This paper investigates combined heat and mass transfer by mixed magneto-convective flow of an electrically conducting flow along a moving radiating vertical flat plate with hydrodynamic slip and thermal convective boundary conditions. The governing transport equations are converted into a system of coupled nonlinear ordinary differential equations with prescribed boundary conditions using similarity variables developed by Lie group theory. The transformed nondimensional boundary value problem is then solved numerically with MAPLE13 quadrature. Excellent correlation with previous nonmagnetic, no-slip studies is achieved. Surface shear stress function and local Nusselt number (heat transfer gradient at the wall) are increased with Richardson number, whereas local Sherwood number is found to initially decrease then subsequently increase. The “thermally thick” scenario (Biot number > 0.1) is investigated and increasing Biot number is observed to enhance shear stress function (skin friction), local Nusselt number, and local Sherwood number. Increasing thermal radiation flux increases thermal boundary layer thickness as does increasing the magnetic field effect. Increasing hydrodynamic slip parameter reduces skin friction but enhances local Nusselt and Sherwood numbers. The study has applications in high-temperature polymeric synthesis and magnetic field flow control.
This is a preview of subscription content, access via your institution.
Buy single article
Instant access to the full article PDF.
Price includes VAT (USA)
Tax calculation will be finalised during checkout.
Altan, T., Oh, S., and Gegel, H., Metal Forming Fundamentals and Applications, Metals Park, Ohio: American Society of Metals, 1979.
Kalpakjian, S. and Schmid, S., Manufacturing Engineering and Technology, Massachusetts: Addison Wesley, Reading, 1989.
Szekely, J., Fluid Flow Phenomena in Metals Processing, New York: Academic Press, 1979.
Fisher, E.G., Extrusion of Plastics, New York: Wiley, 1976.
Poulikakos, D., Transport Phenomena in Material Processing, Advances in Heat Transfer, New York: Academic Press, 1996, vol. 18.
Jaluria, Y., Thermal Processing of Materials: From Basic Research to Engineering, ASME J. Heat Transfer, 2003, vol. 125, pp. 957–979.
Sakiadis, B.C., Boundary Layer Behavior on Continuous Solid Surfaces, Pt. II, The Boundary Layer on a Continuous Flat Surface, AIChE J., 1961, vol. 7, pp. 221–225.
Jaluria, Y., Transport from Continuously Moving Materials Undergoing Thermal Processing, Ann. Rev. Heat Transfer, 1992, vol. 4, pp. 187–245.
Grupka, J.L. and Bobba, K.M., Heat Transfer Characteristics of a Continuous Stretching Surface with Variable Temperature, ASME J. Heat Transfer, 1985, vol. 107, pp. 248–250.
Karwe, M.V. and Jaluria, Y., Experimental Investigation of Thermal Transport from a Heated Moving Plate, Int. J. Heat Mass Transfer, 1992, vol. 35, pp. 493–511.
Bég, O.A., Zueco, J., and Takhar, H.S., Laminar Free Convection from a Continuously-Moving Vertical Surface in Thermally-Stratified Non-Darcian High-Porosity Medium: Network Numerical Study, Int. Comm. Heat Mass Transfer, 2008, vol. 35, pp. 810–816.
Ferdows, M., Uddin, J., and Afify, A.A., Scaling Group Transformation for MHD Boundary Layer Free Convective Heat and Mass Transfer Flow past a Convectively Heated Nonlinear Radiating Stretching Sheet, Int. J. Heat Mass Transfer, 2013, vol. 56, pp. 181–187.
Fang, F., Further Study on a Moving-Wall Boundary-Layer Problem with Mass Transfer, Acta Mech., 2003, vol. 163, pp. 183–188.
Weidman, P.D., Kubitschek, D.G., and Davis, A.M.J., The Effect of a Transpiration on Self-Similar Boundary Layer Flowover Moving Surfaces, Int. J. Eng. Sci., 2006, vol. 44, pp. 730–737.
Zueco, J. and Bég, O.A., Network Numerical Analysis of Hydromagnetic Squeeze Film Flow Dynamics between Two Parallel Rotating Disks with Induced Magnetic Field Effects, Tribology Int., 2010, vol. 43, pp. 532–543.
Rashidi, M.M., Keimanesh, M., Bég, O.A., and Hung, T.K., Magnetohydrodynamic Biorheological Transport Phenomena in a Porous Medium: A Simulation of Magnetic Blood Flow Control and Filtration, Int. J. Num. Meth. Biomed. Eng., 2001, vol. 27, pp. 805–821.
Tripathi, D. and Bég, O.A., Magnetohydrodynamic Peristaltic Flow of a Couple Stress Fluid through Coaxial Channels Containing a Porous Medium, J. Mech. Med. Biol., 2012, vol. 12, pp. 1250088.1–1250088.20.
Shahidian, A., Ghassemi, M., Khorasanizade, S., Abdollahzade, M., and Ahmadi, G., Flow Analysis of Non-Newtonian Blood in a Magnetohydrodynamic Pump, IEEE Trans. Magnet., 2009, vol. 45, pp. 2667–2670.
Rana, P., Bhargava, R., and Bég, O.A., Finite Element Simulation of Unsteady Magneto-Hydrodynamic Transport Phenomena on a Stretching Sheet in a Rotating Nanofluid, Proc. IMechE, Pt. N, J. Nanoeng. Nanosyst., 2012, DOI: 10.1177/1740349912463312.
Zueco, J., Bég, O.A., and Lopez-Ochoa, L.M., Non-Linear Transient Hydromagnetic Partially Ionized Dissipative Couette Flow in a Non-Darcian Porous Medium Channel with Hall, Ion Slip and Joule Heating Effects, Prog. Comp. Fluid Dynam., 2001, vol. 11, pp. 116–129.
Bég, O.A., Bakier, A.Y., Prasad, V.R., and Ghosh, S.K., Nonsimilar, Laminar, Steady, Electrically-Conducting Forced Convection Liquid Metal Boundary Layer Flow with Induced Magnetic Field Effects, Int. J. Therm. Sci., 2009, vol. 48, pp. 1596–1606.
Ghosh, S.K., Bég, O.A., Zueco, J., and Prasad, V.R., Transient Hydromagnetic Flow in a Rotating Channel Permeated by an Inclined Magnetic Field with Magnetic Induction and Maxwell Displacement Current Effects, ZAMP, J. Appl. Math. Phys., 20010, vol. 61, pp. 147–169.
Zueco, J., Bég, O.A., Takhar, H.S., and Prasad, V.R., Thermophoretic Hydromagnetic Dissipative Heat and Mass Transfer with Lateral Mass Flux, Heat Source, Ohmic Heating and Thermal Conductivity Effects: Network Simulation Numerical Study, Appl. Therm. Eng., 2009, vol. 29, pp. 2808–2815.
Chamkha, A.J. and Aly, A.M., MHD Free Convection Flow of a Nanofluid past a Vertical Plate in the Presence of Heat Generation or Absorption Effects, Chem. Eng. Comm., 2011, vol. 198, pp. 425–441.
Uddin, M.J., Khan, W.A., and Ismail, A.I., MHD Free Convective Boundary Layer Flow of a Nanofluid past a Flat Vertical Plate with Newtonian Heating Boundary Condition, PLoS One, 2012, vol. 7, no. 11, e49499.
Bég, O.A., Bakier, A.Y., and Prasad, V.R., Numerical Study of Free Convection Magnetohydrodynamic Heat and Mass Transfer from a Stretching Surface to a Saturated Porous Medium with Soret and Dufour Effects, Comp. Mat. Sci., 2009, vol. 46, pp. 57–65.
Sharma, R., Bhargava, R., and Singh, I.V., Combined Effect of Magnetic Field and Heat Absorption on Unsteady Free Convection and Heat Transfer Flow in a Micropolar Fluid past a Semi-Infinite Moving Plate with Viscous Dissipation Using Element Free Galerkin Method, Appl. Math. Comput., 2010, vol. 217, pp. 308–321.
Bararnia, H., Ghasemi, E., Soleimani, S., Ghotbi, A.R., and Ganji, D.D., Solution of the Falkner-Skan Wedge Flow by HPM-Pade’Method, Adv. Eng. Soft., 2012, vol. 43, pp. 44–52.
Noor, N.F., Abbasbandy, S., and Hashim, I., Heat and Mass Transfer of Thermophoretic MHD Flow over an Inclined Radiate Isothermal Permeable Surface in the Presence of Heat Source/Sink, Int. J. Heat Mass Transfer, 2012, vol. 55, pp. 2122–2128.
Gupta, D., Kumar, L., Bég, O.A., and Singh, B., Finite Element Simulation of Mixed Convection Flow of Micropolar Fluid over a Shrinking Sheet with Thermal Radiation, Proc. IChemE-Part E, J. Process. Mech. Eng., 2012.
Cortell, R., Suction, Viscous Heating and Thermal Radiation Effects on the Flow and Heat Transfer of a Power-Law Fluid past an Infinite Porous Plate, Proc. IChemE, Chem. Eng. Res. Design, 2011, vol. 89, pp. 85–93.
Bhargava, R., Sharma, R., and Bég, O.A., A Numerical Solution for the Effect of Radiation on Micropolar Flow and Heat Transfer past a Horizontal Stretching Sheet through a Porous Medium, 7th SWEAS Int. Conf. on Heat Mass Transfer (HMT’10), University of Cambridge, UK, 2010, pp. 88–96.
Thompson, P.A. and Trojan, S.M., A General Boundary Condition for Liquid Flow at Solid Surfaces, Nature, 1997, p. 389.
Nguyen, N.T. and Wereley, S.T., Fundamentals and Applications of Microfluidics, London: Artech House, 2009.
Khare, R., Keblinski, P., and Yethiraj, A., Molecular Dynamics Simulations of Heat and Momentum Transfer at a Solid-Fluid Interface: Relationship between Thermal and Velocity Slip, Int. J. Heat Mass Transfer, 2006, vol. 49, pp. 3401–3407.
Yazdi, M.H., Abdullah, S., Hashim, I., and Sopian, K., Slip MHD Liquid Flow and Heat Transfer over Non-Linear Permeable Stretching Surface with Chemical Reaction, Int. J. Heat Mass Transfer, 2011, vol. 54, pp. 3214–3225.
Bég, O.A., Zueco, J., and López-Ochoa, L.M., Network Numerical Analysis of Optically Thick Hydromagnetic Slip Flow from a Porous Spinning Disk with Radiation Flux, Variable Thermophysical Properties and Surface Injection Effects, Chem. Eng. Commun., 2010, vol. 198, pp. 360–384.
Kim, B.H., Beskok, A., and Cagin, T., Viscous Heating in Nanoscale Shear Driven Liquid Flows, Microfluid Nanofluid, 2010, vol. 9, pp. 1–40.
Martin, M.J. and Boyd, I.D., Momentumand Heat Transfer in Laminar Boundary Layer with Slip Flow, AIAA J. Thermophys. Heat Transfer, 2006, vol. 20, pp. 710–719.
Tripathi, D., Bég, O.A., and Sosa, J.L., Homotopy Semi-Numerical Simulation of Peristaltic Flow of Generalized Oldroyd-B Fluids with Slip Effects, Comp. Meth. Biomech. Biomed. Eng., 2012, DOI: 10.1080/10255842.2012.688109.
Mattews, M.T. and Hill, J.M., Micro/Nano Thermal Boundary Layer Equations with Slip-Creep-Jump Boundary Conditions, IMA J. Appl. Math., 2007, vol. 72, pp. 894–911.
Prasad, V.R., Rao, A.S., Reddy, N.B., Vasu, B., and Bég, O.A., Modeling Laminar Transport Phenomena in a Casson Rheological Fluid from a Horizontal Circular Cylinder with Partial Slip, Proc. IMechE, Part E, J. Process. Mech. Eng., 2012, DOI: 10.1177/0954408912466350.
Aziz, A., A Similarity Solution for Laminar Thermal Boundary Layer over Flat Plate with Convective Surface Boundary Condition, Comm. Non. Sci. Num. Sim., 2009, vol. 14, pp. 1064–1068.
Ishak, A., Similarity Solutions for Flow and Heat Transfer over Permeable Surface with Convective Boundary Conditions, Appl. Math. Comp., 2010, vol. 217, pp. 837–842.
Makinde, O.D. and Olanrewaju, P.O., Buoyancy Effects on the Thermal Boundary Layer over a Vertical Flat Plate with a Convective Surface Boundary Condition, ASME J. Fluids Eng., 2010, vol. 132, pp. 044502-1–044502-4.
Aziz, A., and Khan, W.A., Natural Convective Boundary Layer Flow of a Nanofluid past a Convectively Heated Vertical Plate, Int. J. Therm. Sci., 2012, vol. 52, pp. 83–90.
Nandeppanavar, M.M., Vajravelu, K., Abel, M.S., and Siddalingappa, M.N., Second-Order Slip Flow and Heat Transfer over a Stretching Sheet with Non-Linear Navier Boundary Condition, Int. J. Therm. Sci., 2012, vol. 58, pp. 143–150.
Bejan, A., Convection Heat Transfer, 3d ed., New York: Wiley, 2004.
Tripathi, D. and Bég, O.A., A Numerical Study of Oscillating Peristaltic Flow of Generalized Maxwell Viscoelastic Fluids through a Porous Medium, Transp. Porous Media, 2012, vol. 95, pp. 337–348.
About this article
Cite this article
Bég, O.A., Uddin, M.J., Rashidi, M.M. et al. Double-diffusive radiative magnetic mixed convective slip flow with Biot and Richardson number effects. J. Engin. Thermophys. 23, 79–97 (2014). https://doi.org/10.1134/S1810232814020015
- Skin Friction
- Richardson Number
- Sherwood Number
- Local Nusselt Number
- Biot Number