Seven rods A , B , C , D , E , F and G are connected as depicted in the figure. Every rod possesses an identical cross-sectional area A and length l . The thermal conductivities of the respective rods are K_A = K_C = K₀ , K_B = K_D = 2K₀ , K_E = 3K₀ , K_F = 4K₀ and K_G = 5K₀ . The rod E is maintained at a steady temperature T₁ , while the rod G is maintained at a steady temperature T₂ ( T₂ > T₁ ). Determine the rate

Step-by-step solution

Let the thermal resistance of a rod be given by R = l KA . The thermal resistances of the given rods are: R_A = l K₀ A R_B = l 2K₀ A = R_A 2 R_C = l K₀ A = R_A R_D = l 2K₀ A = R_A 2 R_F = l 4K₀ A = R_A 4 Since rod E is maintained at a steady temperature T₁ and rod G is maintained at a steady temperature T₂ , they act as isothermal reservoirs. The entire rod E is at T₁ and the entire rod G is at T₂ . Therefore, their thermal conductivities ( K_E and K_G ) do not contribute to the thermal resistance of the heat flow