Question

A composite plane wall consists of a 5-in.-thick layer of insulation (ks = 0.029 Btu/h*ft*°R) and a 0.75-in.-thick layer of siding (ks = 0.058 Btu/h*ft*°R). The inner temperature of the insulation is 67°F. The outer temperature of the siding is -8°F.
Determine at steady state:


(a) the temperature at the interface of the two layers, in °F, and (b) the rate of heat transfer through the wall in Btu/h*ft^2 of surface area.

Answer 1

We have that  the temperature at the interface of the two layers, in °F, and (b) the rate of heat transfer through the wall in Btu/h*ft^2 of surface area is given as

a)    $T_i-12.11^oF$

b) $H_r=3.80 btu/hft^2$

From the question we are told

A composite plane wall consists of a 5-in.-thick layer of insulation (ks = 0.029 Btu/h*ft*°R) and a 0.75-in.-thick layer of siding (ks = 0.058 Btu/h*ft*°R).

The inner temperature of the insulation is 67°F. The outer temperature of the siding is -8°F.

Interface Temperature

Generally the equation for the Terminal resistance   is mathematically given as

$R_1=\frac{t_1}{k_1A}\\\\R_1=14.3667hft^2R/btu\\\\Also\\\\R_2=\frac{t_2}{k_2A}\\\\R_2=1.077hft^2R/btu$

b)

$Heat transfer rate\\\\H_r=\frac{67-8}{15.444}\\\\H_r=3.80 btu/hft^2$

a)Interface Temp(T_i)

$T_i=\frac{67-t_2}{R1}=3.820$

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