Energy Balance Differential Equation

What would be the best way to solve the equation as shown in the attached PDF please?

[darova]

YOu have two undefined functions T and P but only one equation. SOmething is wrong

[Peter Vella]

You are right. Let me check again ...

Answer 1

[Peter Vella]

P and T are dependent on each other .. as per the ideal gas equations in themrodynamics ..

Answer 2

[Guru Mohanty]

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); 
 

[Nicola De Noni]

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!