Consider one-dimensional transient conduction with a convection boundary condition in which the ambient temperature near the surface is a function of time. Determine the energy balance equation for the boundary control volume. How would the solution method need to be modified to accommodate this complexity?

Question

GIVEN
One-dimensional transient conduction where the ambient temperature near the surface is a
function of time
FIND
(a) The difference equation for the boundary control volume and explain how to solve the problem

Answer 1

The difference equation would be derived exactly. Assuming we are the boundary

in question is the left boundary we would have:



Here, the term T will depend on the time step m. Since this function of time is presumably known, a

marching procedure can be used to solve the set of equations for the whole problem.