Energy Balance Differential Equation

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Peter Vella
Peter Vella on 17 Jan 2020
Commented: Nicola De Noni on 22 Aug 2022
What would be the best way to solve the equation as shown in the attached PDF please?
  2 Comments
Peter Vella
Peter Vella on 17 Jan 2020
You are right. Let me check again ...

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Answers (2)

Peter Vella
Peter Vella on 20 Jan 2020
P and T are dependent on each other .. as per the ideal gas equations in themrodynamics ..

Guru Mohanty
Guru Mohanty on 22 Jan 2020
Hi, I understand you are trying to solve the equation. You can do this using dsolve. Here is a sample code.
clc;
clear all;
syms rho cp T(t) mn V Tin P(t) heff Tamb k
P=k*T; % Ideal Gas Equation
eqn= rho*cp*diff(T,1) + mn*cp*(T-Tin)/V - diff(P,1) + heff*(T-Tamb) ==0;
T_sol=dsolve(eqn);
disp(T_sol);
  1 Comment
Nicola De Noni
Nicola De Noni on 22 Aug 2022
Hello @Guru Mohanty, I have a similar problem, can you help me?
cp*M*(dT/dt)= - U*A*(T-T_out(t))
In this energy balance I want to plot the temperature profile.
How can I manage the temperature T_out that changes in time?
Thanks!

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