Question

What are boundary and initial conditions for heat propagation bar? Define a heat conduction problem for one dimensional bar. Introduce the boundary and initial condition for the heat equation. Give graphs and sketches.

Answer 1

The problem involves the concept of unsteady heat transfer in one dimension. A detailed explanation is given in below images.

Although the solution of differential equation is bit complex writing boundary conditions and initial conditons are not that tideous.

Also note here we have taken temperature of both walls same because only then we could solve this type of unsteady transfer problem.

In case when Temperature of both wall are not equal then that equation is solved by assuming steady condtions and then superimposing the solution of that equation with the solution of this one.

Hope the explanation would be helpful to you.