### Heat Transfer in MHD Squeezing Flow using Brinkman Model

#### Abstract

This study investigates squeezing flow of viscous incompressible fluid in a highly permeable medium between 2 parallel, permeable, unsteadily rotating plates in the presence of a magnetic field and radiation. The plates at time *t ^{*}* are separated by a distance

*H*(1-

*at*)

^{*}^{1/2}. Using a similarity transformation, the governing equations have been transformed into a system of non-linear ordinary differential equations. The resulting equations have been solved numerically by a shooting method. Graphs are presented to depict the temperature and heat transfer profiles. The results show a decline in the temperature profiles under the effect of enhanced radiation.

doi:10.14456/WJST.2014.68

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EC Kuhn and CC Yates. Fluid inertia effect on the film pressure between axially oscillating parallel circular plates. ASLE Trans. 1964; 7, 299-303.

JB Hunt. Pressure distribution in a plane fluid film subject to normal sinusoidal excitation. Nature 1966; 211, 1137-9.

PS Gupta and AS Gupta. Squeezing flow between parallel plates. Wear 1977; 45, 177-85.

BS Bhatt and EA Hamza. Similarity solution for the squeezed film flow between two rotating naturally permeable discs. Z. Angew. Math. Mech. 1996; 76, 291-9.

SC Rajvanshi. The flow between two parallel infinite disks, both subjected to normal sinusoidal oscillations. In: Proceedings of the National Academy of Sciences, India, 1971, p. 209-19.

SC Rajvanshi. Effect of axial current induced pinch and velocity slip on the squeeze-film behavior for porous annular disks. In: Proceedings of the National Academy of Sciences, India, 1981, 350-8.

M Singh and SC Rajvanshi. Flow between two parallel pulsating plates. Acta Ciencia Indica 1990; 16, 223-36.

G Gauthier, P Gondret and M Rabaud. Axisymmetric propagating vortices in the flow between a stationary and a rotating disk enclosed by a cylinder. J. Fluid Dynam. 1999; 386, 105-26.

L Schouveiler, PL Gal and MP Chauve. Instabilities in the flow between a rotating and stationary disk. J. Fluid Dynam. 2001; 443, 329-50.

E Serre, E Crespo del Arco and P Bontoux. Annular and spiral patterns in flows between rotating and stationary discs. J. Fluid Dynam. 2001; 434, 65-100.

MA Hossain and HS Takhar. Radiation effect on mixed convection along a vertical plate with uniform surface temperature. Heat Mass Tran. 1996; 31, 243-8.

MA Hossain, MA Alim and DA S Rees. The effect of radiation in free convection from a porous vertical plate. Int. J. Heat Mass Tran. 1999; 42, 181-91.

A Raptis and C Perdikis. Radiation and free convection flow past a moving vertical plate. Int. J. Appl. Mech. Eng. 1999; 4, 817-21.

AJ Chamkha. Hydromagnetic free convection flow over an inclined plate caused by solar radiation. J. Thermophys. Heat Tran. 1997; 11, 312-5.

AJ Chamkha, HS Takhar and VM Soundalgekar. Radiation effects on free convection flow past a semi-infinite vertical plate with mass transfer. Chem. Eng. J. 2001; 84, 335-42.

MA Samad and MM Rahman. Thermal radiation interaction with unsteady MHD flow past a vertical porous plate immersed in a porous medium. J. Nav. Architect. Mar. Eng. 2006; 3, 7-14.

A Postelnicu. The onset of a Darcy-Brinkman convection using a thermal non-equilibrium model, Part-II. Int. J. Therm. Sci. 2008; 47, 1587-94.

MM Rashidi, H Shahmohamadi and S Dinarvand. Analytic approximate solutions for unsteady two-dimensional and axisymmetric squeezing flows between parallel plates. Math. Probl. Eng. 2008; 2008, 1-13.

PR Sharma, V Kumar and P Sharma. Unsteady MHD free convective flow and heat transfer between heated inclined plates with magnetic field in the presence of radiation effects. J. Int. Acad. Phys. Sci. 2010; 14, 181-93.

R Ali and A Shahzad. MHD flow of a non-Newtonian fluid over a vertical stretching sheet with convective boundary condition. Walailak J. Sci. & Tech. 2013; 10, 43-56.

DS Chauhan and V Kumar. Radiation effects on unsteady flow through a channel filled by a porous medium with velocity and temperature slip boundary conditions. Appl. Math. Sci. 2012; 6, 1759-69.

US Rajput and PK Sahu. Natural convection in unsteady hydromagnetic Couette flow through a vertical channel in the presence of thermal radiation. Int. J. Appl. Math. Mech. 2012; 8, 35-56.

SC Rajvanshi, BS Saini and S Wasu. Heat transfer and entropy generation on MHD squeezing flow between two parallel rotating plates using Brinkman model. J. Rajasthan Acad. Phys. Sci. 2013; 12, 181-98.

S Sangapatnam, BR Nandanoor and RP Vallampati. Radiation and mass transfer effects on MHD free convection flow past an impulsively started isothermal vertical plate with dissipation. Therm. Sci. 2009; 13, 171-81.

VR Prasad and NB Reddy. Radiation and mass transfer effects on an unsteady MHD free convection flow past a heated vertical plate in a porous medium with viscous dissipation. Theor. Appl. Mech. 2007; 34, 135-60.

HC Brinkman. A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles. Appl. Sci. Res. 1947; 1, 27-34.

AC Cogley, WG Vincenti and SE Gilles. Differential approximation for radiative transfer in a non-gray gas near equilibrium. Am. Inst. Aeronaut. Astronaut. J. 1968; 6, 551-3.

CY Wang. The squeezing of fluid between two plates. J. Appl. Mech. 1976; 43, 579-83.

EA Hamza. Unsteady flow between two disks with heat transfer in the presence of a magnetic field. J. Phys. D: Appl. Phys. 1992; 25, 1425-31.

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