Analytical Study of Natural Convection in a Cavity With Volumetric Heat Generation
ABSTRACT A semi-analytical method for natural convection in a two dimensional rectangular enclosure, with uniform volumetric heat generation, having insulated horizontal boundaries, and isothermal vertical boundaries, has been studied here. In this method, the governing equations for natural convection, have been solved under the assumption that for a cavity with small aspect ratio, the flow in the central region of the cavity is only in the vertical direction. It is found that for the cavities with small aspect ratio, the temperature in central region of the cavity is nearly constant along the horizontal direction. However, there is a uniform temperature gradient in the vertical direction, which can be related to the maximum temperature in conduction. The velocity profiles and temperature profiles obtained in the present work, are compared with the numerical simulations by Fluent and a fair agreement is found between these results.
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ABSTRACT: In this paper, a theoretical investigation has been carried out to study the combined effect of rotation speed modulation and internal heating on thermal instability in a temperature dependent viscous horizontal fluid layer. Rayleigh–Bénard momentum equation with Coriolis term has been considered to describe the convective flow. The system is rotating about it is own axis with non-uniform rotational speed. In particular, a time-periodic and sinusoidally varying rotational speed has been considered. A weak nonlinear stability analysis is performed to find the effect of modulation on heat transport. Nusselt number is obtained in terms of amplitude of convection and internal Rayleigh number, and depicted graphically for showing the effects of various parameters of the system. The effect of modulated rotation speed is found to have a stabilizing effect for different values of modulation frequency. Further, internal heating and thermo-rheological parameters are found to destabilize the system.07/2014; DOI:10.1016/j.asej.2014.05.005
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ABSTRACT: The generalized integral transform technique (GITT) is employed to obtain a hybrid numerical-analytical solution of natural convection in a cavity with volumetric heat generation. The hybrid nature of this approach allows for the establishment of benchmark results in the solution of non-linear partial differential equation systems, including the coupled set of heat and fluid flow equations that govern the steady natural convection problem under consideration. Through performing the GITT, the resulting transformed ODE system is then numerically solved by making use of the subroutine DBVPFD from the IMSL Library. Therefore, numerical results under user prescribed accuracy are obtained for different values of Rayleigh numbers, and the convergence behavior of the proposed eigenfunction expansions is illustrated. Critical comparisons against solutions produced by ANSYS CFX 12.0 are then conducted, which demonstrate excellent agreement. Several sets of reference results for natural convection with volumetric heat generation in a bi-dimensional square cavity are also provided for future verification of numerical results obtained by other researchers.Brazilian Journal of Chemical Engineering 12/2013; 30(4):883-896. DOI:10.1590/S0104-66322013000400020 · 0.91 Impact Factor
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ABSTRACT: Lattice Boltzmann simulations were conducted for the free convective flow of a low-Prandtl number (Pr = 0.0321) fluid with internal heat generation in a square enclosure having adiabatic top and bottom walls and isothermal side walls. The problem of free convection with volumetric heat source has represented itself in connection with advanced engineering applications, such as water-cooled lithium–lead breeder blankets for nuclear fusion reactors and liquid metal sources of spallation neutrons for subcritical fission systems. A single relaxation time (SRT) thermal lattice Boltzmann method (LBM) was employed. While applying SRT, a D2Q9 model was used to simulate the flow field and temperature field. Results have been obtained for various Rayleigh numbers characterizing internal and external heating from 103 to 106. Flow and temperature fields in terms of stream function and isotherms in the enclosure were predicted for these cases. The temperature of the fluid in the enclosure was found higher than the heated wall temperature at high values of internal Rayleigh numbers. The internal heat generation affected the rate of heat transfer significantly as two convection loops are observed in the enclosure. The average Nusselt number at the heated and cold wall was determined for all the cases.Heat Transfer-Asian Research 09/2014; DOI:10.1002/htj.21162