Assuming k is constant, we have to show that the radial rate of flow of heat in a substance between two concentric spheres is given by
where the
inner sphere has a radius
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Solution: Click For PDF Version
The surface
of the inner sphere of radius
or
Integrating
this equation between the limits
Or
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and temperature
,
and the outer surface has a radius
and temperature
.
.
Let us consider a concentric spherical surface of radius
from
the centre of the spheres. The rate of heat flow across this surface
will be given by the equation
,
we get
