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Research Paper | Mathematics | Kenya | Volume 10 Issue 11, November 2021

Analysis of Turbulent Natural Convection with Localized Heating on the Ceiling and on the Floor and Cooling on Opposite Vertical Walls in a Rectangular Enclosure

Omariba G. Ong'era | Johana K. Sigey ^[6] | Jeconia A. Okelo ^[3] | Stephen M. Karanja

Abstract: In this study, turbulent natural convection was investigated in a three-dimensional rectangular enclosure in the form of a room which has convectional heaters positioned at the center of the ceiling and center of the floor and two convectional windows on the opposite vertical walls. The study aimed at examining the velocity profile and temperature distribution. Numerical solution aimed at governing the momentum and energy equations are attained using Taylor?s central finite difference estimates with suitable set of boundary conditions. The method chosen above alternative solutions because it converges quickly, is stable, inexpensive, and adaptable when using boundary conditions. The central difference approach and the forward difference method are used to solve the differential equations. To generate results, the resulting equations are solved in MATLAB computer software. The results are graphed at various Reynold numbers, Froude numbers, Euler numbers, and a fixed Prandtl number of 0.71 to demonstrate the velocity profile and temperature distribution in the enclosure. The 2D graphs are used to examine the behavior of fluid flow fields. When Froude number is increased, the velocity decreases with increase in room height, an increase in Euler number leads to an increase in fluid velocity and when the Reynolds number is increased, the temperature decreases. The temperature similarly decreases as the height of the room is increased.

Keywords: Turbulent, natural convection; The flow of heat, a three-dimensional rectangular enclosure

Edition: Volume 10 Issue 11, November 2021,

Pages: 523 - 529