For a solid under steady heat conduction, let Lx, Ly and Lz be the length scales in x, y, z directions respectively. and let (delta T)x, (delta T)y and (delta T)z be the maximum temperature difference in x, y, z directions respectively. If the solid has anisotropic thermal conductivities given by kx,ky and kz in x, y, z direction respectively,
(a) conduct the dimensional analysis to obtain conditions under which the problem can be reduced to two dimensional heat conduction in the x-, y- directions. illustrate the situation by drawing a diagram.
(b) Write down the conditions under which the problem remains three dimensional but can be lumped into two dimensional heat conduction in x- and y- directions . Draw the schematic diagram.