# How to solve Energy Balance equation by numerical method

Good Day

I am new to heat transfer technique please give me some suggestion on solving energy balance equation

$$a \frac{\partial T_p}{\partial t}=\frac{\partial}{\partial x}\left(b\frac{\partial T_p}{\partial x}\right)+\frac{\partial}{\partial z}\left(c\frac{\partial T_p}{\partial z}\right)+b$$

which is discretized as

$$a\left(\frac{T_p-T_{p_0}}{\Delta t}\right)=c\left(\frac{T_u-T_p}{\Delta X_u \Delta X}\right)+d\left(\frac{T_D-T_p}{\Delta X_d \Delta X}\right)+e\left(\frac{T_w-T_p}{\Delta Z_w \Delta Z}\right)+f\left(\frac{T_E-T_p}{\Delta Z_E \Delta Z}\right)+b$$

$b=S_c+S_pT_p$

Where $T_p$ is the temperature of solar panel $a,c,d,e,f$ are the constant value.

I am not getting how to proceed with this equation. Please suggest some hints at solutions.

• You need to read an introductory textbook about finite difference methods. The second equation you show above is the equation the temperature at every grid point has to satisfy. This leads to a linear system that you can then solve for the temperature of the next time step. – Wolfgang Bangerth Jan 18 '15 at 15:39
• Can you suggest me some reference book/article for this sir. – Ambaresh Jan 18 '15 at 16:19
• Any book on finite difference methods will do, given that you are missing one of the very first steps of what to do to solve these equations. Go to your library and see what they have. – Wolfgang Bangerth Jan 18 '15 at 18:33