Show that the rate of heat conduction per unit length through a long hollow cylinder of inner

Question:

Show that the rate of heat conduction per unit length through a long hollow cylinder of inner radius ri and outer radius ro, made of a material whose thermal conductivity varies linearly with temperature, is given by

where Ti = temperature at the inner surfaceTo = temperature at the outer surface

L = length of cylinderGIVENA long hollow cylinderThe thermal conductivity varies linearly with temperatureInner radius = riOuter radius = roASSUMPTIONSConduction occurs in the radial direction onlySteady state prevails