A composite wall consist of alternative layers of fir ( 5 cm thick ) , aluminum ( 1 cm thick ), lead ( 1 cm thick ), and corkboard ( 6 cm thick ). The temperature is 6 ! of the outside of the fir and 1 ! on the outside of the corkboard. "lot the temperature #radient throu#h the wall. $oes the temperature profile su##est any simplifyin# assumptions that mi#ht be made in subse%uent analysis of the wall&
"lot the temperature #radient throu#h the wall. Answer
2uestion 3o. * $oes the temperature pro file su##est any si mplifyin# assumptions that mi#ht be made in subse%uent analysis of the wall& Answer 4es, since the thermal conductivity of aluminum and lead are very hi#h than fir and corkboard, they are considered isothermal. Therefore consider only fir and corkboard. fir Tcb 6 ! 1 ! 5 q k T k T L fir L cb
Lfir 5 cm .5 m Lcb 6 cm .6 m Then, 1
1. INTRODUCTION
q
.1* W m K T fir . W m K Tcb .5 m .6 m
1.70 K T .1* W m.K L fir .5 m
*6.8 +m *
There it is e%ual to simplified solution.
1.*
9erify :%uation (1.15).
'olution :%uation (1.15) dTbody Tbody T dt ;or verification only :%uation (1./) dU dT Q mc dt dt :%uation Q Tbody (1.16) T Then mc
dT dt
Tbody T
dT Tbody T dt
Then dTbody dt
Tbody T where mc is constant. q 5 +m * in a 1 cm sl ab and T 1 ! on the cold side. Tabulate the temperature drop throu#h the slab if it is made of
1./
'ilver Aluminum ce 'pruce >nsulation (75 = ma#nesia) /
1. INTRODUCTION
'ilica aero#el
>ndicate which situations would be unreasonable and why. 'olution ? 1 cm .1 m (a) 'ilver 'lab T q k 5 +m* L Si
Thermal conductivity of silver at 1 !, 88.88 = "ure, Table A.1, Appendi A ksi * +m. TSi 5 +m* q * W m K .1 m TSi .1* (b) Alumium 'lab T 5 +m* L alu Thermal conductivity of aluminum at 1 !, 88.88 = "ure, Table A.1, App. A Kalu */0.6 +m.q k
q */0.6 W m K Talu 5 +m * .1 m
Talu .*1 (c) ce 'lab
T 5 +m* L ice Thermal conductivity of ice at 1 !, Table A.1, Appendi A ice at !, kice *.*15 +m.q k
1. INTRODUCTION
3ote there is no ice at 1 !, but continue calculation at !. Tice 5 +m * q *.*15 W m K .1 m Tice **.50 (e) 'pruce 'lab T 5 +m* L Si
q k
Thermal conductivity of spruce at 1 !, Table A.1, Appendi A Ksp .11 +m.- @ * ! (available) TSp * 5 +m .1 m
