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Research Papers

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

[+] Author and Article Information
Sandip Kumar Saha

Mem. ASME
Department of Mechanical Engineering,
Indian Institute of Technology Bombay,
Mumbai 400076, Maharashtra, India
e-mail: sandip.saha@iitb.ac.in

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 July 19, 2019. Assoc. Editor: Gerard F. Jones.

J. Thermal Sci. Eng. Appl 11(6), 061021 (Jul 19, 2019) (12 pages) Paper No: TSEA-19-1043; doi: 10.1115/1.4043742 History: Received January 30, 2019; Accepted May 03, 2019

## Abstract

In this paper, fluid flow pattern and heat transfer behavior are numerically studied in a trapezoidal enclosure inclined at different tilt angles. The enclosure has isothermally heated cylindrical inner wall and cooled cylindrical outer wall, whereas sidewalls have linearly varying temperature profile. The numerical analysis is performed at different Rayleigh numbers (103 ≤ Ra ≤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 deg to 90 deg, while the tilt angle is varied from 5 deg to 175 deg. Governing equations along with the 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 a similar pattern as that in the air (Pr = 0.71) at Ra = 106; however, the strength of heatfunctions increases. With the increase in the aspect ratio of the enclosure, thermally stratified region is found to increase in size. Stronger convection is present in the enclosure with a higher angle between two nonparallel sidewalls.

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## References

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## Figures

Fig. 1

Schematic diagram of the trapezoidal enclosure at a tilt angle of ϕ Fig. 2

Comparison of average Nusselt numbers between the present model and the experimental results Fig. 3

(a) Isotherm, (b) streamfunction, and (c) heatfunction contours for Ra = 103, with air (Pr = 0.71) as the working fluid for AR = 2 and θ = 30 deg Fig. 4

(a) Isotherm, (b) streamfunction, and (c) heatfunction contours for Ra = 104, with air (Pr = 0.71) as the working fluid for AR = 2 and θ = 30 deg Fig. 5

(a) Isotherm, (b) streamfunction, and (c) heatfunction contours for Ra = 105, with air (Pr = 0.71) as the working fluid for AR = 2 and θ = 30 deg Fig. 6

(a) Isotherm, (b) streamfunction, and (c) heatfunction contours for Ra = 106, with air (Pr = 0.71) as the working fluid for AR = 2 and θ = 30 deg Fig. 7

(a) Isotherm, (b) streamfunction, and (c) heatfunction contours for water (Pr = 6.99), (d) isotherm, (e) streamfunction, and (f) heatfunction contours for PCM (Pr = 40) at Ra = 106 for AR = 2 and θ = 30 deg Fig. 8

Isotherm contours for (a) AR = 5 and (d) AR = 10, streamfunction contours for (b) AR = 5 and (e) AR = 10, and heatfunction contours for (c) AR = 5 and (f) AR = 10 for air (Pr = 0.71), θ = 30 deg at Ra = 106 Fig. 9

(a) Isotherm, (b) streamfunction, and (c) heatfunction contours for Ra = 106, with air (Pr = 0.71) as the working fluid for AR = 2 and θ = 10 deg Fig. 10

(a) Isotherm, (b) streamfunction, and (c) heatfunction contours for Ra = 106, with air (Pr = 0.71) as the working fluid for AR = 2 and θ = 20 deg Fig. 11

(a) Isotherm, (b) streamfunction, and (c) heatfunction contours for Ra = 106, with air (Pr = 0.71) as the working fluid for AR = 2 and θ = 45 deg Fig. 12

(a) Isotherm, (b) streamfunction, and (c) heatfunction contours for Ra = 106, with air (Pr = 0.71) as the working fluid for AR = 2 and θ = 60 deg Fig. 13

(a) Isotherm, (b) streamfunction, and (c) heatfunction contours for Ra = 106, with air (Pr = 0.71) as the working fluid for AR = 2 and θ = 90 deg ## Errata

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