10.
The homogeneous spherical wall (inner radius and outer radius
) with thermal conductivity
is in a steady state
with temperature of the inner surface
and of the outer
surface
, respectively. Assuming that due to conservation of energy,
in steady state the same rate of heat transfer
is passing through a spherical surface of any radius, find
the temperature
at an arbitrary radius
. Derive the differential
equation using Fourier’s Law and relation
, where
is the surface
area. Sketch the graph of solution for
and
,
, and determine the rate of heat transfer
.