Unsteady free convection adjacent to an impulsively heated horizontal circular cylinder in porous media

Journal Article · Mon Sep 01 04:00:00 EDT 1997 · Numerical Heat Transfer. Part A, Applications

DOI:https://doi.org/10.1080/10407789708913894· OSTI ID:562031

Bradean, R; Ingham, D B ^[1]; Heggs, P J ^[2]; Pop, I ^[3]

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1. Univ. of Leeds (United Kingdom). Dept. of Applied Mathematical Studies
2. UMIST, Manchester, England (United States). Dept. of Chemical Engineering
3. Univ. of Cluj (Romania). Faculty of Mathematics

An infinitely long circular cylinder embedded horizontally in a porous medium at the same temperature is suddenly heated to a constant temperature. The governing equations are solved numerically for small and large values of the Rayleigh number, and at small times, the results are found to be in very good agreement with the analytical solution as obtained by Pop et al., who uses the method of matched asymptotic expansions. A plume region develops at the top of the cylinder, and two counterrotating vortices form adjacent to the sides of the cylinder. A novel feature of the results is that as convection becomes increasingly more dominant, a single hot cell of fluid forms vertically above the cylinder and rapidly moves away from the cylinder as time increases. The hot cell of fluid occurs at smaller times and distances from the surface of the cylinder as the Rayleigh number increases. The numerical results indicate that the heat and flow penetrate farther upward into the porous media as time increases, whereas the conservation of energy principle shows that the heat penetrates infinitely into the porous media. At very large times the numerical results show reasonable agreement, in the vicinity of the cylinder,m with the steady state solution obtained by Ingham and Pop, which should only be considered as an inner solution to the problem.

• Sponsoring Organization: USDOE
• OSTI ID: 562031
• Journal Information: Numerical Heat Transfer. Part A, Applications, Journal Name: Numerical Heat Transfer. Part A, Applications Journal Issue: 4 Vol. 32; ISSN 1040-7782; ISSN NHAAES
• Country of Publication: United States
• Language: English

Related Subjects

15 GEOTHERMAL ENERGY
42 ENGINEERING
GEOTHERMAL SYSTEMS
NATURAL CONVECTION
NUMERICAL SOLUTION
POROUS MATERIALS
UNSTEADY FLOW