Conjugate Natural Convection in a Closed Domain Containing a Heat-Releasing Element with a Constant Heat-Release Intensity

Abstract

Mathematical modeling of gravitational heat convection in a closed rectangular domain with finitethickness heat-conducting walls in the presence of a heat-releasing element with a constant heat-release intensity located at the base of the domain under conditions of convective-radiative heat transfer on one external boundary is performed. The influence of constitutive parameters (Grashof number and relative thermal conductivity) and flow unsteadiness on local thermohydrodynamic characteristics (streamlines and temperature field ) and on the integral parameter (mean Nusselt number on the inner surface of the solid walls) is analyzed. Results obtained for two models of the heat source (with a constant temperature and with a constant heat-release intensity) are compared.Key words: conjugate heat transfer, natural convection, heat-releasing element with a constant heat-release intensity, laminar flow regime.Introduction. Natural convection as one of the heat-transfer mechanisms plays an important role in various devices: elements of communications-electronics equipment and electronic materiel, industrial facilities for growing bulk monocrystals, heat exchangers and solar collectors, elements of nuclear reactor cooling systems, etc. [1][2][3][4][5][6][7][8][9][10][11][12]. Conjugate problems of heat transfer attract researchers' attention [7-12] because of possible applications of these problems [7,[9][10][11] and the absence of comprehensive models of analyzed processes. For instance, conjugate natural convection of a heat-releasing fluid around a ribbed pipe placed in the central part of a square cavity was numerically simulated in [8]. The angle of tube inclination, the rib size, and the volume heat-release density were found to exert a significant effect on heat-transfer intensity. The optimal position of a local heat source in an open cavity with one wall having a finite thickness was determined in [9]. It was demonstrated that the optimal position of the heater depends both on the heater power and thermophysical characteristics of the wall on which the heater is located and on the geometric characteristics of the solution domain. Conjugate combined heat transfer in an open cavity with one wall having a finite thickness was studied numerically in [10]. The heat flux was uniformly distributed over the inner surface of the wall. The degree of the influence of each energy-transfer mechanism on formation of thermal and hydrodynamic regimes in the cavity was found. Mathematical modeling of conjugate natural convection in a horizontal annular gap between a heat-releasing solid block and isothermal external boundaries was performed in [11]. Distributions of local thermohydrodynamic characteristics were obtained, and the influence of the shape of the inner solid block on the flow and heat-transfer regimes was analyzed. A numerical and experimental analysis of gravitational heat convection in the vicinity of a heated solid wall can be found in [12]. Correlations for the mean Nusselt numbers on the wall surface were obtaine...

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“…Zhu et al [3] take into account the effects of the fluid flow on the sensors for the development of a micromachined inertial gas sensor based on heat M A N U S C R I P T Page 3 convection. Besides that, several geometric configurations of the active hot wall are considered in the literature associated to different enclosure configurations as the octogonal one treated by Saha et al [4] and several others devoted to natural convection as [5][6][7][8] among the latest. In electronic engineering, thermal control equipment often requires the use of thermocouples near the active hot wall.…”