Thermal convection of MHD Blasius and Sakiadis flow with thermal convective conditions and variable properties

A theoretical study on the effect of magnetohydrodynamic field on the classical Blasius and Sakiadis flows of heat transfer characteristics with variable conditions and variable properties are studied in this paper. Hydromagnetic flows and heat transfer in porous media have been considered extensively in recent years due to their occurrence in several engineering processes such as compact heat exchangers, metallurgy, casting, filtration of liquid metals, cooling of nuclear reactors and fusion control. The governing partial differential equations are converted into ordinary differential equations using the suitable similarity transformations. The transformed boundary layer equations like momentum and energy equations are solved numerically by using Runge–Kutta method. The effect of governing physical parameters over the velocity and temperature distributions is demonstrated graphically. Moreover, the local friction factor coefficient and rate of heat transfer in terms of Nusselt number are computed and discussed through tables. We validated the present solutions with already existing studies under limited cases. It is found that the thermal buoyancy parameter enhances the velocity depreciates the temperature field for both the Sakiadis and Blasius flow cases. The influence of Biot number increases skin friction coefficient and local Nusselt number for both Sakiadis and Blasius flow cases.The rate of heat transfer for temperature ratio parameter is high in Blasius flow case when compared with Sakiadis flow case.

[1]  L. Crane.  Flow past a stretching plate , 1970 .

[2]  R. Cortell.  Effects of viscous dissipation and radiation on the thermal boundary layer over a nonlinearly stretching sheet , 2008 .

[3]  Khalil Khanafer,et al.  The effect of radiation on free convection flow of fluid with variable viscosity from a porous vertical plate , 2001 .

[4]  R. J. Goldstein,et al.  Flow and heat transfer in the boundary layer on a continuous moving surface , 1967 .

[5]  Chien-Hsin Chen,et al.  Combined heat and mass transfer in MHD free convection from a vertical surface with Ohmic heating and viscous dissipation , 2004 .

[6]  C. Ng,et al.  Unsteady convective boundary layer flow of a viscous fluid at a vertical surface with variable fluid properties , 2013 .

[7]  P. Olanrewaju,et al.  Radiation and viscous dissipation effects for the Blasius and Sakiadis flows with a convective surface boundary condition , 2011 .

[8]  Ioan Pop,et al.  Boundary layer flow and heat transfer over an unsteady stretching vertical surface , 2009 .

[9]  Bor-Lih Kuo.  Thermal boundary-layer problems in a semi-infinite flat plate by the differential transformation method , 2004, Appl. Math. Comput..

[10]  V. G. Fox,et al.  Heat and Mass Transfer on Moving Continuous Flat Plate with Suction or Injection , 1966 .

[11]  Abdul Aziz,et al.  A similarity solution for laminar thermal boundary layer over a flat plate with a convective surface boundary condition , 2009 .

[12]  M. A. Alim,et al.  The effect of radiation on free convection from a porous vertical plate , 1999 .

[13]  M. Ali,et al.  Heat transfer characteristics of a continuous stretching surface , 1994 .

[14]  P. S. Gupta,et al.  Heat and mass transfer on a stretching sheet with suction or blowing , 1977 .

[15]  L. J. Grubka,et al.  Heat Transfer Characteristics of a Continuous, Stretching Surface With Variable Temperature , 1985 .

[16]  B. C. Sakiadis.  Boundary‐layer behavior on continuous solid surfaces: II. The boundary layer on a continuous flat surface , 1961 .

[17]  M. J. Uddin,et al.  Energy conversion under conjugate conduction, magneto-convection, diffusion and nonlinear radiation over a non-linearly stretching sheet with slip and multiple convective boundary conditions , 2016 .

[18]  Ali J. Chamkha.  Unsteady MHD convective heat and mass transfer past a semi-infinite vertical permeable moving plate with heat absorption , 2004 .

[19]  M. J. Uddin,et al.  Blasius and Sakiadis Slip Flows of Nanofluid with Radiation Effects , 2016 .

[20]  Rafael Cortell Bataller,et al.  Effects of heat source/sink, radiation and work done by deformation on flow and heat transfer of a viscoelastic fluid over a stretching sheet , 2007, Comput. Math. Appl..

[21]  Harmindar S. Takhar,et al.  Radiation effect on mixed convection along a vertical plate with uniform surface temperature , 1996 .

[22]  P. Suriyakumar,et al.  Effect of magnetic field on Blasius and Sakiadis flow of nanofluids past an inclined plate , 2017 .

[23]  M. J. Uddin,et al.  Radiation effects on heat and mass transfer in MHD stagnation-point flow over a permeable flat plate with thermal convective surface boundary condition, temperature dependent viscosity and thermal conductivity , 2012 .

[24]  C. Raju,et al.  A comparative study on heat and mass transfer of the Blasius and Falkner-Skan flow of a bio-convective Casson fluid past a wedge , 2016 .

[25]  A. Raptis,et al.  Heat transfer of a micropolar fluid by the presence of radiation , 1996 .

[26]  S. Mukhopadhyay.  Unsteady boundary layer flow and heat transfer past a porous stretching sheet in presence of variable viscosity and thermal diffusivity , 2009 .

[27]  Rafael Cortell Bataller,et al.  Radiation effects for the Blasius and Sakiadis flows with a convective surface boundary condition , 2008, Appl. Math. Comput..

[28]  Shanshan Yao,et al.  Heat transfer of a generalized stretching/shrinking wall problem with convective boundary conditions , 2011 .

[29]  A. Raptis,et al.  Viscoelastic Flow by the Presence of Radiation , 1998 .

[30]  O. Anwar Bég,et al.  Hydromagnetic transport phenomena from a stretching or shrinking nonlinear nanomaterial sheet with Navier slip and convective heating: A model for bio-nano-materials processing , 2014 .

[31]  W. Khan,et al.  Effect of dissipation on free convective flow of a non-Newtonian nanofluid in a porous medium with gyrotactic microorganisms , 2013 .

[32]  O. Anwar Bég,et al.  Anisotropic Slip Magneto-Bioconvection Flow From A Rotating Cone To A Nanofluid With Stefan Blowing Effects , 2017 .

[33]  Syed Inayat Ali Shah,et al.  Transient MHD Convective Flow of Fractional Nanofluid between Vertical Plates , 2019 .

[34]  M. N. Kabir,et al.  Lie group analysis and numerical solution of magnetohydrodynamic free convective slip flow of micropolar fluid over a moving plate with heat transfer , 2015, Comput. Math. Appl..

[35]  B. R. Kumar,et al.  Comparative study of chemically reacting Blasius and Sakiadis unsteady MHD radiated flow with variable conductivity , 2018 .

[36]  C. H. Chen.  Forced convection over a continuous sheet with suction or injection moving in a flowing fluid , 1999 .

[37]  P. D. McCormack,et al.  Physical Fluid Dynamics , 1973 .

[38]  Waqar A. Khan,et al.  CNTS-Water–Based Nanofluid Over a Stretching Sheet , 2019, BioNanoScience.

[39]  T. C. Chiam.  Heat transfer with variable conductivity in a stagnation-point flow towards a stretching sheet , 1996 .

[40]  O. Anwar Bég,et al.  Numerical solutions for gyrotactic bioconvection in nanofluid-saturated porous media with Stefan blowing and multiple slip effects , 2016, Comput. Math. Appl..

[41]  Lei Wang.  A new algorithm for solving classical Blasius equation , 2004, Appl. Math. Comput..

[42]  Amir-Hasan Kakaee,et al.  Modeling of the air conditions effects on the power and fuel consumption of the SI engine using neural networks and regression , 2017 .

[43]  O. Anwar Bég,et al.  Bioconvection nanofluid slip flow past a wavy surface with applications in nano-biofuel cells , 2017 .