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 tao = 5*C. Determine the tent temperature, tai, with the insulated tent. Also find the inside surface temperature of the tent insulation material, tsi, and the outside surface temperature, tso.
Thermal Conductivity of tent material (k) = .040 W/m*k
Surface Area of Tent (A) = 33m2
Outside air Temp (tao) = 5*C + 273.15 = 278.15K
Convective heat transfer coefficient inside tent(hi) = 7 W/(m2*K)
Convective heat transfer coefficient outside tent(ho) = 10W/(m2*K)
q inside tent = 1500W
Tent Thickness ([tex]\Delta[/tex]x) = .005m
Inside air Temp (tai) = ?
Inside Tent Surface Temp tsi = ?
Outside Tent Surface Temp tso = ?
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 = tso - tao :
q=(10W/m2*K)(33m2)(tso - 278.15K)
For the Heat transfer between the inner and outer surface of the tent (Which is Conduction):
q= -(.04W/m*k)(33m2)(tso - tsi) / .005m
For Heat transfer between the inside air and inner tent surface (which is convection) so [tex]\Delta[/tex]T = tsi - tai :
6.4935k=tsi - tai
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.