematics Chapter 6 Laplace TransformsSarah Brown
The document discusses the Laplace transform method for solving ordinary differential equations (ODEs). It explains that the Laplace transform method involves three steps: (1) transforming the ODE into an algebraic equation called the subsidiary equation, (2) solving the subsidiary equation using algebraic manipulations, and (3) taking the inverse Laplace transform of the solution to obtain the solution to the original ODE. The key advantages of this method are that it allows initial value problems to be solved directly without first finding the general solution, and it can handle nonhomogeneous ODEs and problems with discontinuous inputs.
ch20-Entropy and the Second Law of Thermodynamics.pptsahruldedadri
The document discusses entropy and the second law of thermodynamics. It introduces key concepts such as:
- The entropy postulate which states that entropy always increases for irreversible processes in closed systems.
- How to calculate the change in entropy for reversible and irreversible processes. Entropy is a state function.
- Applications of entropy including Carnot engines, refrigerators, and the limitations they impose by the second law.
- A statistical view of entropy in terms of multiplicity of microscopic configurations and the relationship between entropy and probability.
The document summarizes key concepts from thermodynamics including:
- The Zeroth Law of Thermodynamics states that if two systems are each in thermal equilibrium with a third system, they are in thermal equilibrium with each other.
- The First Law of Thermodynamics states that energy cannot be created or destroyed, only changed in form. For a closed system, the net energy transferred as heat and work equals the net change in internal energy.
- Derivations from the First Law relate internal energy change, enthalpy change, and specific heat capacities for constant volume and constant pressure processes. Relationships between specific heat capacities are also derived for ideal gases.
- Several examples show applying the
This document discusses heat transfer through conduction and various methods for solving the heat equation using finite difference approximations. It introduces the heat equation in Cartesian, cylindrical and spherical coordinates. It discusses boundary conditions and describes setting up a nodal network to discretize the domain. It then presents the finite difference form of the heat equation and describes different cases for nodal finite difference equations, including for interior nodes, nodes at corners or surfaces with convection, and nodes at surfaces with uniform heat flux. It discusses solving the finite difference equations using matrix inversion, Gauss-Seidel iteration, and provides examples.
1. The document describes an experiment to measure Earth's magnetic field using a tangent galvanometer. Connections are made between the galvanometer, battery, ammeter, rheostat and commutator.
2. Readings of current and deflection angle are recorded for different currents by reversing the current. The data is plotted on a graph of tangent of deflection angle vs current.
3. From the slope of the graph and properties of the galvanometer coil, the value of Earth's magnetic field is calculated as 7.6867 x 10-8 T.
Cfd( on finite difference method)assignmentTesfaTsiha
This document provides details of an assignment to determine the temperature distribution in a block using numerical analysis and MATLAB. It describes the block geometry, assumptions made, and steps taken to solve the problem using a numerical technique called the Gauss-Seidel method. The block is divided into a grid and the heat conduction equation is applied to each node to iteratively calculate the temperature at each point. The process is repeated over several iterations until the temperatures converge to a steady solution.
The document discusses the lumped element method (LEM) for analyzing transient heat transfer problems. It defines a lumped system as one where the interior temperature remains uniform over time. The lumped element approach provides a simplification to heat transfer calculations using a lumped parameter called the time constant. The document also covers using the method of separation of variables to solve the heat equation for transient conduction problems, reducing the partial differential equation to ordinary differential equations that can be solved. It provides an example of applying separation of variables to a one-dimensional conduction problem between fixed temperatures.
This file contains slides on NUMERICAL METHODS IN STEADY STATE 1D and 2D HEAT CONDUCTION – Part-I.
The slides were prepared while teaching Heat Transfer course to the M.Tech. students.
Contents: Why Numerical methods? – Advantages – Finite difference formulation from differential eqns – 1D steady state conduction in cartesian coordinates – formulation by energy balance method – different BC’s – Problems
This document contains slides on transient heat conduction from a lecture. It discusses lumped system analysis where the internal conduction resistance is negligible compared to the surface convection resistance. For lumped systems, the temperature at any point in the solid varies only with time. It introduces the Biot and Fourier numbers which are used to determine if lumped system analysis can be applied for a given solid geometry and time. The temperature distribution equation for lumped systems is presented.
This document provides information about two-dimensional steady state heat conduction using the finite difference method. It includes:
1) Derivation of the finite difference equations for interior nodes, nodes on insulated surfaces, and nodes with convection boundary conditions using the energy balance method.
2) Discussion of using shape factors and dimensionless parameters to solve conduction problems and examples of common geometric configurations.
3) Methods for verifying the accuracy of finite difference solutions, including grid refinement studies and comparison to exact solutions.
Heat Conduction with thermal heat generation.pptxBektu Dida
Heat Conduction analysis is done in one dimensional steady state heat conduction considering internal heat generation per unit volume on plane and radial walls. Examples are directly taken from textbooks.
Latif M. Jiji (auth.) - Solutions Manual for Heat Conduction (Chap1-2-3) (200...ezedin4
This document presents the problem of determining the temperature distribution in a plate that is heated by radiation with a non-uniform volumetric heat generation rate. The plate has one surface maintained at a uniform temperature, while the opposite surface is insulated. The governing one-dimensional steady-state heat equation with the variable heat generation term is derived. Boundary conditions of specified temperature at one surface and insulated condition at the other surface are applied. The temperature distribution in the plate is obtained by separating variables and applying the boundary conditions. This gives an expression for the temperature at any point in the plate, including the insulated surface. Dimensional and boundary condition checks are performed to verify the solution.
1. Mass transfer is the movement of a component from one location to another where the concentration is different. It occurs through molecular diffusion and eddy diffusion.
2. Molecular diffusion is the random movement of molecules due to thermal motion. Eddy diffusion is the random macroscopic fluid motion in turbulent flows.
3. Fick's first law states that the rate of molecular diffusion is proportional to the concentration gradient. The rate of mass transfer stops when concentrations are uniform.
This file contains slides on Transient Heat conduction: Part-II
The slides were prepared while teaching Heat Transfer course to the M.Tech. students in the year 2010.
Contents: Semi-infinite solids with different BC’s - Problems - Product solution for multi-dimension systems -
Summary of Basic relations for transient conduction
This document defines key concepts related to set convergence, including:
1) The inner and outer limits of a sequence of sets in topological and normed spaces, which describe the limit inferior and limit superior of the sets.
2) Properties of set convergence like the limit inferior and limit superior being characterized as intersections and unions of the sets over cofinal subsets of the natural numbers.
3) Characterizations of the inner and outer limits of sets in terms of open neighborhoods in topological spaces and open balls in normed spaces.
4) The inner limit of a sequence of sets in a normed space being the points for which the distance to the sets goes to zero as the index increases.
chapter 4 first law of thermodynamics thermodynamics 1abfisho
This document discusses the first law of thermodynamics for closed systems. It begins by defining the first law as the law of conservation of energy, where energy cannot be created or destroyed, only transformed between states. The energy balance is then analyzed for closed systems, where the internal energy, kinetic energy, potential energy, work and heat transfer across boundaries are considered. Several examples are provided to demonstrate applying the first law to calculate changes in internal energy, work, heat transfer and other properties for closed thermodynamic systems undergoing various processes like constant volume, constant pressure and others.
Fluid Mechanics Chapter 4. Differential relations for a fluid flowAddisu Dagne Zegeye
Introduction, Acceleration field, Conservation of mass equation, Linear momentum equation, Energy equation, Boundary condition, Stream function, Vorticity and Irrotationality
This experiment aims to determine the relationship between the saturated temperature and pressure of steam in equilibrium with water between 0 and 14 bars using a Marcet boiler. The measured slope of the temperature-pressure graph is compared to theoretical values from steam tables. Results show a direct proportional relationship between temperature and pressure, with the experimental slope deviating slightly from the theoretical slope due to measurement errors ranging from 0.3-44%. The Marcet boiler can be used to study this relationship and various thermodynamic applications that involve changes in steam properties with pressure and temperature.
application of first order ordinary Differential equationsEmdadul Haque Milon
The document provides information about Group D's presentation which includes 10 members. It lists the members' names and student IDs. It then outlines 3 topics that will be covered: 1) Applications of first order ordinary differential equations, 2) Orthogonal trajectories, and 3) Oblique trajectories. For the first topic, it provides examples of applications in fields like physics, statistics, chemistry, and engineering. It also shows sample problems and solutions related to population growth, curve determination, cooling/warming, carbon dating, and radioactive decay. For the second topic, it defines orthogonal trajectories and provides an example of finding the orthogonal trajectories of a family of parabolas.
Advanced Engineering Mathematics Chapter 6 Laplace TransformsSarah Brown
The document discusses the Laplace transform method for solving ordinary differential equations (ODEs). It explains that the Laplace transform method involves three steps: (1) transforming the ODE into an algebraic equation called the subsidiary equation, (2) solving the subsidiary equation using algebraic manipulations, and (3) taking the inverse Laplace transform of the solution to obtain the solution to the original ODE. The key advantages of this method are that it allows initial value problems to be solved directly without first finding the general solution, and it can handle nonhomogeneous ODEs and problems with discontinuous inputs.
ch20-Entropy and the Second Law of Thermodynamics.pptsahruldedadri
The document discusses entropy and the second law of thermodynamics. It introduces key concepts such as:
- The entropy postulate which states that entropy always increases for irreversible processes in closed systems.
- How to calculate the change in entropy for reversible and irreversible processes. Entropy is a state function.
- Applications of entropy including Carnot engines, refrigerators, and the limitations they impose by the second law.
- A statistical view of entropy in terms of multiplicity of microscopic configurations and the relationship between entropy and probability.
The document summarizes key concepts from thermodynamics including:
- The Zeroth Law of Thermodynamics states that if two systems are each in thermal equilibrium with a third system, they are in thermal equilibrium with each other.
- The First Law of Thermodynamics states that energy cannot be created or destroyed, only changed in form. For a closed system, the net energy transferred as heat and work equals the net change in internal energy.
- Derivations from the First Law relate internal energy change, enthalpy change, and specific heat capacities for constant volume and constant pressure processes. Relationships between specific heat capacities are also derived for ideal gases.
- Several examples show applying the
This document discusses heat transfer through conduction and various methods for solving the heat equation using finite difference approximations. It introduces the heat equation in Cartesian, cylindrical and spherical coordinates. It discusses boundary conditions and describes setting up a nodal network to discretize the domain. It then presents the finite difference form of the heat equation and describes different cases for nodal finite difference equations, including for interior nodes, nodes at corners or surfaces with convection, and nodes at surfaces with uniform heat flux. It discusses solving the finite difference equations using matrix inversion, Gauss-Seidel iteration, and provides examples.
1. The document describes an experiment to measure Earth's magnetic field using a tangent galvanometer. Connections are made between the galvanometer, battery, ammeter, rheostat and commutator.
2. Readings of current and deflection angle are recorded for different currents by reversing the current. The data is plotted on a graph of tangent of deflection angle vs current.
3. From the slope of the graph and properties of the galvanometer coil, the value of Earth's magnetic field is calculated as 7.6867 x 10-8 T.
Cfd( on finite difference method)assignmentTesfaTsiha
This document provides details of an assignment to determine the temperature distribution in a block using numerical analysis and MATLAB. It describes the block geometry, assumptions made, and steps taken to solve the problem using a numerical technique called the Gauss-Seidel method. The block is divided into a grid and the heat conduction equation is applied to each node to iteratively calculate the temperature at each point. The process is repeated over several iterations until the temperatures converge to a steady solution.
The document discusses the lumped element method (LEM) for analyzing transient heat transfer problems. It defines a lumped system as one where the interior temperature remains uniform over time. The lumped element approach provides a simplification to heat transfer calculations using a lumped parameter called the time constant. The document also covers using the method of separation of variables to solve the heat equation for transient conduction problems, reducing the partial differential equation to ordinary differential equations that can be solved. It provides an example of applying separation of variables to a one-dimensional conduction problem between fixed temperatures.
This file contains slides on NUMERICAL METHODS IN STEADY STATE 1D and 2D HEAT CONDUCTION – Part-I.
The slides were prepared while teaching Heat Transfer course to the M.Tech. students.
Contents: Why Numerical methods? – Advantages – Finite difference formulation from differential eqns – 1D steady state conduction in cartesian coordinates – formulation by energy balance method – different BC’s – Problems
This document contains slides on transient heat conduction from a lecture. It discusses lumped system analysis where the internal conduction resistance is negligible compared to the surface convection resistance. For lumped systems, the temperature at any point in the solid varies only with time. It introduces the Biot and Fourier numbers which are used to determine if lumped system analysis can be applied for a given solid geometry and time. The temperature distribution equation for lumped systems is presented.
This document provides information about two-dimensional steady state heat conduction using the finite difference method. It includes:
1) Derivation of the finite difference equations for interior nodes, nodes on insulated surfaces, and nodes with convection boundary conditions using the energy balance method.
2) Discussion of using shape factors and dimensionless parameters to solve conduction problems and examples of common geometric configurations.
3) Methods for verifying the accuracy of finite difference solutions, including grid refinement studies and comparison to exact solutions.
Heat Conduction with thermal heat generation.pptxBektu Dida
Heat Conduction analysis is done in one dimensional steady state heat conduction considering internal heat generation per unit volume on plane and radial walls. Examples are directly taken from textbooks.
Latif M. Jiji (auth.) - Solutions Manual for Heat Conduction (Chap1-2-3) (200...ezedin4
This document presents the problem of determining the temperature distribution in a plate that is heated by radiation with a non-uniform volumetric heat generation rate. The plate has one surface maintained at a uniform temperature, while the opposite surface is insulated. The governing one-dimensional steady-state heat equation with the variable heat generation term is derived. Boundary conditions of specified temperature at one surface and insulated condition at the other surface are applied. The temperature distribution in the plate is obtained by separating variables and applying the boundary conditions. This gives an expression for the temperature at any point in the plate, including the insulated surface. Dimensional and boundary condition checks are performed to verify the solution.
One dim, steady-state, heat conduction_with_heat_generationtmuliya
This file contains slides on One-dimensional, steady-state heat conduction with heat generation.
The slides were prepared while teaching Heat Transfer course to the M.Tech. students in Mechanical Engineering Dept. of St. Joseph Engineering College, Vamanjoor, Mangalore, India, during Sept. – Dec. 2010.
It is hoped that these Slides will be useful to teachers, students, researchers and professionals working in this field.
Ch 2 - Steady state 1-D, Heat conduction.pdfAyaAya64793
This document discusses heat conduction through plane walls and hollow cylinders. It introduces the concepts of one-dimensional steady-state heat conduction without heat generation. The differential equation for heat conduction is derived for plane walls and cylindrical coordinates. Methods to solve for temperature distributions and heat fluxes are presented, including the use of thermal resistance networks and overall heat transfer coefficients. Multilayer walls and composite materials are also analyzed.
This document provides an introduction to heat transfer and the different modes of heat transfer including conduction, convection, radiation, boiling, and condensation. It defines key terms like thermal conductivity and heat flux. Examples of one-dimensional heat conduction through plane walls, cylindrical walls, and multilayer walls are presented. The document also provides sample problems and their solutions for determining heat transfer rates through composite walls and insulated cylinders.
The document summarizes key concepts of heat transfer including the three main modes: conduction, convection, and radiation. It provides equations to calculate heat transfer via these three modes. Specifically, it discusses Fourier's law of conduction, Newton's law of cooling for convection, and Stefan-Boltzmann law for radiation heat transfer. It also introduces important non-dimensional numbers used in heat transfer such as Reynolds number, Prandtl number, Nusselt number, and Stanton number.
Conducción de calor en estado estacionarioNorman Rivera
1. Steady state 1D heat conduction through planar, cylindrical, and spherical walls is analyzed using differential equations. Boundary conditions include convection, radiation, and interfaces.
2. The thermal resistance concept is introduced, where temperatures and heat fluxes across boundaries are related through thermal resistances. Systems with multiple resistances in series or parallel can be analyzed using thermal circuit analogies.
3. Examples of steady state heat conduction include a plane wall with convection on both sides, where the temperature distribution and heat transfer rate are determined.
The document introduces heat conduction analysis in one, two, and three dimensions using rectangular, cylindrical, and spherical coordinate systems. It derives the heat diffusion equation for each system and discusses the concepts of thermal resistance and thermal diffusivity. Key points discussed include:
- Derivation of the general three-dimensional heat conduction equation and simplified forms for steady-state one-dimensional conduction.
- Definition of thermal resistance as the ratio of temperature difference to heat flux.
- Expression of heat transfer through composite walls using thermal resistances in series and parallel.
- Introduction of thermal diffusivity and its relationship to heat conduction properties.
This document discusses heat and mass transfer, specifically focusing on heat conduction. It begins by defining heat transfer and its three main modes: conduction, convection, and radiation. Conduction is defined as the transfer of energy between particles without bulk motion. Applications of heat transfer are discussed, including energy production, refrigeration, manufacturing, and more. The document then covers key topics in conduction, including Fourier's Law of heat conduction, thermal conductivity, steady and unsteady heat conduction, extended surfaces, and thermal resistance networks. Specific cases like multilayer walls, cylinders, spheres, and fins are analyzed.
Solution Manual for Heat Convection second edition by Latif M. Jijiphysicsbook
Solution Manual for Heat Convection
https://unihelp.xyz/solution-manual-for-heat-convection-by-latif-jiji/
****
Solution Manual for Heat Conduction
https://unihelp.xyz/solution-manual-heat-conduction-latif-jiji/
Solution Manual for Heat Convection second edition by Latif M. Jiji
This document discusses heat transfer and conduction heat transfer principles. It defines heat transfer as energy in transit due to a temperature difference. The three modes of heat transfer are conduction, convection, and radiation. Fourier's law of conduction and Newton's law of cooling are described as the basic laws governing conduction and convection. The document also discusses concepts like the heat conduction equation, thermal resistance, boundary conditions, and classification of conduction heat transfer problems.
This document presents an experiment on heat transfer linear conductivity and effect conducted by students at the Polytechnic University of Puerto Rico. The objectives were to determine the thermal conductivity and temperature difference in various materials, study contact resistance, and analyze resistance effects. The theory section covered heat transfer concepts like Fourier's law, thermal conductivity, and thermal contact resistance. The procedure measured temperature distributions and heat flow through uniform and composite walls to calculate conductivity. Safety and references were also provided.
This document provides the problem statement, solution approach, and analysis for determining the total acceleration in an axisymmetric parallel flow in a tube. The key steps are:
1) The axial velocity distribution is given and is independent of axial and angular position.
2) Total acceleration expressions in cylindrical coordinates are applied.
3) For parallel streamlines, the radial velocity is zero.
4) The axial acceleration is found to be zero, and the radial and angular accelerations are also zero. All acceleration components vanish for this parallel flow case.
This document provides an overview of energy, energy transfer, and general energy analysis. It discusses:
1. The different forms and components of energy in a system, including internal, kinetic, and potential energy.
2. The different modes by which energy can transfer across system boundaries, including heat, work, and through mass flows for open systems.
3. Heat transfer occurs solely due to temperature differences, while work transfer is associated with forces and displacements.
4. Key concepts like the first law of thermodynamics, differentials of heat and work, and the classical sign convention for determining the direction of energy transfers.
two dimensional steady state heat conduction Amare Addis
This document provides information about two-dimensional steady state heat conduction using the finite difference method. It includes:
1) Derivation of the finite difference equations for interior nodes, nodes on insulated surfaces, and nodes with convection boundary conditions using the energy balance method.
2) Discussion of using shape factors and dimensionless parameters to simplify solving two-dimensional conduction problems.
3) Methods for verifying the accuracy of finite difference solutions, including grid refinement studies and comparison to exact solutions.
The document presents thermal modeling results for isothermal cuboids and rectangular heat sinks cooled by natural convection. It describes analytical correlations for calculating heat transfer from cuboids and compares the results to experimental data. It also details the META simulation tool, which uses a finite volume method to model conjugate heat transfer between solid and fluid regions. META is used to simulate natural convection cooling over a wide range of Rayleigh numbers for various rectangular heat sink geometries, including base plates, single fins, extended base plates, and raised fins with a base plate. The modeling results are compared to experimental data from previous studies.
lecture pf control system_thermal system_206.pdfAtmacaDevrim
The document discusses thermal systems and concepts such as:
- Thermal systems involve the storage and transfer of energy as heat. Heat flows from higher to lower temperatures.
- The law of conservation of energy applies to thermal systems, where the change in internal energy equals heat supplied minus work done.
- Thermal resistance and capacitance relate temperature differences and heat flow in thermal systems, analogous to voltage and capacitance in electrical systems.
- Heat transfer occurs through conduction, convection and radiation, and can be modeled using concepts like Newton's law of cooling.
Radial Heat Transport in Packed Beds-III: Correlations of Effective Transport...inventionjournals
The reliability and accuracy of experimental with predictions data of two models ("MC model" Marshall and Coberly model, [1] and modified model by Ibrahim et al. [2] are investigated for the effective radial thermal conductivity (Ker), and the wall heat transfer coefficient (hw) in packed beds in the absence of chemical reactions. The results were evaluated by the modified mathematical model as to the boundary bed inlet temperature; (To) number of terms of the solution series and number of experimental points used in the estimate. Very satisfactory was attained between the predicted and measured temperature profiles for a range of experiments. These cover a range of tube to (equivalent) particle diameter ratios from dt /dp = 4 to 10; Reynolds numbers ranged between 3.8-218 for particle, and elevated pressure from 11 to 20 bar for particle catalyst pellets. In all cases the fluid flowing throughout the bed has been air. The results indicate to the choice of the inlet boundary condition can have a large impact on the values of obtained parameters. And model parameters have been shown to be dependent on the pressure inside the reactor. The following correlations for both (hw) and (Ker) respectively under a given conditions obtained by using multiple regressions of our results that based on the modified mathematical model: Nuw = 67.9Re0.883(dt /dp) -0.635(P/Po) -1.354 Ker = 0.2396 + 0.0041Re The results accuracy of these correlations obtained from the modified mathematical model are more than the results accuracy of correlations obtained from MC model with respect to experimental data; these accuracy of both correlations reach up to 91% and 65% for (hw) and (Ker) respectively; which these results indicate to the reliability
GATE Mechanical Engineering notes on Heat Transfer. Use these notes as a preparation for GATE Mechanical Engineering and other engineering competitive exams. For full course visit https://mindvis.in/courses/gate-2018-mechanical-engineering-online-course or call 9779434433.
Semelhante a Conduction with Thermal Energy Generation.pdf (20)
Introduction- e - waste – definition - sources of e-waste– hazardous substances in e-waste - effects of e-waste on environment and human health- need for e-waste management– e-waste handling rules - waste minimization techniques for managing e-waste – recycling of e-waste - disposal treatment methods of e- waste – mechanism of extraction of precious metal from leaching solution-global Scenario of E-waste – E-waste in India- case studies.
The CBC machine is a common diagnostic tool used by doctors to measure a patient's red blood cell count, white blood cell count and platelet count. The machine uses a small sample of the patient's blood, which is then placed into special tubes and analyzed. The results of the analysis are then displayed on a screen for the doctor to review. The CBC machine is an important tool for diagnosing various conditions, such as anemia, infection and leukemia. It can also help to monitor a patient's response to treatment.
International Conference on NLP, Artificial Intelligence, Machine Learning an...gerogepatton
International Conference on NLP, Artificial Intelligence, Machine Learning and Applications (NLAIM 2024) offers a premier global platform for exchanging insights and findings in the theory, methodology, and applications of NLP, Artificial Intelligence, Machine Learning, and their applications. The conference seeks substantial contributions across all key domains of NLP, Artificial Intelligence, Machine Learning, and their practical applications, aiming to foster both theoretical advancements and real-world implementations. With a focus on facilitating collaboration between researchers and practitioners from academia and industry, the conference serves as a nexus for sharing the latest developments in the field.
Comparative analysis between traditional aquaponics and reconstructed aquapon...bijceesjournal
The aquaponic system of planting is a method that does not require soil usage. It is a method that only needs water, fish, lava rocks (a substitute for soil), and plants. Aquaponic systems are sustainable and environmentally friendly. Its use not only helps to plant in small spaces but also helps reduce artificial chemical use and minimizes excess water use, as aquaponics consumes 90% less water than soil-based gardening. The study applied a descriptive and experimental design to assess and compare conventional and reconstructed aquaponic methods for reproducing tomatoes. The researchers created an observation checklist to determine the significant factors of the study. The study aims to determine the significant difference between traditional aquaponics and reconstructed aquaponics systems propagating tomatoes in terms of height, weight, girth, and number of fruits. The reconstructed aquaponics system’s higher growth yield results in a much more nourished crop than the traditional aquaponics system. It is superior in its number of fruits, height, weight, and girth measurement. Moreover, the reconstructed aquaponics system is proven to eliminate all the hindrances present in the traditional aquaponics system, which are overcrowding of fish, algae growth, pest problems, contaminated water, and dead fish.
Batteries -Introduction – Types of Batteries – discharging and charging of battery - characteristics of battery –battery rating- various tests on battery- – Primary battery: silver button cell- Secondary battery :Ni-Cd battery-modern battery: lithium ion battery-maintenance of batteries-choices of batteries for electric vehicle applications.
Fuel Cells: Introduction- importance and classification of fuel cells - description, principle, components, applications of fuel cells: H2-O2 fuel cell, alkaline fuel cell, molten carbonate fuel cell and direct methanol fuel cells.
KuberTENes Birthday Bash Guadalajara - K8sGPT first impressionsVictor Morales
K8sGPT is a tool that analyzes and diagnoses Kubernetes clusters. This presentation was used to share the requirements and dependencies to deploy K8sGPT in a local environment.
Electric vehicle and photovoltaic advanced roles in enhancing the financial p...IJECEIAES
Climate change's impact on the planet forced the United Nations and governments to promote green energies and electric transportation. The deployments of photovoltaic (PV) and electric vehicle (EV) systems gained stronger momentum due to their numerous advantages over fossil fuel types. The advantages go beyond sustainability to reach financial support and stability. The work in this paper introduces the hybrid system between PV and EV to support industrial and commercial plants. This paper covers the theoretical framework of the proposed hybrid system including the required equation to complete the cost analysis when PV and EV are present. In addition, the proposed design diagram which sets the priorities and requirements of the system is presented. The proposed approach allows setup to advance their power stability, especially during power outages. The presented information supports researchers and plant owners to complete the necessary analysis while promoting the deployment of clean energy. The result of a case study that represents a dairy milk farmer supports the theoretical works and highlights its advanced benefits to existing plants. The short return on investment of the proposed approach supports the paper's novelty approach for the sustainable electrical system. In addition, the proposed system allows for an isolated power setup without the need for a transmission line which enhances the safety of the electrical network
Use PyCharm for remote debugging of WSL on a Windo cf5c162d672e4e58b4dde5d797...shadow0702a
This document serves as a comprehensive step-by-step guide on how to effectively use PyCharm for remote debugging of the Windows Subsystem for Linux (WSL) on a local Windows machine. It meticulously outlines several critical steps in the process, starting with the crucial task of enabling permissions, followed by the installation and configuration of WSL.
The guide then proceeds to explain how to set up the SSH service within the WSL environment, an integral part of the process. Alongside this, it also provides detailed instructions on how to modify the inbound rules of the Windows firewall to facilitate the process, ensuring that there are no connectivity issues that could potentially hinder the debugging process.
The document further emphasizes on the importance of checking the connection between the Windows and WSL environments, providing instructions on how to ensure that the connection is optimal and ready for remote debugging.
It also offers an in-depth guide on how to configure the WSL interpreter and files within the PyCharm environment. This is essential for ensuring that the debugging process is set up correctly and that the program can be run effectively within the WSL terminal.
Additionally, the document provides guidance on how to set up breakpoints for debugging, a fundamental aspect of the debugging process which allows the developer to stop the execution of their code at certain points and inspect their program at those stages.
Finally, the document concludes by providing a link to a reference blog. This blog offers additional information and guidance on configuring the remote Python interpreter in PyCharm, providing the reader with a well-rounded understanding of the process.
artificial intelligence and data science contents.pptxGauravCar
What is artificial intelligence? Artificial intelligence is the ability of a computer or computer-controlled robot to perform tasks that are commonly associated with the intellectual processes characteristic of humans, such as the ability to reason.
› ...
Artificial intelligence (AI) | Definitio
AI assisted telemedicine KIOSK for Rural India.pptx
Conduction with Thermal Energy Generation.pdf
1. 20ME301T – Heat Transfer
Dr. Rajesh Patel
Mechanical Engineering Department
School of Technology
Pandit Deendayal Petroleum University
Conduction with Thermal Energy
Generation
2. Conduction with Thermal Energy
Generation
In the preceding section of Steady State, 1-D
heat conduction analysis, we considered
conduction problems for which the
temperature distribution in a medium was
determined solely by conditions at the
boundaries of the medium.
The objective of this study is to consider
situations for which thermal energy is
being generated due to conversion from
some other energy form.
3. Conduction with Thermal Energy
Generation
A common thermal energy generation process involves:
Exothermic Chemical Reaction
Conversion from electrical to thermal energy in a
current-carrying medium (Ohmic, or resistance, or
Joule heating).
The rate at which energy is generated by
passing a current I through a medium of
electrical resistance Re is
4. Conduction with Thermal Energy
Generation
If this power generation (W) occurs uniformly
throughout the medium of volume V, the
volumetric generation rate (W/m3) is then
5. Heat Conduction with Thermal Energy
Generation in a Plane Wall
Consider the plane wall with uniform energy generation per unit volume
( is constant) and the surfaces are maintained at Ts,1 and Ts,2.
6. Heat Conduction with Thermal Energy
Generation in a Plane Wall
For steady state, 1-D heat conduction with heat
generation in a isotropic material (constant thermal
conductivity k), above equation will be reduced to
(1)
The general solution of Eqn. (1) is given by
(2)
7. Heat Conduction with Thermal Energy
Generation in a Plane Wall
(2)
Boundary Conditions:
B.C - I At x = -L T(-L) = Ts,1 (3)
B. C –II At x = L T(L) = Ts,2 (4)
Substituting B.C’s in Eqn. (2) , The constants may be evaluated as
(5)
Substituting constants
C1 and C2 in Eqn. (2)
8. Heat Conduction with Thermal Energy
Generation in a Plane Wall
Eqn. (6) represents the temperature distribution
(6)
9. Heat Conduction with Thermal Energy
Generation in a Plane Wall
(6)
Case-I: Symmetric boundary conditions
The temperature distribution is then symmetrical about
the mid-plane as shown in Figure. Ts,1 = Ts,2 = Ts
For the symmetric boundary conditions, Eqn. (6)
will be reduced to;
(7)
10. Heat Conduction with Thermal Energy
Generation in a Plane Wall
Case-I: Symmetric boundary conditions
(7)
The maximum temperature exists at the mid-
plane (x=0)
(8)
Combining Eqn. (7) and (8), temperature distribution can be written as;
(9)
11. Heat Conduction with Thermal Energy
Generation in a Plane Wall
Case-I: Symmetric boundary conditions
Note that at the plane of symmetry in Figure, the
temperature gradient is zero, (dT/dx)x=0 = 0.
Accordingly, there is no heat transfer across this
plane, and it may be represented by the
adiabatic surface
(9)
12. Heat Conduction with Thermal Energy
Generation in a Plane Wall
Case-I: Symmetric boundary conditions
(9)
Above results (equations) can be applied to
plane walls that are perfectly insulated on one
side (x=0) and maintained at a fixed temperature
Ts on the other side (x = L).
13. Heat Conduction with Thermal Energy
Generation in a Plane Wall
Case-I: Symmetric boundary conditions
Estimation of surface temperature Ts
Applying the energy balance at the surface at x = L
(Heat Conduction at surface at x = L) = (Heat
convection from surface x = L)
(1)
(2)
14. Heat Conduction with Thermal Energy
Generation in a Plane Wall
Case-I: Symmetric boundary conditions
(1)
(2)
Getting value of (dT/dx)x=L from Eqn. (1)
and substituting in Eqn. (2)
(3)
15. Radial Heat Conduction with Thermal
Energy Generation in a Cylinder
For steady-state conditions the rate at which heat
is generated within the cylinder must equal the
rate at which heat is convected from the surface
of the cylinder to a moving fluid.
For steady state,radial heat conduction with heat generation in a isotropic
material (constant thermal conductivity k), above equation will be reduced to
(1)
(2)
16. Radial Heat Conduction with Thermal
Energy Generation in a Cylinder
(2)
Integrating above equation twice, the general
solution for the temperature distribution can be
written as;
(3)
Boundary Conditions:
B.C - I At r = 0 (dT/dr) r=0) = 0 (4)
B. C –II At r = r T = Ts (5)
Substituting B.C’s into Eqn. (3), C1 and C2 can be estimated as;
17. Radial Heat Conduction with Thermal
Energy Generation in a Cylinder
(2)
(3)
Substituting C1 and
C2 into Eqn. (3)
(4)
Represents temperature distribution
For steady state radial heat
conduction with heat generation on
cylindrical component
18. Radial Heat Conduction with Thermal
Energy Generation in a Cylinder
Centerline temperature can be evaluated as
(4)
(5)
From Eqn (4) and (5), the temperature distribution in non-dimensional form
can be written as
19. Radial Heat Conduction with Thermal
Energy Generation in a Cylinder
(4)
Estimation of surface temperature Ts
From Overall Energy balance
(Heat Generation rate in system) = (Heat Convection from Surface)