Steady one-dimensional heat conduction takes place in a long slab of width W (in the direc...

Steady one-dimensional heat conduction takes place in a long slab of width W (in the direction of heat flow, x) and thickness Z. The slab’s thermal conductivity varies with temperature as k = k*/(T* + T) , where Tis the temperature (in K) , and k* (in W/m) and T* (in K) are two constants. The temperatures at x = 0 and x = W are T0 and Tw, respectively. Show that the heat flux in steady Operation is given by

Also, calculate the heat flux for T* = 1000 K, T0 = 600 K, Tw = 400 K, k* = 7 × 104 W/m, and W= 20 cm.