Consider a cylindrical tube whose inner and outer radii are r i and r o . Heat flow in the tube wall can occur in the axial direction along the length of the tube and in the radial direction. If the...

Consider a cylindrical tube whose inner and outer radii are r_i
and r_o. Heat flow in the tube wall can occur in the axial direction along the length of the tube and in the radial direction. If the tube surface is insulated, there will be no radial heat flow, and the heat flow in the axial direction is given by

where L is the length of the tube,
T is the temperature difference between the ends a distance L apart, and A is area of the solid cross section (see Figure 7.7.7a). If only the ends of the tube are insulated, then the heat flow will be entirely radial. Derive an expression for the conductive resistance in the radial direction.

Figure 7.7.7a