Conjugate Heat Transfer in Uniformly Heated Enclosure Filled with Micropolar Fluid
H. Imtiaz and F. M. Mahfouz

doi:10.3970/cmes.2015.108.171
Source CMES: Computer Modeling in Engineering & Sciences, Vol. 108, No. 3, pp. 171-192, 2015
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Keywords Conjugate heat transfer, concentric annulus, thermal conductivity ratio, Rayleigh number, micropolar fluid, natural convection.
Abstract

This paper investigates numerically the conjugate heat transfer in a concentric enclosure that is formed between two concentric cylinders and filled with micropolar fluid. The wall of inner cylinder is considerably thick, while the wall of outer cylinder is very thin. The inner cylinder is heated from inner side through constant heat flux, whereas the outer cylinder is cooled and maintained at constant temperature. The induced buoyancy driven flow and associated conjugate heat transfer are predicted numerically by solving flow and energy governing equations considering a combination of finite difference and Fourier spectral methods. The study investigates the effect of controlling parameters on both flow and thermal fields, keeping focus on inner wall temperature. The controlling parameters are Rayleigh number Ra, dimensionless thickness of inner wall, inner cylinder fluid thermal conductivity ratio Kr, and material parameters of micropolar fluid (\(\lambda\), B and D). The study shows that the steady dimensionless mean inner wall temperature \(\bar{\phi_{I}}\) decreases with increase in Kr and Ra, and decrease in the vortex viscosity D. The study also shows that the increase in thickness of inner wall at Kr \(<\) 1 leads to increase in steady \(\bar{\phi_{I}}\). While in case of Kr \(>\) 1, for a given value of Ra and D, \(\bar{\phi_{I}}\) assumes maximum value at certain thickness of inner wall. In general, the study demonstrates that, for same geometrical and flow parameters, \(\bar{\phi _{I}}\) is more in case of micropolar fluids as compared to Newtonian fluids.

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