As shown in Fig P244 the 6inthick exterior wall of a buildin

As shown in Fig. P2.44, the 6-in.-thick exterior wall of a building has an average thermal conductivity of 0.32 Btu/h ft .degree R. At steady state, the temperature of the wall decreases linearly from T_1 = 70 Degree F on the inner surface to T_2 on the outer surface. The outside ambient air temperature is T_0 = 25degreeF and the convective heat transfer coefficient is 5.1 Btu/h .ft ^2 . degreeR. Determine (a) the temperature T2 in degree F, and (b) the rate of heat transfer through the wall, in Btu/h per ft^2 of surface area.

Solution

convectice heat transfer coefficient h = q / A (T2- 25)

                                                                 let us consider q = 1Btu/ h , and A = 1ft ^2

                                                 T2 = ( 1 / 5.1) + 25 F

                                                      T2 = 25.1960 F .

rate of heat transfer per ft^2 , between T1 and T2

   Q´ = kA (T1-T2) / L          with A = 1 ft^2 and L = 6 inch = 0.5ft

                                                            = 0.32 (70 - 25.1960) / 0.5

                                                            = 28.674 Btu /h per ft^2