Temperature funtion along X of a solar collector

In summary, the problem involves finding the temperature as a function of the length (x) of a 1m wide solar heat collector. The collector transfers 500 W/m^2 of heat to the air inside at 100% efficiency. The air entering the collector has a specific heat of 1000 J/(kg*K), a mass flow rate of 0.02 kg/s, and a temperature of 15C. The ambient air temperature is also 15C. The convective heat transfer coefficients for the air to film and film to ambient are 45 W/(m^2*K) and 12 W/(m^2*K), respectively.To solve the problem, the
  • #1
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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Added Word image of the collector
 

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Related to Temperature funtion along X of a solar collector

What is a solar collector?

A solar collector is a device that collects and absorbs solar radiation to convert it into heat or electricity.

What is the temperature function along X?

The temperature function along X refers to the change in temperature along the horizontal axis of the solar collector. This can be measured at different points along the collector to understand how the temperature varies.

Why is the temperature function important for a solar collector?

The temperature function is important for a solar collector because it helps to determine the efficiency of the collector in converting solar energy into heat. It also helps to identify any potential issues or areas for improvement in the design of the collector.

How does the temperature function affect the performance of a solar collector?

The temperature function directly affects the performance of a solar collector. Higher temperatures along the collector can result in increased efficiency and heat production, while lower temperatures can decrease efficiency and potentially lead to decreased performance.

What factors can affect the temperature function along X in a solar collector?

The temperature function can be affected by a variety of factors, including the angle and orientation of the collector, the type and quality of materials used, the weather conditions, and any shading or obstructions that may block the sun's rays.

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