An Efficient Numerical Simulation of 2D Natural Convection in an Inclined Cavity with Internal Heat Generation Using Differential Quadrature Method

Israa  ALESBE; Sattar  ALJABAIR; Jalal M.  JALIL

doi:10.48048/wjst.2021.20601

Authors

Israa ALESBE Department of Mechanical Engineering, University of Technology, Baghdad, Iraq
Sattar ALJABAIR Department of Mechanical Engineering, University of Technology, Baghdad, Iraq
Jalal M. JALIL Electromechanical Engineering Department, University of Technology, Baghdad, Iraq

DOI:

https://doi.org/10.48048/wjst.2021.20601

Keywords:

DQ method, Natural convection, Numerical method, Internal heat generation

Abstract

Natural laminar convective fluid flow has been simulated inside inclined rectangular cavities with and without internal heat generation for different aspect ratios and inclination angles. The most important basic dimensionless parameters for this problem are the external Rayleigh number (Ra_E) and the internal Rayleigh number (Ra_I), where Ra_E refers to the effects of the differential heating of the side walls and Ra_I refers to the amount of heat produced internally. Results were obtained for 4 cases with 192 tests: case (1), Ra_I= 0 without internal source generation, and cases (2, 3, and 4) with internal source generation for Ra_I = Ra_E, 10 Ra_E, and 100 Ra_E, respectively. In all cases, the parameters of study changed as 10³ ≤ Ra_E ≤10⁶, 0 ≤ Ra_I ≤ 10⁷, inclination angle from 0 to 60 deg., and aspect ratios of the enclosure from 0.5 to 2. Results were represented graphically for flow and thermal fields as a streamline, isothermal contours, and Nusselt number. The computed results show that the strength of convection currents is measured by the internal energy. Finally, it is illustrated that by using a few grid points and a shorter CPU time for calculation, the present method can produce accurate numerical results. Also, increase in Ra_I leads to increasing heat transfer rate and its direction out from the cavity at both hot and cold walls. For lower values of Ra_I, heat transfer diffusion is more prominent, while for higher values of Ra_I, convection outweighs diffusion.

HIGHLIGHTS

Natural laminar convective fluid flow inside inclined rectangular cavities with and without internal heat generation for different aspect ratios and inclination angles has been simulated
The most important basic dimensionless parameters, the external Rayleigh number (Ra_E) and the internal Rayleigh number (Ra_I) are studied
DQ method performance was excellent
The obtained computational results indicate that the strength of the convection currents depends on the internal energy
Accurate numerical results can be obtained by the present method using a few grid points and shorter CPU time for calculation

GRAPHICAL ABSTRACT

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