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Volume 5, Issue 3, June 2019, Page: 44-56
Numerical Simulation of Natural Convection in a Rectangular Cavity with Heated Triangle and Internal Heat Generation
Md. Shirazul Hoque Mollah, Department of Mathematics, Dhaka University of Engineering & Technology, Gazipur, Bangladesh
Md. Shahidul Alam, Department of Mathematics, Dhaka University of Engineering & Technology, Gazipur, Bangladesh
Md. Abdul Alim, Department of Mathematics, Bangladesh University of Engineering and Technology, Dhaka, Bangladesh
Received: Aug. 9, 2019;       Accepted: Sep. 18, 2019;       Published: Oct. 9, 2019
Abstract
Free convection flow and heat transfer in a rectangular cavity with heated triangle and internal heat generation is investigated numerically. A finite element analysis is performed to investigate the effects of uniform heating and is also used for solving the Navier-Stokes and Energy balance equations. The horizontal bottom wall is divided into three equal sections. The middle section of the horizontal bottom wall, bottom side of the triangle and left vertical left wall in the enclosure were kept temperature at Th. The other two parts of the horizontal bottom wall and the other two sides of the triangle were kept thermal insulation while the right vertical walls and the top wall of the cavity were maintained constant temperature Tc with Th>Tc. The physical problems are represented mathematically by different sets of governing equations along with corresponding boundary conditions. The dimensionless Parameters in the equations are performed for Heat generation (λ), Rayleigh number (Ra) and Prandtl number (Pr). The streamlines, isotherms, average Nusselt number, velocity profiles and temperature distribution of the fluid in the enclosure are presented graphically. The numerical results indicate that the Heat Generation and Rayleigh number have strong influence on the streamlines and isotherms. Also the mentioned parameters have significant effect on average Nusselt number at the hot wall and average temperature of the fluid in the enclosure.
Keywords
Finite Element Method, Heat Generation, Numerical Simulation, Natural Convection, Rectangle Cavity
Md. Shirazul Hoque Mollah, Md. Shahidul Alam, Md. Abdul Alim, Numerical Simulation of Natural Convection in a Rectangular Cavity with Heated Triangle and Internal Heat Generation, International Journal of Theoretical and Applied Mathematics. Vol. 5, No. 3, 2019, pp. 44-56. doi: 10.11648/j.ijtam.20190503.12
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