A penalty finite element analysis with biquadratic elements has been carried out to investigate natural convection flows within an isosceles triangular enclosure with an aspect ratio of 0.5. Two cases of thermal boundary conditions are considered with uniform and nonuniform heating of bottom wall. The numerical solution of the problem is illustrated for Rayleigh numbers (Ra), $103\u2a7dRa\u2a7d105$ and Prandtl numbers (Pr), 0.026$\u2a7dPr\u2a7d$1000. In general, the intensity of circulation is found to be larger for nonuniform heating at a specific Pr and Ra. Multiple circulation cells are found to occur at the central and corner regimes of the bottom wall for a small Prandtl number regime (Pr=0.026−0.07). As a result, the oscillatory distribution of the local Nusselt number or heat transfer rate is seen. In contrast, the intensity of primary circulation is found to be stronger, and secondary circulation is completely absent for a high Prandtl number regime (Pr=0.7–1000). Based on overall heat transfer rates, it is found that the average Nusselt number for the bottom wall is $2$ times that of the inclined wall, which is well, matched in two cases, verifying the thermal equilibrium of the system. The correlations are proposed for the average Nusselt number in terms of the Rayleigh number for a convection dominant region with higher Prandtl numbers (Pr=0.7 and 10).

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# Finite Element Simulation on Natural Convection Flow in a Triangular Enclosure Due to Uniform and Nonuniform Bottom Heating

S. Roy

,
S. Roy

Department of Mathematics,

sjroy@iitm.ac.in
Indian Institute of Technology Madras

, Chennai-600036, India
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Tanmay Basak

,
Tanmay Basak

Department of Chemical Engineering,

tanmay@iitm.ac.in
Indian Institute of Technology Madras

, Chennai-600036, India
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Ch. Thirumalesha

,
Ch. Thirumalesha

Department of Chemical Engineering,

Indian Institute of Technology Madras

, Chennai-600036, India
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Ch. Murali Krishna

Ch. Murali Krishna

Department of Mathematics,

Indian Institute of Technology Madras

, Chennai-600036, India
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S. Roy

Department of Mathematics,

Indian Institute of Technology Madras

, Chennai-600036, Indiasjroy@iitm.ac.in

Tanmay Basak

Department of Chemical Engineering,

Indian Institute of Technology Madras

, Chennai-600036, Indiatanmay@iitm.ac.in

Ch. Thirumalesha

Department of Chemical Engineering,

Indian Institute of Technology Madras

, Chennai-600036, India
Ch. Murali Krishna

Department of Mathematics,

Indian Institute of Technology Madras

, Chennai-600036, India*J. Heat Transfer*. Mar 2008, 130(3): 032501 (10 pages)

**Published Online:**March 6, 2008

Article history

Received:

July 19, 2006

Revised:

August 30, 2007

Published:

March 6, 2008

Citation

Roy, S., Basak, T., Thirumalesha, C., and Krishna, C. M. (March 6, 2008). "Finite Element Simulation on Natural Convection Flow in a Triangular Enclosure Due to Uniform and Nonuniform Bottom Heating." ASME. *J. Heat Transfer*. March 2008; 130(3): 032501. https://doi.org/10.1115/1.2804934

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