Investigation of the effect of MHD slip flow on heat transfer between parallel plates with second order slip boundary conditions

Purpose The purpose of this paper is to investigate the three fundamental flows (namely, both the plates moving in opposite directions, the lower plate is moving and other is at rest, and both the plates moving in the direction of flow) of the Ree-Eyring fluid between infinitely parallel plates with the effects of magnetic field, porous medium, heat transfer, radiation and slip boundary conditions. Moreover, the intention of the study is to examine the effect of different physical parameters on the fluid flow. Design/methodology/approach The mathematical modeling is performed on the basis of law of conservation of mass, momentum and energy equation. The modeling of the present problem is considered in Cartesian coordinate system. The governing equations are non-dimensionalized using appropriate dimensionless quantities in all the mentioned cases. The closed-form solutions are presented for the velocity and temperature profiles. Findings The graphical results are presented for the velocity and temperature distributions with the pertinent parameters of interest. It is observed from the present results that the velocity is a decreasing function of Hartmann number. Temperature increases with the increase of Ree-Eyring fluid parameter, radiation parameter and temperature slip parameter. Originality/value First time in the literature, the authors obtained closed-form solutions for the fundamental flows of Ree-Erying fluid between infinitely parallel plates with the effects of magnetic field, porous medium, heat transfer, radiation and slip boundary conditions. Moreover, the results of this paper are new and original.

Download Full-text

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

International Journal of Numerical Methods for Heat &amp Fluid Flow ◽

10.1108/hff-06-2018-0264 ◽

2019 ◽

Vol 29 (5) ◽

pp. 1786-1814 ◽

Cited By ~ 3

Author(s):

A.A. Avramenko ◽

N.P. Dmitrenko ◽

I.V. Shevchuk ◽

A.I. Tyrinov ◽

V.I. Shevchuk

Keyword(s):

Heat Transfer ◽

Nusselt Number ◽

Analytical Solution ◽

Boundary Conditions ◽

Rotation Rate ◽

Second Order ◽

Temperature Profiles ◽

Slip Boundary Conditions ◽

Content Type ◽

Slip Boundary

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.

Download Full-text

The Effect of Viscous Dissipation on Two-Dimensional Microchannel Heat Transfer

Microelectromechanical Systems ◽

10.1115/imece2006-16121 ◽

2006 ◽

Cited By ~ 2

Author(s):

Jennifer van Rij ◽

Tim Ameel ◽

Todd Harman

Keyword(s):

Heat Transfer ◽

Viscous Dissipation ◽

Slip Flow ◽

Second Order ◽

Slip Boundary Conditions ◽

Pressure Work ◽

Axial Conduction ◽

Slip Boundary ◽

Nusselt Numbers ◽

Slip Flow Regime

Microchannel convective heat transfer characteristics in the slip flow regime are numerically evaluated for two-dimensional, steady state, laminar, constant wall heat flux and constant wall temperature flows. The effects of Knudsen number, accommodation coefficients, viscous dissipation, pressure work, second-order slip boundary conditions, axial conduction, and thermally/hydrodynamically developing flow are considered. The effects of these parameters on microchannel convective heat transfer are compared through the Nusselt number. Numerical values for the Nusselt number are obtained using a continuum based three-dimensional, unsteady, compressible computational fluid dynamics algorithm that has been modified with slip boundary conditions. Numerical results are verified using analytic solutions for thermally and hydrodynamically fully developed flows. The resulting analytical and numerical Nusselt numbers are given as a function of Knudsen number, the first- and second-order velocity slip and temperature jump coefficients, the Peclet number, and the Brinkman number. Excellent agreement between numerical and analytical data is demonstrated. Viscous dissipation, pressure work, second-order slip terms, and axial conduction are all shown to have significant effects on Nusselt numbers in the slip flow regime.

Download Full-text

Convective heat transfer and entropy generation analysis on Newtonian and non-Newtonian fluid flows between parallel-plates under slip boundary conditions

International Journal of Heat and Mass Transfer ◽

10.1016/j.ijheatmasstransfer.2013.11.020 ◽

2014 ◽

Vol 70 ◽

pp. 664-673 ◽

Cited By ~ 49

Author(s):

Mostafa Shojaeian ◽

Ali Koşar

Keyword(s):

Heat Transfer ◽

Boundary Conditions ◽

Convective Heat Transfer ◽

Convective Heat ◽

Newtonian Fluid ◽

Entropy Generation ◽

Fluid Flows ◽

Parallel Plates ◽

Slip Boundary Conditions ◽

Slip Boundary

Download Full-text

IMPACT OF NANOFLUIDS ON EXTERNAL AND INTERNAL FLOW VIA NAVIER-STOKES AND CONVECTION-DIFFUSION EQUATIONS FOR PARALLEL PLATES WITH SLIP BOUNDARY CONDITIONS

10.26678/abcm.encit2020.cit20-0586 ◽

2020 ◽

Author(s):

Ricardo Costa ◽

Marcos Curi

Keyword(s):

Boundary Conditions ◽

Internal Flow ◽

Diffusion Equations ◽

Navier Stokes ◽

Parallel Plates ◽

Slip Boundary Conditions ◽

Convection Diffusion ◽

Slip Boundary

Download Full-text

Iterative Methods for Solving the Fractional form of Axisymmetric Squeezing Fluid Flow between Tow Infinite Parallel Plates with Slip Boundary Conditions

Applied Mathematics & Information Sciences ◽

10.18576/amis/150504 ◽

2021 ◽

Vol 15 (5) ◽

pp. 561-569

Keyword(s):

Fluid Flow ◽

Boundary Conditions ◽

Iterative Methods ◽

Parallel Plates ◽

Slip Boundary Conditions ◽

Slip Boundary

Download Full-text

Poiseuille Number Correlations of Gas Flow in Concentric Micro Annular Tubes

Volume 13: Nano-Manufacturing Technology; and Micro and Nano Systems, Parts A and B ◽

10.1115/imece2008-67127 ◽

2008 ◽

Author(s):

Chungpyo Hong ◽

Yutaka Asako ◽

Koichi Suzuki

Keyword(s):

Boundary Conditions ◽

Gas Flow ◽

Slip Flow ◽

Tube Length ◽

Slip Boundary Conditions ◽

Slip Boundary ◽

Rarefaction Effect ◽

Wide Range ◽

Poiseuille Number ◽

Fast Flow

Poiseuille number, the product of friction factor and Reynolds number (f · Re) for quasi-fully developed concentric micro annular tube flow was obtained for both no-slip and slip boundary conditions. The numerical methodology is based on the Arbitrary-Lagrangian-Eulerian (ALE) method. The compressible momentum and energy equations were solved for a wide range of Reynolds and Mach numbers for both isothermal flow and no heat conduction flow conditions. The detail of the incompressible slip Poiseuille number is kindly documented and its value defined as a function of r* and Kn is represented. The outer tube radius ranges from 50 to 150μm with the radius ratios of 0.2, 0.5 and 0.8 and selected tube length is 0.02m. The stagnation pressure, pstg is chosen in such away that the exit Mach number ranges from 0.1 to 0.7. The outlet pressure is fixed at the atmospheric pressure. In the case of fast flow, the value of f · Re is higher than that of incompressible slip flow theory due to the compressibility effect. However in the case of slow flow the value of f · Re is slightly lower than that of incompressible slip flow due to the rarefaction effect, even the flow is accelerated. The value of f · Re obtained for no-slip boundary conditions is compared with that of obtained for slip boundary conditions. The values of f · Re obtained for slip boundary conditions are predicted by f · Re correlations obtained for no-slip boundary conditions since rarefaction effect is relatively small for the fast flow.

Download Full-text