Question about initial and boundary conditions with the heat equation

[patricio ramos]

I am seeing the heat conduction differential equation, and I was wondering about a boundary condition when the equation is of transient (unsteady) nature.

When analyzing boundary conditions at the surface of say, a sphere, the temperature does not depend on time. For example, if you have conduction, but at the surface you have convection, the boundary condition is written like this:

$$-k* dT(r,t)/dx = h(T(r)-Tsurrounding)$$

r is the radius of the sphere, t is time and h is the convection coefficient. I notice that T is independent on time when writing radiation and convection boundary conditions. Why is this? Is it because the temperature at the surface is constant even if the problem is transient?

Thanks

 

[Chestermiller]

The temperature on the surface is not constant in time, and your equation should read:$$-k* dT(r,t)/dx = h(T(r,t)-Tsurrounding)$$