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MET 214 Module 3

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MET 214 Module 3

  2. 2. INTRODUCTION• When a fluid flows past a stationary solid surface ,a thin film of fluid is postulated as existing between the flowing fluid and the stationary surface• It is also assumed that all the resistance to transmission of heat between the flowing fluid and the body containing the fluid is due to the film at the stationary surface.
  3. 3. Increasing Advection U , T Tu Ts T(y) U(y)
  4. 4. Heat transfer co-efficient(h): ability of the fluid carry away heat from the surfaceswhich in turn depends upon velocities and other thermal properties.unit :w/m2 k or w/m2oC Fluid motion induced by external means
  5. 5. Chilled water pipes Hot air rising QoutQin Cool air falling
  6. 6. • The amount of heat transferred Q across this film is given by the convection equationWhereh: film co-efficient of convective heat transfer,W/m2KA: area of heat transfer parallel to the direction of fluid flow, m2.T1:solid surface temperature, 0C or KT2: flowing fluid temperature, 0C or K∆t: temperature difference ,K
  7. 7. • Laminar flow of the fluid is encountered at Re<2100.Turbulent flow is normally at Re>4000.Sometimes when Re>2100 the fluid flow regime is considered to be turbulent• Reynolds number=• Prandtl number=• Nusselt number=• Peclet number=
  8. 8. • Grashof number=• Where in SI system• D: pipe diameter,m• V :fluid velocity,m/s• :fluid density,kg/m3• μ :fluid dynamic viscosity N.s/m2 or kg/m.s• ᵧfluid kinematic viscosity, m2/s :
  9. 9. • K:fluid thermal conductivity,w/mK• h: convective heat transfer coefficient,w/m2.K• Cp:fluid specific heat transfer,J/Kg.K• g:acceleration of gravity m/s2• β:cubical coefficient of expansion of fluid=• ∆t:temperature difference between surface and fluid ,K
  10. 10. Functional Relation Between Dimensionless Groups in Convective Heat Transfer• For fluids flowing without a change of phase(i.e without boiling or condensation),it has been found that Nusselt number (Nu) is a function of Prandtl number(Pr) and Reynolds number(Re) or Grashof number(Gr).• Thus for natural convection• And for forced convection
  11. 11. Empirical relationships for Force Convection• Laminar Flow in tubes:• Turbulent Flow in Tubes: For fluids with a Prandtl number near unity ,Dittus and Boelter recommend:• Turbulent Flow among flat plates:• Problem:
  12. 12. Empirical Relationships for natural convection• Where a and b are constants. Laminar and turbulent flow regimes have been observed in natural convection,10<7<GrPr<109 depending on the geometry.• Horizontal Cylinders: when 104<GrPr<109(laminar flow)andNu=0.129(GrPr)0.33
  13. 13. when 109<GrPr<1012 (turbulent flow)Problem:Vertical surfaces:Nu=0.59(GrPr)0.25 4When 10 <GrPr<109(laminar flow)Nu=0.129(GrPr)0.33 9When 10 <GrPr<1012 (turbulent flow)Horizontal flat surfaces:fluid flow is most restricted in the case of horizontal surfaces.Nu=0.54(GrPr)0.25
  14. 14. 5When 10 <GrPr<108(laminar flow)Nu=0.14(GrPr)0.33 8whenGrPrᵧ10 (turbulent flow)Problem:
  15. 15. Laminar and Turbulent Flow 1Viscous sublayer Buffer Layer 2 3 Turbulent region 2 1Laminar Transition Turbulent
  16. 16. Velocity profiles in the laminar and turbulent areas are very different U U  y y  0, Lam y y  0,Turb Which means that the convective coefficient must be differentLaminar Transition Turbulent
  17. 17. OVERALL HEAT TRANSFER CO-EFFICIENT FOR CONDUCTIVE –CONVECTIVE SYSTEMS• One of the common process heat transfer applications consists of heat flow from a hot fluid, through a solid wall, to a cooler fluid on the other side. The fluid flowing from one fluid to another fluid may pass through several resistances, to overcome all these resistance we use overall heat transfer• Newtons Law may be conveniently re-written asWhere h=convective heat transfer co- efficient,W/m2-k
  18. 18. • A=area normal to the direction of heat flux,m2• ∆T=temperature difference between the solid surface and the fluid,K.• It is often convenient to express the heat transfer rate for a combined conductive convective problem in the form(1),with h replaced by an overall heat transfer coefficient U.We now determine U for plane and cylindrical wall systems.
  19. 19. Figure 1• Plane wallOr1/Ahi and 1/Ah0 are known as thermal resistances due to convective boundaries or the convective resistances(K/W)Conductive heat flow Q=kAdt/dx=KA(T1-T2)/x
  20. 20. • Comparing the equations we get
  21. 21. problems• Radial SystemsThe Fourier law gives