Performing Iterations in EES

Performing
Manual and Automated Iterations
in
Engineering Equation Solver (EES)
Examples from Heat Transfer
Naveed ur Rehman
http://www.naveedurrehman.com/
4th June, 2018

All the EES codes shown in the
examples are available at:
https://goo.gl/KExGFi
2

A problem that doesn’t require
iterative solution
3

A problem that doesn’t require iterative solution
𝑄 = ℎ𝐴 𝑇𝑠 − 𝑇𝑎
Let’s say:
𝑄 = 2000𝑊
𝐴 = 1𝑚2
𝑇𝑎 = 25°𝐶
ℎ = 10𝑃
Where,
𝑃 = 𝑃𝑟 𝑇𝑎 for ‘Air’
Find 𝑇𝑠?
Note: The Prandtl number, which is a
material property, is required at a known
temperature (Ta=25⁰C).
No iteration is needed!
4

A problem that doesn’t require iterative solution
Let’s say:
𝑄 = 2000𝑊
𝐴 = 1𝑚2
𝑇𝑎 = 25°𝐶
ℎ = 10𝑃
Where,
𝑃 = 𝑃𝑟 𝑇𝑎 for ‘Air’
Find 𝑇𝑠?
Q = h*A*(Ts-Ta)
Q = 2000 [W]
A = 1 [m^2]
Ta = 25 [C]
h = 10*P
P = prandtl(Air,T=Ta)
EES Codes (Code-1.EES)
5

A problem that require iterative
solution
6
Performing manual iteration in EES

A problem that require iterative solution
Let’s say:
𝑄 = 2000𝑊
𝐴 = 1𝑚2
𝑇𝑎 = 25°𝐶
ℎ = 10𝑃
Where,
𝑃 = 𝑃𝑟 𝑇𝑠 for ‘Air’
Find 𝑇𝑠?
Note: The Prandtl number, which is a material
property, is required at an unknown temperature!
This problem can not be solved without performing
iteration.
7
MANUAL

Let’s say:
𝑄 = 2000𝑊
𝐴 = 1𝑚2
𝑇𝑎 = 25°𝐶
ℎ = 10𝑃
Where,
Find 𝑇𝑠?
Q = h*A*(Ts-Ta)
Q = 2000 [W]
A = 1 [m^2]
Ta = 25 [C]
h = 10*P
P = prandtl(Air,T=Ts)
EES Codes (Code-2.EES) Wrong approach!
8
MANUAL

Let’s say:
𝑄 = 2000𝑊
𝐴 = 1𝑚2
𝑇𝑎 = 25°𝐶
ℎ = 10𝑃
Where,
Find 𝑇𝑠?
Q = h*A*(Ts-Ta)
Q = 2000 [W]
A = 1 [m^2]
Ta = 25 [C]
h = 10*P
Ts_guess = 100 [C]
check = Ts_guess - Ts
P = prandtl(Air,T=Ts_guess)
EES Codes (Code-3.EES) Right approach!
Assume some ‘guess’ value of
the unknown variable. Your
guess will correct only when
the difference between the
solution and your guess will
be ‘0’ i.e. check = 0
Evaluate
material
property at
guess value.
9
MANUAL

Check is not ‘0’ so
an iteration is
required.
Set the guess
variable value to the
current solution.
Let’s say:
𝑄 = 2000𝑊
𝐴 = 1𝑚2
𝑇𝑎 = 25°𝐶
ℎ = 10𝑃
Where,
Find 𝑇𝑠?
Q = h*A*(Ts-Ta)
Q = 2000 [W]
A = 1 [m^2]
Ta = 25 [C]
h = 10*P
Ts_guess = 305.9 [C]
10
MANUAL

Let’s say:
𝑄 = 2000𝑊
𝐴 = 1𝑚2
𝑇𝑎 = 25°𝐶
ℎ = 10𝑃
Where,
Find 𝑇𝑠?
Q = h*A*(Ts-Ta)
Q = 2000 [W]
A = 1 [m^2]
Ta = 25 [C]
h = 10*P
11
Check is still not ‘0’
so another iteration
is required.
Set the guess
variable value to the
current solution.
MANUAL

Let’s say:
𝑄 = 2000𝑊
𝐴 = 1𝑚2
𝑇𝑎 = 25°𝐶
ℎ = 10𝑃
Where,
Find 𝑇𝑠?
Q = h*A*(Ts-Ta)
Q = 2000 [W]
A = 1 [m^2]
Ta = 25 [C]
h = 10*P
Check is approx. ‘0’
so no further
iteration is required.
The current solution
(or guess) is the final
answer.
12
MANUAL

solution
13
Performing automated iteration in EES

Let’s say:
𝑄 = 2000𝑊
𝐴 = 1𝑚2
𝑇𝑎 = 25°𝐶
ℎ = 10𝑃
Where,
Find 𝑇𝑠?
14
Same problem
AUTOMATED

15
Subprogram solver(Ts_guess : Ts)
Q = h*A*(Ts-Ta)
Q = 2000 [W]
A = 1 [m^2]
Ta = 25 [C]
h = 10*P
End
EES Codes (Code-4.EES) Step #1
Create a ‘solver ‘ subprogram as
shown containing the original
codes of your main problem.
Make sure that you are
evaluating the material
properties at the guess value.
AUTOMATED

Procedure control(Ts_guess : Ts)
nmax = 100
dTmin = 0.001
n:=0
Ts := Ts_guess
Repeat
T = Ts
Call solver(T : Ts)
n := n +1
dT = abs(T-Ts)
Until ( (n=nmax) or (dT < dTmin))
End
16
Create a ‘control‘ procedure to
control the flow of iterations.
There is no need to change
anything else in this procedure.
‘nmax’ is the maximum number of iterations (100 is
more than enough!)
dTmin is the stopping condition, similar to ‘check’. If
you want to be super precise, use dTmin=0
AUTOMATED

Ts_guess = 100 [C]
Call control(Ts_guess : Ts)
17
Write these codes outside any
procedure or subprogram.
Yes, this is the initial guess.
AUTOMATED

solution
18
and getting more than single output

Let’s say:
𝑄 = 2000𝑊
𝐴 = 1𝑚2
𝑇𝑎 = 25°𝐶
ℎ = 10𝑃
Where,
Find 𝑇𝑠, P and ℎ?
19
Same problem but
required variables
are more than
single.
AUTOMATED
Multiple outputs

Subprogram solver(Ts_guess : Ts, P, h)
Q = h*A*(Ts-Ta)
Q = 2000 [W]
A = 1 [m^2]
Ta = 25 [C]
h = 10*P
End
20
More variables at output
AUTOMATED
Multiple outputs

Procedure control(Ts_guess : Ts, P, h)
nmax = 100
dTmin = 0.001
n:=0
Ts := Ts_guess
Repeat
T = Ts
Call solver(T : Ts, P, h)
n := n +1
dT = abs(T-Ts)
End
21
AUTOMATED
Multiple outputs

Ts_guess = 100 [C]
Call control(Ts_guess : Ts, P, h)
22
AUTOMATED
Multiple outputs

solution
23
and working with inputs from outside
subprogram

24
EES Codes (Code-6.EES)
Subprogram solver(Ts_guess, Q, A, Ta : Ts, P, h)
Q = h*A*(Ts-Ta)
h = 10*P
End
Procedure control(Ts_guess, Q, A, Ta : Ts, P, h)
nmax = 100
dTmin = 0.001
n:=0
Ts := Ts_guess
Repeat
T = Ts
Call solver(T, Q, A, Ta : Ts, P, h)
n := n +1
dT = abs(T-Ts)
End
Q = 2000 [W]
A = 1 [m^2]
Ta = 25 [C]
Ts_guess = 100 [C]
Call control(Ts_guess, Q, A, Ta : Ts, P, h)
Step #1 Step #2 Step #3
AUTOMATED
Multiple inputs and outputs

Performing
Manual and Automated Iterations
in
Engineering Equation Solver (EES)
Examples from Heat Transfer
Thank you! Naveed ur Rehman
http://www.naveedurrehman.com/

Performing Iterations in EES

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