- #1

Fr34k

- 20

- 0

## Homework Statement

Lets say we have a 2D rectangular plate with a point heat source and some boundary conditions. I would like to solve and understand step by step the solution to this second order differential equation. Let's say dimensions of rectangular are a and b. 2 opposite sides are at a fixed temperature T1 and the other 2 are insulated. The initial temperature of the "body" is let's say T0. Our source is a δ source somewhere on the rectangular (x,y) and starts at t0. We ignore the heat dissipation due to convection and radiation. How would the temperature distribution look like T(x,y,t)? We also know the k-thermal conductivity, ρ density and c thermal diffusivity.

## Homework Equations

[itex]\nabla^2T-\frac{1}{k}\frac{\delta T}{\delta t}+\frac{q(x,y,t)}{c}=0[/itex]

And please don't just tell/write the solution. I would like to understand the method of solving these type of problems. I have been reading lots of books on differential equations with simpler problems or similar problems but I can not put 1 and 1 together to solve this exact situation.

I thank you all for your time in advance.