A house has a composite wall of wood, fiberglass insulation, and plaster board,
ID: 1718143 • Letter: A
Question
A house has a composite wall of wood, fiberglass insulation, and plaster board, as indicated in the sketch. On a cold winter day, the convection heat transfer coefficients are ho = 60 and h, = 30w/m^2K. The total wall surface area is 350 m^2 Determine a symbolic expression for the total thermal resistance of the wall, including inside and outside convection effects for the prescribed conditions. Determine the total heat loss through the wall. If the wind were blowing violently, raising f to 300 , determine the percentage increase in the heat loss. Which resistance is the dominate mechanism determining the heat loss?Explanation / Answer
>> There are fivethermal resistances:
1). R1 = Resistance due to convection across left surface
R1 = (1/hiA)
As, A = Area = 350 m2
=> R1 = (1/(30*350) = 9.52*10-5 .........(1).........
2). R2 = Resistance due to conduction across plastic board
R2 = (L/kpA)
L = Thickness = 10 mm = 0.01 m
=> R2 = (0.01/(kp*350) = (2.86/kp)*10-5 .........(2).........
3). R3 = Resistance due to conduction across glass fibre
R3 = (L/kgA)
L = Thickness = 100 mm = 0.1 m
=> R3 = (0.1/(kb*350) = (28.57/kb)*10-5 .........(3).........
4). R4 = Resistance due to conduction across plywood siding
R4 = (L/ksA)
L = Thickness = 20 mm = 0.02 m
=> R4 = (0.02/(ks*350) = (5.71/ks)*10-5 .........(4).........
5). R5 = Resistance due to convection across right surface
R5 = (1/hoA)
As, A = Area = 350 m2
=> R5 = (1/(60*350) = 4.76*10-5 .........(5).........
As, Net Resistance, R = R1 + R2 + R3 + R4 + R5
From (1), (2), (3), (4) and (5),
=> R = 9.52*10-5 + (2.86/kp)*10-5 + (28.57/kb)*10-5 + (5.71/ks)*10-5 + 4.76*10-5
=> R = Total thermal resistance = [14.28 + (2.86/kp)+ (28.57/kb) + (5.71/ks) ]10-5 ......ANSWER....PART (a)...
>> Part (b).
>> Q = Total heat Loss Through Wall = dT/R = (ti - To)/R = 35/R , R = Total Thermal Resistance
>> Part (c).
Now, ho = 300 W/m2-K
=> (R5)new = (1/(300*350) = (R5)/5 = 0.952*10-5
=> Rnew = [10.48 + (2.86/kp)+ (28.57/kb) + (5.71/ks) ]10-5
So, Qnew = 35/Rnew
>> When Values of kg, kp and ks are known, then exact change in rate can be findedby: (Qnew - Q)/Q
>> Part (d).
Exactly can be said by knowing the values of kg, kp and ks ,
The one having the maximum resistance is responsible mostly to minimize the heat loss....
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