Numerical study of natural convection in a vertical porous annulus with discrete heating.

*(English)*Zbl 1211.80026Summary: In this paper natural convection flows in a vertical annulus filled with a fluid-saturated porous medium has been investigated when the inner wall is subject to discrete heating. The outer wall is maintained isothermally at a lower temperature, while the top and bottom walls, and the unheated portions of the inner wall are kept adiabatic. Through the Brinkman-extended Darcy equation, the relative importance of discrete heating on natural convection in the porous annulus is examined. An implicit finite difference method has been used to solve the governing equations of the flow system. The analysis is carried out for a wide range of modified Rayleigh and Darcy numbers for different heat source lengths and locations. It is observed that placing of the heater in lower half of the inner wall rather than placing the heater near the top and bottom portions of the inner wall produces maximum heat transfer. The numerical results reveal that an increase in the radius ratio, modified Rayleigh number and Darcy number increases the heat transfer, while the heat transfer decreases with an increase in the length of the heater. The maximum temperature at the heater surface increases with an increase in the heater length, while it decreases when the modified Rayleigh number and Darcy number increases. Further, we find that the size and location of the heater effects the flow intensity and heat transfer rate in the annular cavity.

##### MSC:

80A20 | Heat and mass transfer, heat flow (MSC2010) |

76R10 | Free convection |

76S05 | Flows in porous media; filtration; seepage |

80M20 | Finite difference methods applied to problems in thermodynamics and heat transfer |

76M20 | Finite difference methods applied to problems in fluid mechanics |

##### Keywords:

natural convection; annulus; discrete heating; porous medium; radii ratio; Brinkman-extended Darcy model
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\textit{M. Sankar} et al., Int. J. Heat Mass Transfer 54, No. 7--8, 1493--1505 (2011; Zbl 1211.80026)

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