# Create a model to solve an energy balance

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kasim on 30 Mar 2020
Commented: kasim on 1 Apr 2020
Hi, I am trying to use MATLAB to create a model that can solve a set of equations. I have attached an image of the equations I am trying to solve. Essentially, there are 3 unknowns, Tout, Tp & Tg.
I wanted to ask which would be the best way to solve this on MATLAB, i have tried to use matrices but the temperatures I am getting are very high. Is there any other method that could be used to solve these equations?
Kind regards

darova on 30 Mar 2020
Try fsolve
kasim on 30 Mar 2020
Again, thank you!
with regards to this line: [Tg Tout Tp Tm hrpg hrgs] = deal(x(1),x(2),x(3),x(4),x(5),x(6));
is this the order in which the answers are outputted? i.e. Tg = Value 1, Tout = Value 2
darova on 30 Mar 2020
Yes
Experiment with x0 (initial guess) for different outputs

Alex Sha on 31 Mar 2020
Hi, I get two solutions:
No. 1 2
tg -328.861557610457 -549.471818197512
tm 1.72830356360143 -541.712011528394
hrpg -0.00727597589137702 -11.1180945451184
tp 326.846969797053 -548.48073838475
hrgs 0.0134500837438822 -4.90776624779464
tout -326.543392872797 -1413.42402305679

kasim on 31 Mar 2020
Hi, I have found a mistake in my model, which is perhaps why you're getting different results.
eq1 should read as ag*I + hg*(Tg-Tm) + hrpg*(Tp-Tg) + (hw+hrgs)*(Tg-Ta)
Perhaps this may provide some accurate values?
Alex Sha on 1 Apr 2020
then the result will be:
tm: 330.112356511329
tg: 329.614806294714
hrpg: 2.41746002404232
tp: 330.611779336469
hrgs: 7.81080204482525
tout: 330.224713022658
Feval:
9.35251875944232E-12
-6.95421498164706E-12
-1.83834281131112E-10
-5.6843418860808E-14
-3.1827873669954E-12
-3.30402372128447E-13
kasim on 1 Apr 2020
Hi, Could you show me how you coded this?