MHD and Heat Transfer Analysis of Nanofluid Flow Past a Vertical Porous Plate
Author(s):
K. S. Arjun*, K. Rakesh
Affiliation(s):
Department of Mechanical Engineering, Indian Institute of Technology (Indian School of Mines), Dhanbad, India,
Cite this paper
K. S. Arjun, K. Rakesh, “MHD and Heat Transfer Analysis of Nanofluid Flow Past a Vertical Porous Plate”,Journal of Mechanical Engineering Research and Developments, vol. 40, no. 4, pp. 650-659, 2017. DOI: 10.7508/jmerd.2017.04.013
ABSTRACT: A numerical analysis is performed on the buoyancy and magnetic effects on a steady two-dimensional boundary layer flow of an electrically conducting incompressible Al2O3-water nanofluid past a convectively heated porous vertical plate with variable suction and no slip boundary condition using Ansys FLUENT 15.0. The effects of the solid volume fractions of nanoparticle, magnetic field strength (Hartmann number), buoyancy effect (Grashof number), suction/injection parameter, viscous dissipation parameter (Eckert number) and intensity of Newtonian heating (Biot number) on the dimensionless heat transfer rate (Frossling number) are discussed. Increasing solid volume fraction of alumina-water nanofluid and using low strength magnetic field enhances surface cooling effect compared to conventional base fluids. Suction parameter and buoyancy effect are found relatively better contributing parameters in enhancing heat transfer rates. The best heat transfer rate was noticed with Hartmann number of 10-15, nanofluid volume fraction of 0.2, Biot number of 0.12, Eckert number of 0.1, Grashof number of zero and suction parameter of one. Rate of heat transfer increases with increase in intensity of Newtonian heating, suction parameter and volume fraction of Al2O3 nanoparticles whereas heat transfer.
Keywords : Magneto Hydro Dynamics; Heat Transfer; Nanofluid; Vertical Porous Plate; Convective Heating; Computational Fluid Dynamics.
References
[1] R. Moreau, Magnetohydrodynamics. Dordrecht, Netherlands: Kluwer Academic Publishers, 1990.
[2] S.Y. Ibrahim and O.D. Makinde, “Chemically reacting MHD boundary layer flow of heat and mass transfer past a moving vertical plate with suction”, Scientific Research and Essays, vol. 5, no. 19, pp. 2875-2882, 2010.
[3] A.K. Singh, H.R. Gholami and V.M. Soundalgekar, “Transient free convection flow between two vertical parallel plates”, Heat and Mass Transfer, vol. 31, pp. 329-333, 1996.
[4] O.D. Makinde, “Free-convection flow with thermal radiation and mass transfer past a moving vertical porous plate”, International Communications in Heat and Mass Transfer, vol. 32, pp. 1411-1419, 2005.
[5] O.D. Makinde, B.I. Olajuwon and A.W. Gbolagade, “Adomian decomposition approach to a boundary layer flow with thermal radiation past a moving vertical porous plate”, International Journal of Applied Mathematics and Mechanics, vol. 3, no. 3, pp. 62-70, 2007.
[6] M.E. Ali, “Heat transfer characteristics of a continuous stretching surface”, Warme Stoffuberttragung, vol. 29, pp. 227-234, 1994.
[7] S.P.A. Devi and J. Andrews, “Laminar Boundary Layer Flow on a Nanofluid over a flat plate”, International Journal of Maths and Mechanics, vol. 7,no. 6, pp. 52-71, 2011.
[8] C. Popa, G. Polidori, A. Arfaoui and S. Fohanno, “Heat and Mass Transfer in External Boundary Layer Flows using Nanofluids”, Heat and Mass Transfer – Modeling and Simulation, vol. 5, pp. 95-116, 2011.
[9] O.D. Makinde and A. Aziz, “MHD mixed convection from a vertical plate embedded in a porous medium with a convective boundary condition”, Int J Therm Sci., vol. 49, pp. 1813-1820, 2010.
[10] A. Ishak, “Similarity solutions for flow and heat transfer over a permeable surface with convective boundary condition”, Appl Math Comput., vol. 217, pp. 837-842, 2010.
[11] S.S. Nourazar, H.M. Matin and M. Simiari, “The HPM Applied to MHD Nanofluid Flow over a Horizontal Stretching Plate”, Journal of Applied Mathematics., vol. 17, pp. 1-18, 2011.
[12] M.A.A. Hamad, I. Pop and A.I. Ismail, “Magnetic field effects on free convection flow of a nanofluid past a vertical semi-infinite flat plate”, Nonlinear Analysis: Real World Applications, vol. 12, pp. 1338–1346, 2011.
[13] M.A.A. Hamad, “Analytical solution of natural convection flow of a nanofluid over a linearly stretching sheet in the presence of magnetic field”, International Communications in Heat and Mass Transfer, vol. 38, pp. 487–492, 2011.
[14] B. Ghasemi, S.M. Aminossadati and A. Raisi, “Magnetic field effect on natural convection in a nanofluid-filled square enclosure”, International Journal of Thermal Sciences, vol. 50, pp. 1748-1756, 2011.
[15] A.Y. Ghaly and M.A. Seddeek, “Chebyshev finite difference method for the effects of chemical reaction, heat and mass transfer on laminar flow along a semi-infinite horizontal plate with temperature dependent viscosity”, Chaos Solitons & Fractals, vol. 19, no. 1, pp. 61-70, 2004.
[16] O.D. Makinde and A. Ogulu, “The effect of thermal radiation on the heat and mass transfer flow of a variable viscosity fluid past a vertical porous plate permeated by a transverse magnetic field”, Chem. Eng. Commun., vol. 195, no. 12, pp. 1575-1584, 2008.
[17] A. Aziz, “A similarity solution for laminar thermal boundary layer over a flat plate with a convective surface boundary condition”, Commun Nonlinear Sci Numer Simul, vol. 14, pp. 1064-1068, 2009.
[18] P.R. Sharma and U. Mishra, “Effects of mass transfer on unsteady MHD flow and heat transfer past an infinite porous vertical moving plate”, Ind. Jour. Theo. Phys., vol. 50, pp. 109-116, 2002.
[19] K. Venkateswarlu and J.A. Rao, “Viscous Fluid Past a Vertical Plate under Oscillatory Suction Velocity”, Journal of The Institution of Engineers (India): Series C., vol. 85, pp. 20, 2005.
[20] H. Poonia and R.C. Chaudhary, “MHD free convection and mass transfer flow over an infinite vertical porous plate with viscous dissipation”, Theo. Appl. Mech., vol. 37, no. 4, pp. 263 – 287, 2010.
[21] K. Bhattacharyya, “Boundary layer flow with diffusion and first order chemical reaction over a porous flat plate subject to suction/injection and with variable wall concentration”, Chem. Eng. Res. Bull., vol. 15, pp. 6–11, 2011.
[22] M.J. Uddin, M.A.A. Hamad and A.I.M. Ismail, “Investigation of heat mass transfer for combined convective slips flow: a lie group analysis”, Sains Malaysiana, vol. 41, no. 9, pp. 1139-1148, 2012.
[23] D. Kumar, M.B. Sharma and B.S. Yadav, “A study on MHD flow and heat transfer along a porous flat plate with mass transfer”, Ultra Sci., vol. 24B, no. 2, pp. 327–334, 2012.
[24] K. Gangadhar, N.B. Reddy and P.K. Kameswaran, “Similarity solution of hydro magnetic heat and mass transfer over a vertical plate with a convective surface boundary condition and chemical reaction”, Int. J. Nonlinear Sci., vol. 13, no. 3, pp. 298–307, 2012.
[25] P. Singh and M. Kumar, “Mass transfer in MHD flow of alumina water nanofluid over a flat plate under slip conditions”, Alexandria Engineering Journal, vol. 54, no. 3, pp. 383-387, 2015.
[26] O.D. Makinde, “Similarity solution of hydromagnetic heat and mass transfer over a vertical plate with a convective surface boundary condition”, International Journal of the Physical Sciences, vol. 5, no. 6, pp. 700-710, 2010.
[27] O.D. Makinde, “Computational Modelling of MHD Unsteady Flow and Heat Transfer Toward a Flat Plate with Navier Slip and Newtonian Heating”, Brazilian Journal of Chemical Engineering, vol. 29, no. 1, pp. 159-166, 2012.
[28] M.T. Matthews and J.M. Hill, “A note on the boundary layer equations with linear slip boundary condition”, Applied Mathematics Letters, vol. 21, pp. 810-813, 2008.
[29] R. Kumar and K. Chand, “Effect of slip conditions and hall current on unsteady MHD flow of a viscoelastic fluid past an infinite vertical porous plate through porous medium”, International Journal of Engineering Science and Technology, vol. 3, no. 4, pp. 3124-3123, 2011.
[30] B.R. Rout, S. K. Parida and S. Panda, “MHD heat and mass transfer of chemical reaction fluid flow over a moving vertical plate in presence of heat source with convective surface boundary condition”, Int J Chem Eng., vol. 2013, pp. 1-10, 2013.
[31] S.M. Ibrahim and N.B. Reddy, “Similarity solution of heat and mass transfer for natural convection over a moving vertical plate with internal heat generation and a convective boundary condition in the presence of thermal radiation, viscous dissipation and chemical radiation”, ISRN Thermodyn., vol. 2013, pp. 1-10, 2013.
[32] A.B. Kasaeian and S. Nasiri, “Convection Heat Transfer Modeling of Nano- fluid Tio Using Different Viscosity Theories”, Int. J. Nanosci. Nanotechnol., vol. 11, no. 1, pp. 45-51, 2015.
[33] C.V. Popa, A.B. Kasaeian, S. Nasiri, A. Korichi and G. Polidori, “Natural Convection Heat and Mass Transfer Modeling for Cu/Water and CuO/Water Nanofluids”, Advances in mechanical engineering, pp. 1-7, 2013.
[34] A.K. Tiwari, P. Ghosh and J. Sarkar, “Performance comparison of the plate heat exchanger using different nanofluids”, Experimental Thermal and Fluid Science, vol. 49, pp. 141-151, 2013.
[35] S.P.A. Devi and T.E. Priya, “MHD Slip Flow and Convective Heat Transfer of Nanofluids over a Permeable Stretching Surface”, International Journal of Science and Research, vol. 4, no, 4, pp. 138-147, 2015.
[36] M. Sheikholeslami, M.G. Bandpy and S. Soleimani, “Two phase simulation of nanofluid flow and heat transfer using heatline analysis”, International Communications in Heat and Mass Transfer, vol. 43, pp. 73-81, 2013.
[37] A. Malvandi, F. Hedayati and D.D. Ganji, “Slip effects on unsteady stagnation point flow of a nanofluid over a stretching sheet”, Powder Technology, vol. 253, pp. 377–384, 2014.
[38] P. Singh and M. Kumar, “MHD Slip Flow of Alumina Water Nanofluid over a Flat Plate”, International Journal of Engineering & Technical Research, vol. 2, pp. 142-147, 2014.
[39] W.N. Mutuku-Njane and O.D. Makinde, “MHD Nanofluids Flow over a Permeable Vertical Plate with Convective heating”, Journal of Computational and Theoretical Nanoscience, vol. 11,no. 3, pp. 667-675, 2014.
[40] Ansys, ANSYS Fluent 15.0 Theory Guide. Canonsburg, PA, USA: ANSYS Inc., pp. 1-780, 2013.
[41] A.V. Kuznetsov and D.A.L. Nield, “Natural convective boundary- layer flow of a nanofluid past a vertical plate”, International Journal of Thermal Sciences, vol. 49, pp. 243–247, 2010.
O.D. Makinde and A. Aziz, “Boundary layer flow of a nanofluid past a stretching sheet with a convective boundary condition”, Int. J. Thermal Sciences, vol. 50, pp. 1326-1332, 2011
[2] S.Y. Ibrahim and O.D. Makinde, “Chemically reacting MHD boundary layer flow of heat and mass transfer past a moving vertical plate with suction”, Scientific Research and Essays, vol. 5, no. 19, pp. 2875-2882, 2010.
[3] A.K. Singh, H.R. Gholami and V.M. Soundalgekar, “Transient free convection flow between two vertical parallel plates”, Heat and Mass Transfer, vol. 31, pp. 329-333, 1996.
[4] O.D. Makinde, “Free-convection flow with thermal radiation and mass transfer past a moving vertical porous plate”, International Communications in Heat and Mass Transfer, vol. 32, pp. 1411-1419, 2005.
[5] O.D. Makinde, B.I. Olajuwon and A.W. Gbolagade, “Adomian decomposition approach to a boundary layer flow with thermal radiation past a moving vertical porous plate”, International Journal of Applied Mathematics and Mechanics, vol. 3, no. 3, pp. 62-70, 2007.
[6] M.E. Ali, “Heat transfer characteristics of a continuous stretching surface”, Warme Stoffuberttragung, vol. 29, pp. 227-234, 1994.
[7] S.P.A. Devi and J. Andrews, “Laminar Boundary Layer Flow on a Nanofluid over a flat plate”, International Journal of Maths and Mechanics, vol. 7,no. 6, pp. 52-71, 2011.
[8] C. Popa, G. Polidori, A. Arfaoui and S. Fohanno, “Heat and Mass Transfer in External Boundary Layer Flows using Nanofluids”, Heat and Mass Transfer – Modeling and Simulation, vol. 5, pp. 95-116, 2011.
[9] O.D. Makinde and A. Aziz, “MHD mixed convection from a vertical plate embedded in a porous medium with a convective boundary condition”, Int J Therm Sci., vol. 49, pp. 1813-1820, 2010.
[10] A. Ishak, “Similarity solutions for flow and heat transfer over a permeable surface with convective boundary condition”, Appl Math Comput., vol. 217, pp. 837-842, 2010.
[11] S.S. Nourazar, H.M. Matin and M. Simiari, “The HPM Applied to MHD Nanofluid Flow over a Horizontal Stretching Plate”, Journal of Applied Mathematics., vol. 17, pp. 1-18, 2011.
[12] M.A.A. Hamad, I. Pop and A.I. Ismail, “Magnetic field effects on free convection flow of a nanofluid past a vertical semi-infinite flat plate”, Nonlinear Analysis: Real World Applications, vol. 12, pp. 1338–1346, 2011.
[13] M.A.A. Hamad, “Analytical solution of natural convection flow of a nanofluid over a linearly stretching sheet in the presence of magnetic field”, International Communications in Heat and Mass Transfer, vol. 38, pp. 487–492, 2011.
[14] B. Ghasemi, S.M. Aminossadati and A. Raisi, “Magnetic field effect on natural convection in a nanofluid-filled square enclosure”, International Journal of Thermal Sciences, vol. 50, pp. 1748-1756, 2011.
[15] A.Y. Ghaly and M.A. Seddeek, “Chebyshev finite difference method for the effects of chemical reaction, heat and mass transfer on laminar flow along a semi-infinite horizontal plate with temperature dependent viscosity”, Chaos Solitons & Fractals, vol. 19, no. 1, pp. 61-70, 2004.
[16] O.D. Makinde and A. Ogulu, “The effect of thermal radiation on the heat and mass transfer flow of a variable viscosity fluid past a vertical porous plate permeated by a transverse magnetic field”, Chem. Eng. Commun., vol. 195, no. 12, pp. 1575-1584, 2008.
[17] A. Aziz, “A similarity solution for laminar thermal boundary layer over a flat plate with a convective surface boundary condition”, Commun Nonlinear Sci Numer Simul, vol. 14, pp. 1064-1068, 2009.
[18] P.R. Sharma and U. Mishra, “Effects of mass transfer on unsteady MHD flow and heat transfer past an infinite porous vertical moving plate”, Ind. Jour. Theo. Phys., vol. 50, pp. 109-116, 2002.
[19] K. Venkateswarlu and J.A. Rao, “Viscous Fluid Past a Vertical Plate under Oscillatory Suction Velocity”, Journal of The Institution of Engineers (India): Series C., vol. 85, pp. 20, 2005.
[20] H. Poonia and R.C. Chaudhary, “MHD free convection and mass transfer flow over an infinite vertical porous plate with viscous dissipation”, Theo. Appl. Mech., vol. 37, no. 4, pp. 263 – 287, 2010.
[21] K. Bhattacharyya, “Boundary layer flow with diffusion and first order chemical reaction over a porous flat plate subject to suction/injection and with variable wall concentration”, Chem. Eng. Res. Bull., vol. 15, pp. 6–11, 2011.
[22] M.J. Uddin, M.A.A. Hamad and A.I.M. Ismail, “Investigation of heat mass transfer for combined convective slips flow: a lie group analysis”, Sains Malaysiana, vol. 41, no. 9, pp. 1139-1148, 2012.
[23] D. Kumar, M.B. Sharma and B.S. Yadav, “A study on MHD flow and heat transfer along a porous flat plate with mass transfer”, Ultra Sci., vol. 24B, no. 2, pp. 327–334, 2012.
[24] K. Gangadhar, N.B. Reddy and P.K. Kameswaran, “Similarity solution of hydro magnetic heat and mass transfer over a vertical plate with a convective surface boundary condition and chemical reaction”, Int. J. Nonlinear Sci., vol. 13, no. 3, pp. 298–307, 2012.
[25] P. Singh and M. Kumar, “Mass transfer in MHD flow of alumina water nanofluid over a flat plate under slip conditions”, Alexandria Engineering Journal, vol. 54, no. 3, pp. 383-387, 2015.
[26] O.D. Makinde, “Similarity solution of hydromagnetic heat and mass transfer over a vertical plate with a convective surface boundary condition”, International Journal of the Physical Sciences, vol. 5, no. 6, pp. 700-710, 2010.
[27] O.D. Makinde, “Computational Modelling of MHD Unsteady Flow and Heat Transfer Toward a Flat Plate with Navier Slip and Newtonian Heating”, Brazilian Journal of Chemical Engineering, vol. 29, no. 1, pp. 159-166, 2012.
[28] M.T. Matthews and J.M. Hill, “A note on the boundary layer equations with linear slip boundary condition”, Applied Mathematics Letters, vol. 21, pp. 810-813, 2008.
[29] R. Kumar and K. Chand, “Effect of slip conditions and hall current on unsteady MHD flow of a viscoelastic fluid past an infinite vertical porous plate through porous medium”, International Journal of Engineering Science and Technology, vol. 3, no. 4, pp. 3124-3123, 2011.
[30] B.R. Rout, S. K. Parida and S. Panda, “MHD heat and mass transfer of chemical reaction fluid flow over a moving vertical plate in presence of heat source with convective surface boundary condition”, Int J Chem Eng., vol. 2013, pp. 1-10, 2013.
[31] S.M. Ibrahim and N.B. Reddy, “Similarity solution of heat and mass transfer for natural convection over a moving vertical plate with internal heat generation and a convective boundary condition in the presence of thermal radiation, viscous dissipation and chemical radiation”, ISRN Thermodyn., vol. 2013, pp. 1-10, 2013.
[32] A.B. Kasaeian and S. Nasiri, “Convection Heat Transfer Modeling of Nano- fluid Tio Using Different Viscosity Theories”, Int. J. Nanosci. Nanotechnol., vol. 11, no. 1, pp. 45-51, 2015.
[33] C.V. Popa, A.B. Kasaeian, S. Nasiri, A. Korichi and G. Polidori, “Natural Convection Heat and Mass Transfer Modeling for Cu/Water and CuO/Water Nanofluids”, Advances in mechanical engineering, pp. 1-7, 2013.
[34] A.K. Tiwari, P. Ghosh and J. Sarkar, “Performance comparison of the plate heat exchanger using different nanofluids”, Experimental Thermal and Fluid Science, vol. 49, pp. 141-151, 2013.
[35] S.P.A. Devi and T.E. Priya, “MHD Slip Flow and Convective Heat Transfer of Nanofluids over a Permeable Stretching Surface”, International Journal of Science and Research, vol. 4, no, 4, pp. 138-147, 2015.
[36] M. Sheikholeslami, M.G. Bandpy and S. Soleimani, “Two phase simulation of nanofluid flow and heat transfer using heatline analysis”, International Communications in Heat and Mass Transfer, vol. 43, pp. 73-81, 2013.
[37] A. Malvandi, F. Hedayati and D.D. Ganji, “Slip effects on unsteady stagnation point flow of a nanofluid over a stretching sheet”, Powder Technology, vol. 253, pp. 377–384, 2014.
[38] P. Singh and M. Kumar, “MHD Slip Flow of Alumina Water Nanofluid over a Flat Plate”, International Journal of Engineering & Technical Research, vol. 2, pp. 142-147, 2014.
[39] W.N. Mutuku-Njane and O.D. Makinde, “MHD Nanofluids Flow over a Permeable Vertical Plate with Convective heating”, Journal of Computational and Theoretical Nanoscience, vol. 11,no. 3, pp. 667-675, 2014.
[40] Ansys, ANSYS Fluent 15.0 Theory Guide. Canonsburg, PA, USA: ANSYS Inc., pp. 1-780, 2013.
[41] A.V. Kuznetsov and D.A.L. Nield, “Natural convective boundary- layer flow of a nanofluid past a vertical plate”, International Journal of Thermal Sciences, vol. 49, pp. 243–247, 2010.
O.D. Makinde and A. Aziz, “Boundary layer flow of a nanofluid past a stretching sheet with a convective boundary condition”, Int. J. Thermal Sciences, vol. 50, pp. 1326-1332, 2011