# Mathematical modelling of heat transfer in liquid flat-plate solar collector tubes

Open access

## Mathematical modelling of heat transfer in liquid flat-plate solar collector tubes

The paper presents a one-dimensional mathematical model for simulating the transient processes which occur in the liquid flat-plate solar collector tubes. The proposed method considers the model of collector tube as one with distributed parameters. In the suggested method one tube of the collector is taken into consideration. In this model the boundary conditions can be time-dependent. The proposed model is based on solving the equation describing the energy conservation on the fluid side. The temperature of the collector tube wall is determined from the equation of transient heat conduction. The derived differential equations are solved using the implicit finite difference method of iterative character. All thermo-physical properties of the operating fluid and the material of the tube wall can be computed in real time. The time-spatial heat transfer coefficient at the working fluid side can be also computed on-line. The proposed model is suitable for collectors working in a parallel or serpentine tube arrangement. As an illustration of accuracy and effectiveness of the suggested method the computational verification was carried out. It consists in comparing the results found using the presented method with results of available analytic solutions for transient operating conditions. Two numerical analyses were performed: for the tube with temperature step function of the fluid at the inlet and for the tube with heat flux step function on the outer surface. In both cases the conformity of results was very good. It should be noted, that in real conditions such rapid changes of the fluid temperature and the heat flux of solar radiation, as it was assumed in the presented computational verification, do not occur. The paper presents the first part of the study, which aim is to develop a mathematical model for simulating the transient processes which occur in liquid flat-plate solar collectors. The experimental verification of the method is a second part of the study and is not presented in this paper. In order to perform this verification, the mathematical model would be completed with additional energy conservation equations. The experimental verification will be carry out in the close future.

Goswami D. Y., Vijayaraghavan S., Lu S., Tamm G.: New and emerging developments in solar energy. Solar Energy 76 (2004), 33-43.

Fan J., Shah L. J., Furbo S.: Flow distribution in a solar collector panel with horizontally inclined absorber strips. Solar Energy 81 (2007), 1501-1511.

Burch J., Christensen C., Salasovich J., Thornton J.: Simulation of an unglazed collector system for domestic hot water and space heating and cooling. Solar Energy 77 (2004), 399-406.

Zueva G. A., Magiera J.: Mathematical model of heat transfer in a solar collector and its experimental validation. Theoretical Foundations of Chemical Engineering 35 (2001) 6, 604-608.

Razavi J., Riazi M. R., Mahmoodi M.: Rate of heat transfer in polypropylene tubes in solar water heaters. Solar Energy 74 (2003), 441-445.

Morrison G. L., Budihardjo I., Behnia M.: Water-in-glass evacuated tube solar collectors. Solar Energy 76 (2004), 135-140.

Augustus M. L., Kumar S.: Mathematical modeling and thermal performance analysis of unglazed transpired solar collectors. Solar Energy 81 (2007), 62-75.

Duffie J. A., Beckman W. A.: Solar Engineering of Thermal Processes, 2nd ed. Wiley Interscience, New York 1991.

Weitbrecht V., Lehmann D., Richter A.: Flow distribution in solar collectors with laminar flow conditions. Solar Energy 73 (2002), 433-441.

Wang X. A., Wu L. G.: Analysis and performance of flat-plate solar collector arrays. Solar Energy 45 (1990) 2, 71-78.

Karatasou S., Santamouris M., Geros V.: On the calculation of solar utilizability for south oriented flat plate collectors tilted to an angle equal to the local latitude. Solar Energy 80 (2006), 1600-1610.

Pluta Z.: Fundamentals of Solar Energy Thermal Conversion. Warsaw University of Technology, Warsaw 2000 (in Polish).

Gerald C. F., Wheatley P. O.: Applied numerical analysis. Addison-Wesley Publishing Company, New York 1994.

Serov E. P., Korolkov B. P.: Dynamics of steam generators. Energia, Moscow 1981 (in Russian).

# Archives of Thermodynamics

## The Journal of Committee on Thermodynamics and Combustion of Polish Academy of Sciences

### Journal Information

CiteScore 2016: 0.54

SCImago Journal Rank (SJR) 2016: 0.319
Source Normalized Impact per Paper (SNIP) 2016: 0.598

### Metrics

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 153 153 22