Heat transfer problem for cooling a solar panel

[davidhe96]

I am currently trying to solve a problem for my dissertation. Help would be greatly appreciated. :)

A silicon solar panel of area 1m^2 is being warmed by the sun. It achieves a constant temperature of 80 degrees celcius.
I am trying to cool this panel which is constantly being provided solar radiation. The equilibrium temperature would be 80, however, I am trying to cool it down to 50 degrees celcius. Would the rate at which I need to expel the energy simply be q= c*(80-50)m? c- being specific heat, m being mass and delta T being temp difference? In that case I obtained a value of 4.96 kJ per second.
I am trying to cool this panel using flowing water which is at 30 degrees celcius. How would I calculate the mass flow rate of water to obtain desirable cooling? Thank you for your time!

 

[jrmichler]

Of the total solar energy entering the panel, some is reflected, some is converted to electricity, and the rest is converted to heat. Find the amount of heat by subtracting reflected energy and electricity from the solar insolation. Those numbers are available from the panel data sheet and some internet searching.

You know that an uncooled panel will stabilize at 80 deg C. At that temperature, the heat conducted, convected, and radiated will be equal to the heat from solar energy that you calculated above. As a simple approximation, assume that heat conducted, convected, and radiated is proportional to the temperature difference between the panel and the ambient air. The difference between the panel heat loss at 80 deg C and 50 deg C is the amount of heat that you need to remove by water cooling.

The water enters at 30 deg C. The water leaving temperature is dependent on heat transfer from panel to water and on water flow rate. It will be lower then the cooled panel temperature. A good starting assumption is that the water will leave at about 45 deg C.

Now that you have the amount of heat (kJ/sec), and a temperature difference (45 - 30 deg C), you can calculate the water flow rate. When you write it up, you may want to discuss, or at least mention, the assumptions and simplifications.

 

[russ_watters]

A silicon solar panel of area 1m^2 is being warmed by the sun. It achieves a constant temperature of 80 degrees celcius.
I am trying to cool this panel which is constantly being provided solar radiation. The equilibrium temperature would be 80, however, I am trying to cool it down to 50 degrees celcius. Would the rate at which I need to expel the energy simply be q= c*(80-50)m? c- being specific heat, m being mass and delta T being temp difference? In that case I obtained a value of 4.96 kJ per second.
I am trying to cool this panel using flowing water which is at 30 degrees celcius. How would I calculate the mass flow rate of water to obtain desirable cooling?

No, you kind of have the tail wagging the dog there. You need to find the heat rejection first. The manufacturer of the solar panels should have documentation to help. It may be a little tricky since it is convective and might not be quite linear with temperature.

Anyway, after you have the heat you need to reject, if you know your incoming water temperature you pick a desired delta-t and use that equation to find flow rate.

Ultimately, where are you rejecting the heat to? Is this a closed loop cooling tower system? Tap water?

 

[davidhe96]

No, you kind of have the tail wagging the dog there. You need to find the heat rejection first. The manufacturer of the solar panels should have documentation to help. It may be a little tricky since it is convective and might not be quite linear with temperature.

Anyway, after you have the heat you need to reject, if you know your incoming water temperature you pick a desired delta-t and use that equation to find flow rate.

Ultimately, where are you rejecting the heat to? Is this a closed loop cooling tower system? Tap water?

I am not understanding what you mean

0.233 (mass of silicon) x 30 (temp I am trying to reduce silicon by) x 0.71 (specific heat capacity of silicon) = 4.96kJ wouldn't this be the heat required to be rejected?

since equilibrium is at 80 degrees, is 4.96kJ what would be required to be rejected per second to keep panel at 50?

 

[russ_watters]

I am not understanding what you mean

0.233 (mass of silicon) x 30 (temp I am trying to reduce silicon by) x 0.71 (specific heat capacity of silicon) = 4.96kJ wouldn't this be the heat required to be rejected?

since equilibrium is at 80 degrees, is 4.96kJ what would be required to be rejected per second to keep panel at 50?

No, the heat capacity of silicon is irrelevant. This is a steady state continuous heat flow problem. The sun provides a certain flow rate and all of that heat gets removed. When the silicon is at constant temperature, it is not gaining or losing temperature and the net heat flow is zero.

 

[davidhe96]

No, the heat capacity of silicon is irrelevant. This is a steady state continuous heat flow problem. The sun provides a certain flow rate and all of that heat gets removed. When the silicon is at constant temperature, it is not gaining or losing temperature and the net heat flow is zero.

I see, if I wanted to keep it at a lower temperature, I would have to remove the radiation from the sun. That means with a flow rate of water, the lowest temperature of the silicon I can achieve is 30 degrees C, but the flow rate of water would have to be increased drastically. For my problem the radiation of sun is 973W.m^2. To simplify this problem, I am attempting to cool a 1m^2 panel to 50 degrees. To simplify the problem, we can use simple convection of fluid over a flat plane. How can I proceed from here?

 

[russ_watters]

How can I proceed from here?

Where are you getting or how are you cooling that water?

 

[davidhe96]

Where are you getting or how are you cooling that water?

the water is from a reservoir and starts off at 30 degrees celcius.

 

[haruspex]

If you have a layer of water flowing across the glass surface it will warm as it traverses the glass. The heat transfer will be by conduction, not so much by convection. Also, it’s not the glass that has to be kept cool, it’s the light sensitive medium.
So I would take the water temperature to be a function of distance travelled, and you need the last part of that to be cool enough.
Edit... I was thinking of the water as being on top, but likely it is underneath. Same principles though.

 

[anorlunda]

How would I calculate the mass flow rate of water to obtain desirable cooling?

Some things are difficult to calculate. We might know the equations, but we do not know the calibration of the parameters.

Must you calculate, or can you experiment?

Must you have the minimum water to achieve the cooling goal, or merely enough water to achieve the goal?

Is this a passive system, or an active system? In an active system you measure the temperature, then adjust a valve or something to change the flow until the desired temperature is reached. That is a closed-loop active system.