An insulate wall has a thickness of 20 mm and a thermal cond

An insulate wall has a thickness of 20 mm and a thermal conductivity of k = 0.05 W/m middot K. The height and width of the wall are 5 m and 10 m, respectively. In a winter day, the outside surface temperature of the wall is -5 degree C and the inside surface of the wall is maintained at 22 degree C. (You must follow the procedure by listing assumptions and drawing schematic for all problems in order to receive full credit.) What is the temperature difference between the inner and outer surfaces of the wall both in degree C and in K? What is the conduction heat flux through the wall? Which direction is the heat flux? What is the rate of heat transfer through the wall?

Solution

(a) Temperature difference in K= Temperature difference in ºC= 22- (-5) = 27 K = 27 ºC

(b) For one dimensional heat conduction, heat flux q is given by

     q= -k (dT/dx) = -k (T₁ – T₂)/L= -0.05 x (27/0.02) = -67.5 W/m² (from inside to outside)

(c) Rate of heat transfer Q= qA= -67.5 x (5x 10) = -3375 W (from inside to outside)