Question about initial and boundary conditions with the heat equation

In summary, when analyzing boundary conditions in a transient heat conduction differential equation, the temperature at the surface of a sphere does not depend on time. This is due to the fact that the temperature on the surface is not constant in time and is affected by convection and radiation. The boundary condition is written with the convection coefficient and the difference between the surface temperature and the surrounding temperature.
  • #1
patricio ramos
8
0
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
 
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  • #2
The temperature on the surface is not constant in time, and your equation should read:$$-k* dT(r,t)/dx = h(T(r,t)-Tsurrounding)$$
 

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