## THERMAL SCIENCE

International Scientific Journal

### PROGNOSTIC POTENTIAL OF FREE CONVECTION MODELS FOR ANALYSIS OF THERMAL CONDITIONS OF HEAT SUPPLY OBJECTS

**ABSTRACT**

The article shows the results of mathematical simulation of convective turbulent heat transfer in the closed domain with heat-conducting walls and the source of heat emission. The system of equations in the model of thermal conductivity for the solid walls and Navier-Stokes equations for gas are solved. The article examines the possible versions of the calculation of the turbulent regime in the geometrically simple air region by means of conducting the simulation within the framework of algebraic models (Van Driest and Prandtl-Reichardt), and k-ε model. On the basis of the obtained results the authors made a conclusion about the possibility of applying the algebraic model of Prandtl to describe the integral characteristics of turbulent flows in the conditions of natural convection in a geometrically simple area when the air heated by the heat source is moved by the lifting force. Besides, the temperature fields for a typical real object of heat supply are simulated in the article. The values of the dimensionless heat exchange coefficient at the air-wall interface are determined. The comparative analysis of two quite significantly different approaches to determine the average temperature in the heated room, i. e. the traditional balance approach and the approach based on the considered system of partial differential equations is executed. It is concluded that the balance models of the calculation of the temperature regime can adequately describe real temperatures of heat supply objects only for very large values of the characteristic times of the processes in question.

**KEYWORDS**

PAPER SUBMITTED: 2015-06-25

PAPER REVISED: 2017-04-13

PAPER ACCEPTED: 2017-04-17

PUBLISHED ONLINE: 2017-05-06

**THERMAL SCIENCE** YEAR

**2018**, VOLUME

**22**, ISSUE

**1**, PAGES [545 - 556]

- Nouanegue H., Muftuoglu A., Bilgen E., Conjugate heat transfer by natural convection, conduction and radiation in open cavities , International Journal of Heat and Mass Transfer, 51 (2008), 25-26, pp. 6054-6062.
- Kuznetsov G.V., Sheremet M.A., Two-dimensional problem of natural convection in a rectangular domain with local heating and heat-conducting boundaries of finite thickness, Fluid Dynamics, 41 (2006), 6, pp. 881-890.
- Kumar P., Eswaran V., The effect of radiation on natural convection in slanted cavities of angle = 45o and 60o, International Journal of Thermal Sciences, 67 (2013), pp. 96-106.
- Lari K., Baneshi M., Gandjalikhan Nassab S.A., Komiya A.S., Maruyama Combined heat transfer of radiation and natural convection in a square cavity containing participating gases, International Journal of Heat and Mass Transfer, 54 (2011), pp. 5087-5099.
- Roslan R., Saleh H., Hashim I., Bataineh A.S., Natural convection in an enclosure containing a sinusoidally heated cylindrical source, International Journal of Heat and Mass Transfer, 70 (2014), pp. 119-127.
- Éliton Fontana, Claudia A. Capeletto, Adriano da Silva, Viviana C. Mariani, Three-dimensional analysis of natural convection in a partially-open cavity with internal heat source, International Journal of Heat and Mass Transfer, 61 (2013), pp. 525-542.
- Kuznetsov G.V., Sheremet M.A., Conjugate natural convection in an enclosure with local heat sources, Computational Thermal Sciences, 1 (2009), 3, pp. 341-360.
- Kuznetsov G.V., Sheremet M.A., Conjugate natural convection in an enclosure with a heat source of constant heat transfer rate, International Journal of Heat and Mass Transfer, 54 (2011), 1-3, pp. 260-268.
- Maksimov, V.I., Nagornova, T.A. Influence of heatsink from upper boundary on the industrial premises thermal conditions at gas infrared emitter operation, EPJ Web of Conferences, 76 (2014), Article number 01006.
- Kuznetsov, G.V., Kurilenko, N.I., Maksimov, V.I., Mamontov, G. Ya., Nagornova, T.A., Heat transfer under heating of a local region of a large production area by gas infrared radiators / convection in an enclosure with a heat source of constant heat transfer rate, Journal of Engineering Physics and Thermophysics, 86 (2013), 3, pp. 519-524.
- Nagornova T.A., Thermal regimes of the work zones of production floor areas under the conditions of local heating and heat dissipation through an upper boundary, Chemical and Petroleum Engineering, Volume 51, Issue 3, July 2015, Article number A005, pp. 171-176.
- Maksimov V.I., Nagornova T.A., Glazyrin V.P., Conjugate heat transfer in a closed volume with the local heat sources and non-uniform heat dissipation on the boundaries of heat conducting walls, EPJ Web of Conferences, 110 (2016), 01038.
- Rohdin P., Moshfegh B., Numerical modelling of industrial indoor environments: A comparison between different turbulence models and supply systems supported by field measurements, Building and Environment, 46 (2011), pp. 2365-2374.
- Dixit H.N., Babu V., Simulation of high Rayleigh number natural convection in a square cavity using the lattice Boltzmann method, International Journal of Heat and Mass Transfer, 49 (2006), pp. 727-739.
- Tuncer Cebeci, Analysis of Turbulent Flows with Computer Programs, - 3th ed. - Butterworth-Heinemann, Elsevier Ltd., 2013, 450 p.
- Blazek J., Computational fluid dynamics. Principles and Applications., - 3th ed. - Butterworth-Heinemann, Elsevier Ltd., 2015, 447 p.
- David S-K., Ting Basics of engineering turbulence, Academic Press, Elsevier Inc., 2016, 234 p.
- Maksimov V.I., Nagornova T.A., Kurilenko N.I., Verification of Conjugate Heat Transfer Models in a Closed Volume with Radiative Heat Source, MATEC Web of Conferences, 72 (2016), Article number 01061.
- Kuznetsov G.V., Maksimov V.I., Sheremet M.A., Natural convection in a closed parallelepiped with a local energy source, Journal of Applied Mechanics and Technical Physics, 54 (2013) 4, pp. 588-595.
- Launder B.E., Spalding D.B., The numerical computation of turbulent flows, Comput. Methods Appl. Mech. Eng., 3 (1974), pp. 269-289.
- Cengel Yu. A., Chajar A. J., Heat and Mass Transfer, Fundamentals and Applications, - 4th ed. - New York: McGraw-Hill, 2011.
- Vincenzo Bianco, Federico Scarpa, Luca A. Tagliafico, Estimation of primary energy savings by using heat pumps for heating purposes in the residential sector, Applied Thermal Engineering, 114 (2017), 938-947.
- Erika Zvingilaite, Modelling energy savings in the Danish building sector combined with internalisation of health related externalities in a heat and power system optimisation model, Energy Policy, 55 (2013), 57-72.