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Heat transfer of incompressible flow in a rotating microchannel with slip boundary conditions of second order

A.A. Avramenko (Institute of Engineering Thermophysics, Kiev, Ukraine)
N.P. Dmitrenko (Institute of Engineering Thermophysics, Kiev, Ukraine)
I.V. Shevchuk (Fakultät fu¨r Informatik und Ingenieurwissenschaften, Technische Hochschule Köln, Gummersbach, Germany)
A.I. Tyrinov (Institute of Engineering Thermophysics, Kiev, Ukraine)
V.I. Shevchuk (Ruetz System Solutions GmbH, Munich, Germany)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Article publication date: 10 December 2018

Issue publication date: 10 June 2019

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Abstract

Purpose

The paper aims to consider heat transfer in incompressible flow in a rotating flat microchannel with allowance for boundary slip conditions of the first and second order. The novelty of the paper encompasses analytical and numerical solutions of the problem, with the latter based on the lattice Boltzmann method (LBM). The analytical solution of the problem includes relations for the velocity and temperature profiles and for the Nusselt number depending on the rotation rate of the microchannel and slip velocity. It was demonstrated that the velocity profiles at high rotation rates transform from parabolic to M-shaped with a minimum at the channel axis. The temperature profiles tend to become uniform (i.e. almost constant). An increase in the channel rotation rate contributes to the increase in the Nusselt number. An increase in the Prandtl number causes a similar effect. The trend caused by the effect of the second-order slip boundary conditions depends on the closure hypothesis. It is shown that heat transfer in a flat microchannel can be successfully modeled using the LBM methodology, which takes into account the second-order boundary conditions.

Design/methodology/approach

The paper is based on the comparisons of an analytical solution and a numerical solution, which employs the lattice Boltzmann method. Both mathematical approaches used the first-order and second-order slip boundary conditions. The results obtained using both methods agree well with each other.

Findings

The analytical solution of the problem includes relations for the velocity and temperature profiles and for the Nusselt number depending on the rotation rate of the microchannel and slip velocity. It was demonstrated that the velocity profiles at high rotation rates transform from parabolic to M-shaped with a minimum at the channel axis. The temperature profiles tend to become uniform (i.e. almost constant). The increase in the channel rotation rate contributes to the increase in the Nusselt number. An increase in the Prandtl number causes the similar effect. The trend caused by the effect of the second-order slip boundary conditions depends on the closure hypothesis. It is shown that heat transfer in a flat microchannel can be successfully modeled using the LBM methodology, which considers the second-order boundary conditions.

Originality/value

The novelty of the paper encompasses analytical and numerical solutions of the problem, whereas the latter are based on the LBM.

Keywords

Citation

Avramenko, A.A., Dmitrenko, N.P., Shevchuk, I.V., Tyrinov, A.I. and Shevchuk, V.I. (2019), "Heat transfer of incompressible flow in a rotating microchannel with slip boundary conditions of second order", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 29 No. 5, pp. 1786-1814. https://doi.org/10.1108/HFF-06-2018-0264

Publisher

:

Emerald Publishing Limited

Copyright © 2018, Emerald Publishing Limited

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