The rate of flow of heat depends on the nature of material, cross-sectional area and…

The rate of flow of heat depends on the nature of material, cross-sectional area and temperature gradient. If a material of conductivity k has set up a temperature gradient in x direction, then rate of heat flow at cross-section having area A is \(\frac{\mathrm{dQ}}{\mathrm{dt}}=\mathrm{k} \mathrm{~A} \frac{\mathrm{dT}}{\mathrm{dx}}\) 
Between any two points of conductor, if temperature difference is \(\Delta \mathrm{T}\) and rate of heat flow is H, then the resistance or opposition offered by the material to flow is defined as =\(\frac{\Delta \mathrm{T}}{\mathrm{H}}\). Now consider two very thin concentric metallic shells A and B of radii R₁ and R₂ (R₂ > R₁) and temperature T₁ and T₂ (T₁ > T₂) respectively. The hollow space between them is filled with sand of thermal conductivity k.
The rate of heat flow through the sand is