I am an engineering student reading for an M.Sc. degree by research. As part of my studies, I am working on a project which regards data monitoring and control of solar cooling systems for industrial wine production. The project deals with two different, independent cooling systems. One cooling system consists of a conventional chiller driven by photo-voltaic panels. The second system is a vapour absorption chiller driven by heat from solar collectors.

As part of my project at the initial stage, I should model each component of the two systems which are based on heat transfer and thermodynamics. I am sending this email to ask you whether you have some time to help me with the following query. Basically, the problem that I’m currently facing regards the model of the heat pipe solar collector (in Ref (1) and Ref (2) you can find a brief of these type of solar collectors basic principles). The model of the solar collectors should give the output temperature of water with respect to the solar radiation. What I am after is a differential equation which describes the rate of heat transfer at the heat exchanger (or the condenser) of a heat pipe (the variables that the model considers are the variation of temperatures). So, I started from

q=m L (1)

Where m is the mass of the liquid inside the heat pipe and L is the latent heat of evaporation of the same liquid (Ref (2) shows how the working fluid cycles inside the heat pipe). Since the required equation is the rate of heat transfer, by taking the time derivative on both sides of the above equation, the following is obtained:

q ̇= m ̇ L (2)

Where m ̇ is the condensate flow rate. So, the two types of equation I have found through research, which were either of the form on Equation 2 or the heat transfer is constant.

My question is, have you ever met an equation which relates the flow rate which the change in temperatures in the heat pipe? Or do you have any literature to refer to me please?

Ref (1):

http://greenterrafirma.com/evacuated...collector.html
Ref (2):

http://www.apricus.com/html/solar_co...m#.VGvGnIvtLa4
Your help would be greatly appreciated. Thanks in advance.