Temperature funtion along X of a solar collector

[Wildcat04]

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!

 

[Wildcat04]

Added Word image of the collector