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## Homework Statement

A tent being considered for cold-weather conditions has insulation on the top and sides with a conductivity, k = 0.040 W/(m*K) and a thickness, l = 0.50 cm. The tent (and surrounding medium) has the following conditions: a heater (inside the tent) producing heat at a rate of 1500 W, the total surface area of the tent is 33 m2, an average heat transfer coefficient between the inside air and inside surface of hi = 7 W/(m2*K), an average heat transfer coefficient between the outside air and outside surface of ho = 10 W/(m2*K), and an outside temperature of t

_{ao}= 5*C. Determine the tent temperature, t

_{ai}, with the insulated tent. Also find the inside surface temperature of the tent insulation material, t

_{si}, and the outside surface temperature, t

_{so}.

Thermal Conductivity of tent material (k) = .040 W/m*k

Surface Area of Tent (A) = 33m

^{2}

Outside air Temp (t

_{ao}) = 5*C + 273.15 = 278.15K

Convective heat transfer coefficient inside tent(h

_{i}) = 7 W/(m2*K)

Convective heat transfer coefficient outside tent(h

_{o}) = 10W/(m2*K)

q inside tent = 1500W

Tent Thickness ([tex]\Delta[/tex]x) = .005m

Inside air Temp (t

_{ai}) = ?

Inside Tent Surface Temp t

_{si}= ?

Outside Tent Surface Temp t

_{so}= ?

## Homework Equations

Convection:

q=h*A*[tex]\Delta[/tex]T

Conduction:

q=-k*A*[tex]\Delta[/tex]T / [tex]\Delta[/tex]x

## The Attempt at a Solution

For Outside Air to outside tent Surface (Which is convection) so [tex]\Delta[/tex]T = t

_{so}- t

_{ao}:

q=(10W/m

^{2}*K)(33m

^{2})(t

_{so}- 278.15K)

For the Heat transfer between the inner and outer surface of the tent (Which is Conduction):

q= -(.04W/m*k)(33m

^{2})(t

_{so}- t

_{si}) / .005m

For Heat transfer between the inside air and inner tent surface (which is convection) so [tex]\Delta[/tex]T = t

_{si}- t

_{ai}:

1500W=(7W/m

^{2}*k)(33m

^{2})([tex]\Delta[/tex]T)

[tex]\Delta[/tex]T=6.4935k

6.4935k=t

_{si}- t

_{ai}

I got this far, I know I have to set some equations equal to each other but every time I attempted that I end up having about 2-3 unknowns in one equation...please point me in the right direction to solve this.

Thank you