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Wildcat04
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Homework Statement
1m wide solar heat collector that is x long. Find the temperature as a function of x.
500 W/m^2 transferred from the collector to the air within the collector, 100%.
Air enters the collector has the following properties:
cp = 1000 J/(kg*K)
m = 0.02 kg/s
T= 15C
Ambient Air T = 15C
Convective heat transfer coefficients
Heat air to film = 45 W(m^2*K)
Film to ambient = 12 W/(m^2*K)
Homework Equations
0 = qtot - qair + qconv
qtot - total heat transfer
qair = heat transfer to the air in the collector
qconv = heat lost to ambient through the film via convection
1/htot = 1 / h1 + 1 / h2
qair = m * cp * Area * (Tx - Ti)
qconv = htot * Area * (Tx - Tinf)
The Attempt at a Solution
1/htot = 1 / 12 + 1 / 45
htot = 9.47 W/(m^2*k)
Area = 1m * x
Area = x
qair = 0.02 * 1000 * x * (Tx - Ti)
qair = 20x*(Tx - Ti)
qconv = 9.47x * (Tx - Tinf)
Now comes where I am getting stuck. I know that I need to set up a differential equation, however it has been quite a while since I have taken the class and I am having trouble getting it set up properly to arrive at the correct solutionn
Correct solution: T = 15 + 52.8*[1-e^(-.474 x)]
Any prod in the right direction would be greatly appriciated!
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