A Steady-State Heat Flow Problem for a Quarter Infinite Solid

The steady-state temperature field T(x, y) in a homogeneous solid x≥0, y≥0, z arbitrary is studied when the flow out the face y=0 is a prescribed function g(x). Along the face x=0 either the condition T=0 or k(∂T/∂x) = hT is assumed. Of especial interest is the temperature at the face y=0 and the flow at the face x=0; particular attention is paid to the case g(x)=0 for x>a>0. The results have application to situations in which heat is being drawn off at the corner of a solid.