Analysis of Radiation Heat Transfer of a Micropolar Fluid with Variable Properties over a Stretching Sheet in the Presence of Magnetic Field

Document Type : Full Lenght Research Article

Authors

1 M.Sc. of Mechanical Engineering, K. N. Toosi University of Technology,Tehran, Iran

2 Faculty of Mechanical Engineering, K. N. Toosi University of Technology,Tehran, Iran

Abstract

The present study deals with the analysis of the effects of radiative heat transfer of micropolar fluid flow over a porous and stretching sheet in the presence of magnetic field. The dynamic viscosity and thermal conductivity coefficient have formulated by temperature-dependent relations to obtain more exact results. The flow is supposed two-dimensional, incompressible, steady and laminar and the applied magnetic field is assumed uniform. On the other hand, the velocity of the isothermal stretching sheet varies linearly with the distance from a fixed point on the sheet. The governing equations have extracted using the theory of micropolar fluid and the boundary layer approximation. Then they have been solved by similarity solution relationships, shooting method and fourth-order Runge-Kutta method. The results express that the presence and increase of variable thermal conductivity parameter, magnetism, radiation and variable viscosity parameter cause to decrease of heat transfer from the sheet, while increase of material parameter, Prandtl number and suction parameter increase the rate of heat transfer from the sheet. Also the values of dimensionless velocity are enhanced by increase of variable thermal conductivity parameter, material parameter and radiation parameter. On the other hand, the values of dimensionless angular velocity are completely influenced by the values of the velocity gradient.

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References

[1].              A.C.Eringen, Simple microfluids, International Journal of Engineering Science, 2, 205-217, (1964).
[2].              M.W.Heruska, L.T.Watson, K.K. Sankara, Micropolar flow past a porous stretching sheet, Computers and Fluids, 14, 117-129,(1986).
[3].              I.A.Hassanien, A.A.Abdullah, R.S.R.Gorla, Numerical solutions for heat transfer in a micropolar fluid over a stretching sheet, Applied Mechanics and Engineering, 3, 377-391,(1998).
[4].              S.N.Odda, A.M.Farhan, Chebyshev finite difference method for the effects of variable viscosity and variable thermal conductivity on heat transfer to a micro-polar fluid from a non-isothermal stretching sheet with suction and blowing, Chaos, Solitons & Fractals, 30, 851-858,(2006).
[5].              N.A.Yacob, A.Ishak, I.Pop, Melting heat transfer in boundary layer stagnation-point flow towards a stretching/shrinking sheet in a micropolar fluid, Computers & Fluids, 47, 16-21,(2011).
[6].              M.M.Rahman, M.A.Rahman, M.A.Samad, M.S.Alam, Heat transfer in a micropolar fluid along a non-linear stretching sheet with a temperature-dependent viscosity and variable surface temperature, International Journal of Thermophysics, 30, 1649–1670,(2009).
[7].              N.A.Yacob, A.Ishak, Micropolar fluid flow over a shrinking sheet, Maccanica, 47, 293-299,(2012).
[8].              A.Ishak, Y.Y.Lok, I.Pop, Stagnation-Point flow over a shrinking sheet in a micropolar fluid, Chemical Engineering Communications, 197, 1417-1427,(2010).
[9].              S.Nadeem, S.Abbasbandy, M.Hussain, Series solutions of boundary layer flow of a micropolar fluid near the stagnation point towards a shrinking sheet, Zeitschrift für Naturforschung A, 64, 575-582,(2009).
[10].            M.M.Rahman, Convective flows of micropolar fluids from radiate isothermal porous surfaces with viscous dissipation and Joule heating, Communications in Nonlinear Science and Numerical Simulation, 14, 3018-3030,(2009).
[11].            A.Ishak, Thermal boundary layer flow over a stretching sheet in a micropolar fluid with radiation effect, Meccanica, 45, 367-373,(2010).
[12].            M.M.Rashidi, S.A.Mohimanian pour, S.Abbasbandy, Analytic approximate solutions for heat transfer of a micropolar fluid through a porous medium with radiation, Communications in Nonlinear Science and Numerical Simulation, 16, 1874-1889,(2011).
[13].            K.Bhattacharyya, S.Mukhopadhyay, G.C.Layek, I.Pop, Effects of thermal radiation on micropolar fluid flow and heat transfer over a porous shrinking sheet, International Journal of Heat and Mass Transfer, 55, 2945-2952,(2012).
[14].            M.A.A.Mahmoud, S.E.Waheed, Variable fluid properties and thermal radiation effects on flow and heat transfer in micropolar fluid film past moving permeable infinite flat plate with slip velocity, Applied Mathematics and Mechanics, 33, 663-678,(2012).
[15].            M.Hussain, M.Ashraf, S.Nadeem, M.Khan, Radiation effects on the thermal boundary layer flow of a micropolar fluid towards a permeable stretching sheet, Journal of the Franklin Institute, 350, 194-210,(2013).
[16].            E.M.A.Elbashbeshy, Radiation effect on heat transfer over a stretching surface, Canadian Journal of Physics, 78, 1107-1112,(2000).
[17].            M.A.A.Mahmoud, S.E.Waheed, MHD flow and heat transfer of a micropolar fluid over a nonlinear stretching surface with variable surface heat flux and heat generation,the Canadian journal of chemical engineering, 89, 1408-1415,(2011).
[18].            M.A.A.Mahmoud, Thermal radiation effects on MHD flow of a micropolar fluid over a stretching surface with variable thermal conductivity, Physica A,  Statistical Mechanics and its Applications, 375, 401-410,(2007).
[19].            K.Das, Influence of thermophoresis and chemical reaction on MHD micropolar fluid flow with variable fluid properties, International Journal of Heat and Mass Transfer, 55, 7166-7174,(2012).
[20].            H.Kummerer, Similar laminar boundary layers in incompressible micropolar fluids, Rheologica Acta, 16, 261-265,(1977).
[21].            M.A.Hossain, M.K.Chowdhury, Mixed convection flow of micropolar fluid over an isothermal plate with variable spin gradient viscosity, Acta Mechanica, 131, 139-151,(1998).
[22].            K.K.Sankara, L.T.Watson, Micropolar flow past a stretching sheet, Journal of Applied Mathematics and Physics, 36, 845-853,(1985).
[23].            T.Y.Na, I.Pop, Boundary layer flow of a micropolar fluid due to a stretching wall, Archive of Applied Mechanics, 67, 229-236,(1997).
[24].            D.Philip, P.Chandra, Flow of Eringen fluid (simple microfluid) through an artery with mild stenosis, International journal of engineering science, 34, 87-99,(1996).
[25].            A.C.Eringen, Theory of micropolar fluids, Journal of Mathematics and Mechanics, 16, 1-18,(1965).
[26].            M.Q.Brewster, Thermal Radiative Transfer and properties, John Wiley and Sons, (1972).
[27].            J.Chen, C.Lian,J.D.Lee, Theory and simulation of micropolar fluid dynamics, Proceedings of the Institution of Mechanical Engineers, Part N,  Journal of Nanoengineering and Nanosystems, 224, 31-39,(2010).
[28].            S.K.Jena, M.N.Mathur, Similarity solutions for laminar free convection flow of a thermomicropolar fluid past a non-isothermal vertical flat plate, International Journal of Engineering Science, 19, 1431-1439,(1981).
[29].            G.S.Guram, A.C.Smith, Stagnation flow of micropolar fluids with strong and weak interactions, Computers & Mathematics with Applications, 6, 213-233,(1980).
[30].            G.Ahmadi, Self-similar solution of incompressible micropolar boundary layer flow over a semi-infinite plate, International Journal of Engineering Science, 14, 639-646,(1976).
[31].            J.Peddieson, An application of themicropolar fluid model to the calculation of turbulent shear flow, International Journal of Engineering Science, 10, 23-32,(1972).
[32].            G.Bugliarello, J.Sevilla, Velocity distribution and other characteristics of steady and pulsatile blood flow in fine glass tubes, Biorheology, 7, 85-107, (1970).
[33].            W.M.Kays, Convective heat and mass transfer,McGraw-Hill, New York, (1966).
[34].            M.Arunachalam, N.R.Rajappa, Thermal boundary layer in liquid metals with variable thermal conductivity, Applied Scientific Research, 34, 179-187,(1978).
[35].            D.Knezevic, V.Savic, Mathematical modeling of changing of dynamical viscosity, as a function of temperature and pressure, of mineral oils for hydraulic systems, Facta Universitatis (Series: Mechanical Engineering), 4, 27-34,(2006).
[36].            M.Yurusoy, M.Pakdemirli, Approximate analytical solutions for the flow of a third-grade fluid in pipe, International Journal of Non-Linear Mechanics, 37, 187-95,(2002).
[37].            J.X.Ling, A.Dybbs, Forced convection over a flat plate submersed in a porous medium: variable viscosity case, ASME, Paper 87-WA/HT-23, ASME winter annual meeting, Boston, Massachusetts, 13-18,(1987).
[38].            F.C.Lai, F.A.Kulacki, The effect of variable viscosity on convective heat transfer along a vertical surface in a saturated porous medium, International Journal of Heat and Mass Transfer, 33, 1028-1031,(1990).
[39].            K.V.Prasad, K.Vajravelu, P.S.Datti, The effects of variable fluid properties on the hydro-magnetic flow and heat transfer over a non-linearly stretching sheet, International Journal of Thermal Sciences, 49, 603-610,(2010).
[40].            L.J.Grubka, K.M.Bobba, Heat transfer characteristics of a continuous, stretching surface with variable temperature, ASME Journal of Heat Transfer, 107, 248-250, (1985).
[41].            M.E.Ali, Heat transfer characteristics of a continuous stretching surface, Heat and Mass Transfer, 29, 227-234,(1994).
[42].            C.H.Chen, Laminar mixed convection adjacent to vertical, continuously stretching sheets, Heat and Mass Transfer, 33, 471-476, (1998).

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History

  • Receive Date: 16 September 2015
  • Revise Date: 12 February 2016
  • Accept Date: 06 May 2016

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