Unsteady mixed convective heat transfer of two immiscible fluids confined between long vertical wavy wall and parallel flat wall

doi:10.1007/s10483-012-1596-6

Applied Mathematics and Mechanics (English Edition) ›› 2012, Vol. 33 ›› Issue (7): 931-950.doi: https://doi.org/10.1007/s10483-012-1596-6

Unsteady mixed convective heat transfer of two immiscible fluids confined between long vertical wavy wall and parallel flat wall

J. C. UMAVATHI¹, I. C. LIU², M. SHEKAR¹

1. Department of Mathematics, Gulbarga University, Karnataka 585106, India;
2. Department of Civil Engineering, National Chi Nan University, Nantou 54561, Taiwan, China

收稿日期:2011-05-18 修回日期:2011-12-28 出版日期:2012-07-10 发布日期:2012-07-10
通讯作者: J. C. UMAVATHI, Professor, Ph.D., E-mail: jc_umall@yahoo.com E-mail:jc_umall@yahoo.com
基金资助:
Project supported by the Major Research Projects of University Grants Commission of India (No.F.No. 37-178 (2009))

Unsteady mixed convective heat transfer of two immiscible fluids confined between long vertical wavy wall and parallel flat wall

J. C. UMAVATHI¹, I. C. LIU², M. SHEKAR¹

1. Department of Mathematics, Gulbarga University, Karnataka 585106, India;
2. Department of Civil Engineering, National Chi Nan University, Nantou 54561, Taiwan, China

Received:2011-05-18 Revised:2011-12-28 Online:2012-07-10 Published:2012-07-10
Supported by:
Project supported by the Major Research Projects of University Grants Commission of India (No.F.No. 37-178 (2009))

摘要/Abstract

摘要： The combined effects of thermal and mass convection of viscous incom-pressible and immiscible fluids through a vertical wavy wall and a smooth flat wall are analyzed. The dimensionless governing equations are perturbed into a mean part (the zeroth-order) and a perturbed part (the first-order). The first-order quantities are ob-tained by the perturbation series expansion for short wavelength, in which the terms of the exponential order arise. The analytical expressions for the zeroth-order, the first-order, and the total solutions are obtained. The numerical computations are presented graph-ically to show the salient features of the fluid flow and the heat transfer characteristics. Separate solutions are matched at the interface by using suitable matching conditions. The shear stress and the Nusselt number are also analyzed for variations of the governing parameters. It is observed that the Grashof number, the viscosity ratio, the width ratio, and the conductivity ratio promote the velocity parallel to the flow direction. A reversal effect is observed for the velocity perpendicular to the flow direction.

关键词: piezoelectric material, inclusion, dislocation, image force, mixed convection, wavy wall, immiscible fluid, perturbation method

Abstract: The combined effects of thermal and mass convection of viscous incom-pressible and immiscible fluids through a vertical wavy wall and a smooth flat wall are analyzed. The dimensionless governing equations are perturbed into a mean part (the zeroth-order) and a perturbed part (the first-order). The first-order quantities are ob-tained by the perturbation series expansion for short wavelength, in which the terms of the exponential order arise. The analytical expressions for the zeroth-order, the first-order, and the total solutions are obtained. The numerical computations are presented graph-ically to show the salient features of the fluid flow and the heat transfer characteristics. Separate solutions are matched at the interface by using suitable matching conditions. The shear stress and the Nusselt number are also analyzed for variations of the governing parameters. It is observed that the Grashof number, the viscosity ratio, the width ratio, and the conductivity ratio promote the velocity parallel to the flow direction. A reversal effect is observed for the velocity perpendicular to the flow direction.

Key words: piezoelectric material, inclusion, dislocation, image force, mixed convection, wavy wall, immiscible fluid, perturbation method

中图分类号:

O357.1

J. C. UMAVATHI;I. C. LIU;M. SHEKAR. Unsteady mixed convective heat transfer of two immiscible fluids confined between long vertical wavy wall and parallel flat wall[J]. Applied Mathematics and Mechanics (English Edition), 2012, 33(7): 931-950.

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Unsteady mixed convective heat transfer of two immiscible fluids confined between long vertical wavy wall and parallel flat wall

Unsteady mixed convective heat transfer of two immiscible fluids confined between long vertical wavy wall and parallel flat wall

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