The temperature of the two outer surfaces of a composite slab consisting of two materials having coefficients of thermal conductivity K and 2K and thickness x and 4x, respectively are T2 and T1(T2 >T1). The rate of heat transfer through the slab, in steady state is KAT2−T1Xf with f equal to

The two plates arc connected in series. Their total thermal resistance is given by RS=R1+R2=XKA+4X2KA=3XKAThe rate of flow of heat through the composite plate is given by  Qt=ΔθRS=T2−T1(3x/KA)=KAT2−T13x                                     =KAT2−T1x×13Comparing with given equation, we get  f=13.