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TECHNICAL BRIEFS

# Natural Convection in a Cavity With a Wavy Wall Heated From Below and Uniformly Cooled From the Top and Both Sides

[+] Author and Article Information
Amaresh Dalal

Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur-208 016, Indiaamaresh@iitk.ac.in

Manab Kumar Das1

Department of Mechanical Engineering, Indian Institute of Technology Guwahati, Guwahati-781 039, Indiamanab@iitg.ernet.in

1

Corresponding author.

J. Heat Transfer 128(7), 717-725 (Feb 18, 2006) (9 pages) doi:10.1115/1.2194044 History: Received June 28, 2005; Revised February 18, 2006

## Abstract

In this paper, natural convection inside a two-dimensional cavity with a wavy right vertical wall has been carried out. The bottom wall is heated by a spatially varying temperature and other three walls are kept at constant lower temperature. The integral forms of the governing equations are solved numerically using finite-volume method in the non-orthogonal body-fitted coordinate system. The semi-implicit method for pressure linked equation algorithm with higher-order upwinding scheme are used. The streamlines and isothermal lines are presented for three different undulations (1, 2 and 3) with different Rayleigh number and a fluid having Prandtl number 0.71. Results are presented in the form of local and average Nusselt number distribution for a selected range of Rayleigh number $(100–106)$.

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## Figures

Figure 1

Flow configuration and boundary condition for three undulations case

Figure 2

Streamline contour plot for λ=0.05

Figure 3

Maximum and minimum stream function distribution for λ=0.05

Figure 4

Isotherm contour plot for λ=0.05

Figure 5

Local Nusselt number distribution on the wavy wall

Figure 6

Local Nusselt number distribution on the wavy wall for different amplitudes

Figure 7

Average Nusselt number distribution on the wavy wall for various Ra and amplitude

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