Numerical Study of Laminar Natural Convection Heat Transfer in Inclined Trapezoidal Enclosure

[+] Author and Article Information
Sandip K. Saha

Department of Mechanical Engineering Indian Institute of Technology Bombay, Powai Mumbai, Maharashtra 400076 India sandip.saha@iitb.ac.in

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the Journal of Thermal Science and Engineering Applications. Manuscript received January 30, 2019; final manuscript received April 29, 2019; published online xx xx, xxxx. Assoc. Editor: Gerard F. Jones.

ASME doi:10.1115/1.4043742 History: Received January 30, 2019; Accepted May 03, 2019


In this paper, fluid flow pattern and heat transfer behaviour are numerically studied in a trapezoidal enclosure inclined at different tilt angles. The enclosure has isothermally heated inner and cooled upper walls, whereas sidewalls have linearly varying temperature profile. The numerical analysis is performed at different Rayleigh numbers (103Ra ≤106) and Prandtl numbers (0.71 ≤ Pr ≤ 40) assuming steady, incompressible, laminar, Newtonian, and two-dimensional flow. The angle between two nonparallel sidewalls is varied from 10° to 90°, while tilt angle is changed in the range of 5 ° to 175 °. Governing equation along with Poisson type equation for heatfunctions are solved to obtain fluid flow and direction of heat flow in the trapezoidal enclosure. At low Raleigh number, the isotherms are smooth indicating the dominance of conduction heat transfer dominates. The streamlines, isotherms and heatlines in high Prandtl number (Pr = 6.99 ad 40) fluids show similar pattern as that in air (Pr = 0.71) at Ra = 106, however the strength of heatfunctions increases. With the increase in aspect ratio of the enclosure, thermally stratified region is found to increase in size. Stronger convection is present in the enclosure with higher angle between two non-parallel sidewalls.

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