Effects of thermal radiation and magnetohydrodynamics on Ree-Eyring fluid flows through porous medium with slip boundary conditions

2019 ◽  
Vol 15 (2) ◽  
pp. 492-507 ◽  
Author(s):  
K. Ramesh ◽  
Sartaj Ahmad Eytoo
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Porous Medium ◽  
Boundary Conditions ◽  
Closed Form ◽  
Parallel Plates ◽  
Slip Boundary Conditions ◽  
Content Type ◽  
Closed Form Solutions ◽  
Slip Boundary

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.

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

2019 ◽  
Vol 29 (5) ◽  
pp. 1786-1814 ◽  
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.

scholarly journals EFFECTS OF SLIP ON THE VON KÁRMÁN SWIRLING FLOW AND HEAT TRANSFER IN A POROUS MEDIUM

2015 ◽  
Vol 39 (2) ◽  
pp. 357-366 ◽  
Author(s):  
Bikash Sahoo ◽  
Sébastien Poncet ◽  
Fotini Labropulu
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Boundary Conditions ◽  
Disk Surface ◽  
Partial Slip ◽  
Fluid Temperature ◽  
Slip Boundary Conditions ◽  
Slip Boundary ◽  
Porosity Parameter ◽  
Flow And Heat Transfer

Numerical solutions are obtained for the fully coupled and highly nonlinear system of differential equations, arising due to the steady Kármán flow and heat transfer of a viscous fluid in a porous medium. The conventional no-slip boundary conditions are replaced by partial slip boundary conditions owing to the roughness of the disk surface. Combined effects of the slip λ and porosity γ parameters on the momentum and thermal boundary layers are studied in detail. Both parameters produce the same effects on the mean velocity profiles, such that all velocity components are reduced by increasing either λ or γ. The temperature slip factor β has a dominating influence on the temperature profiles by decreasing the fluid temperature in the whole domain. The porosity parameter strongly decreases the heat transfer coefficient at the wall for low values of β and tends to an asymptotical limit around 0.1 for β ≃ 10. The porosity parameter γ increases the moment coefficient at the disk surface, which is found to monotonically decrease with λ.

Numerical study of unsteady MHD Couette flow and heat transfer of nanofluids in a rotating system with convective cooling

2016 ◽  
Vol 26 (5) ◽  
pp. 1567-1579 ◽  
Author(s):  
Ahmada Omar Ali ◽  
Oluwole Daniel Makinde ◽  
Yaw Nkansah-Gyekye
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Couette Flow ◽  
Numerical Study ◽  
Integration Scheme ◽  
Parallel Plates ◽  
Content Type ◽  
Flow And Heat Transfer ◽  
Mhd Couette Flow ◽  
Rotating Channel

Purpose – The purpose of this paper is to investigate numerically the unsteady MHD Couette flow and heat transfer of viscous, incompressible and electrically conducting nanofluids between two parallel plates in a rotating channel. Design/methodology/approach – The nanofluid is set in motion by the combined action of moving upper plate, Coriolis force and the constant pressure gradient. The channel rotates in unison about an axis normal to the plates. The nonlinear governing equations for velocity and heat transfer are obtained and solved numerically using semi-discretization, shooting and collocation (bvp4c) techniques together with Runge-Kutta Fehlberg integration scheme. Findings – Results show that both magnetic field and rotation rate demonstrate significant effect on velocity and heat transfer profiles in the system with Cu-water nanofluid demonstrating the highest velocity and heat transfer efficiency. These numerical results are in excellent agreements with the results obtained by other methods. Practical implications – This paper provides a very useful source of information for researchers on the subject of hydromagnetic nanofluid flow in rotating systems. Originality/value – Couette flow of nanofluid in the presence of applied magnetic field in a rotating channel is investigated.

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