Numerical solution of thermo-solutal mixed convective slip flow from a radiative plate with convective boundary condition
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摘要
A mathematical model for mixed convective slip flow with heat and mass transfer in the presence of thermal radiation is presented. A convective boundary condition is included and slip is simulated via the hydrodynamic slip parameter. Heat generation and absorption effects are also incorporated. The Rosseland diffusion flux model is employed. The governing partial differential conservation equations are reduced to a system of coupled, ordinary differential equations via Lie group theory method. The resulting coupled equations are solved using shooting method. The influences of the emerging parameters on dimensionless velocity, temperature and concentration distributions are investigated. Increasing radiative-conductive parameter accelerates the boundary layer flow and increases temperature whereas it depresses concentration. An elevation in convection-conduction parameter also accelerates the flow and temperatures whereas it reduces concentrations. Velocity near the wall is considerably boosted with increasing momentum slip parameter although both temperature and concentration boundary layer thicknesses are decreased. The presence of a heat source is found to increase momentum and thermal boundary layer thicknesses but reduces concentration boundary layer thickness. Excellent correlation of the numerical solutions with previous non-slip studies is demonstrated. The current study has applications in bioreactor diffusion flows and high-temperature chemical materials processing systems.
A mathematical model for mixed convective slip flow with heat and mass transfer in the presence of thermal radiation is presented. A convective boundary condition is included and slip is simulated via the hydrodynamic slip parameter. Heat generation and absorption effects are also incorporated. The Rosseland diffusion flux model is employed. The governing partial differential conservation equations are reduced to a system of coupled, ordinary differential equations via Lie group theory method. The resulting coupled equations are solved using shooting method. The influences of the emerging parameters on dimensionless velocity, temperature and concentration distributions are investigated. Increasing radiative-conductive parameter accelerates the boundary layer flow and increases temperature whereas it depresses concentration. An elevation in convection-conduction parameter also accelerates the flow and temperatures whereas it reduces concentrations. Velocity near the wall is considerably boosted with increasing momentum slip parameter although both temperature and concentration boundary layer thicknesses are decreased. The presence of a heat source is found to increase momentum and thermal boundary layer thicknesses but reduces concentration boundary layer thickness. Excellent correlation of the numerical solutions with previous non-slip studies is demonstrated. The current study has applications in bioreactor diffusion flows and high-temperature chemical materials processing systems.
A mathematical model for mixed convective slip flow with heat and mass transfer in the presence of thermal radiation is presented. A convective boundary condition is included and slip is simulated via the hydrodynamic slip parameter. Heat generation and absorption effects are also incorporated. The Rosseland diffusion flux model is employed. The governing partial differential conservation equations are reduced to a system of coupled, ordinary differential equations via Lie group theory method. The resulting coupled equations are solved using shooting method. The influences of the emerging parameters on dimensionless velocity, temperature and concentration distributions are investigated. Increasing radiative-conductive parameter accelerates the boundary layer flow and increases temperature whereas it depresses concentration. An elevation in convection-conduction parameter also accelerates the flow and temperatures whereas it reduces concentrations. Velocity near the wall is considerably boosted with increasing momentum slip parameter although both temperature and concentration boundary layer thicknesses are decreased. The presence of a heat source is found to increase momentum and thermal boundary layer thicknesses but reduces concentration boundary layer thickness. Excellent correlation of the numerical solutions with previous non-slip studies is demonstrated. The current study has applications in bioreactor diffusion flows and high-temperature chemical materials processing systems.
引文
[1]WANG C.Y.Flow due to a stretching boundary with partial slip-an exact solution of the Navier-Stokes equations[J].Chemical Engineering Science,2002,57(17):3745-3747.
[2]MUKHOPADHYAY S.,Effects of slip on unsteady mixed convective flow and heat transfer past a porous stretching surface[J].Nuclear Engineering and Design,2011,241(8):2660-2665.
[3]IRELAND P.M.,JAMESON G.J.Foam slip on surfaces of intermediate or low wettability[J].Chemical Engineering Science,2009,64(17):3859-3867.
[4]KHALED A.R.A.,VAFAI K.Analysis of oscillatory flow disturbances and thermal characteristics inside fluidic cells due to fluid leakage and wall slip conditions[J].Journal of Biomechanics,2004,37(5):721-729.
[5]ULMANELLA U.,HO C.M.Molecular effects on boundary condition in micro/nanoliquid flows[J].Physics of Fluids,2008,20(10):101512.
[6]BOCQUET L.,BARRAT J.L.Flow boundary conditions from nano-to micro-scales[J].Soft Matter,2007,3(6):685-693.
[7]WANG C.Y.The effect of slip on the flow in a rotating channel[J].Chemical Engineering Communications,2013,200(4):587-594.
[8]NANDY S.K.Unsteady flow of Maxwell fluid in the presence of nanoparticles toward a permeable shrinking surface with Navier slip[J].Journal of the Taiwan Institute of Chemical Engineers,2015,52:22-30.
[9]IBá?EZ G.Entropy generation in MHD porous channel with hydrodynamic slip and convective boundary conditions[J].International Journal of Heat and Mass Transfer,2015,80:274-280.
[10]BéG O.A.,UDDIN M.J.and RASHIDI M.M.et al.Double-diffusive radiative magnetic mixed convective slip flow with Biot and Richardson number effects[J].Journal of Engineering Thermophysics,2014,23(2):79-97.
[11]UNAL C.,BOHL W.R.and PASAMEHMETOGLU K.O.Modeling of heat and mass transfer in accelerator targets during postulated accidents[J].Nuclear Engineering and Design,2000,196(2):185-200.
[12]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[J].Proceedings of the Institution of Mechanical Engineers,Part N:Journal of Nanoengineering and Nanosystems,2013,227(2):77-99.
[13]ZUECO J.,BéG O.A.and TAKHAR H.S.et al.Thermophoretic hydromagnetic dissipative heat and mass transfer with lateral mass flux,heat source,Ohmic heating and thermal conductivity effects:Network simulation numerical study[J].Applied Thermal Engineering,2009,29(14):2808-2815.
[14]WU Z.,CHEN G.Q.Approach to transverse uniformity of concentration distribution of a solute in a solvent flowing along a straight pipe[J].Journal of Fluid Mechanics,2014,740:196-213.
[15]WU Z.,FU X.and WANG G.Concentration distribution of contaminant transport in wetland flows[J].Journal of Hydrology,2015,525:335-344.
[16]MAHMOUD M.A.Variable fluid properties and thermal radiation effects on mixed convection flow over a horizontal surface[J].International Journal for Computational Methods in Engineering Science and Mechanics,2010,11(5):299-303.
[17]GUPTA D.,KUMAR L.and BéG O.A.et al.Finite element simulation of mixed convection flow of micropolar fluid over a shrinking sheet with thermal radiation[J].Proceedings of the Institution of Mechanical Engineers,Part E:Journal of Process Mechanical Engineering,2014,228(1):61-72.
[18]KHAN W.A.,UDDIN M.J.and ISMAIL A.I.M.Effects of radiation on Blasius slip flow of oxide nanofluids with Merkin boundary condition[J].Proceedings of the Institution of Mechanical Engineers,Part N:Journal of Nanomaterials Nanoengineering and Nanosystems,2013,227(1):3-9.
[19]BEJAN A.Convection heat transfer(Chapter 4)[M].4th Edition,New York,USA:Wiley,2013.
[20]KARNIADAKIS G.,BESKOK A.and ALURU N.Microflows and nanoflows fundamentals and simulation[M].New York,USA:Springer Science,2005.
[21]UDDIN M.J.,BéG O.A.and AZIZ A.et al.Group analysis of free convection flow of a magnetic nanofluid with chemical reaction[J].Mathematical Problems in Engineering,2015,2015:ID621503.
[22]OSTRACH S.An analysis of laminar free-convection flow and heat transfer about a flat plate parallel to the direction of the generating body force[R].National Advisory Committee for Aeronautics,Report No.NACA-TR-1111,1953,63-79.
[23]TRIPATHI D.,BéG O.A.A numerical study of oscillating peristaltic flow of generalized Maxwell viscoelastic fluids through a porous medium[J].Transport in Porous Media,2012,95(2):337-348.
[2]MUKHOPADHYAY S.,Effects of slip on unsteady mixed convective flow and heat transfer past a porous stretching surface[J].Nuclear Engineering and Design,2011,241(8):2660-2665.
[3]IRELAND P.M.,JAMESON G.J.Foam slip on surfaces of intermediate or low wettability[J].Chemical Engineering Science,2009,64(17):3859-3867.
[4]KHALED A.R.A.,VAFAI K.Analysis of oscillatory flow disturbances and thermal characteristics inside fluidic cells due to fluid leakage and wall slip conditions[J].Journal of Biomechanics,2004,37(5):721-729.
[5]ULMANELLA U.,HO C.M.Molecular effects on boundary condition in micro/nanoliquid flows[J].Physics of Fluids,2008,20(10):101512.
[6]BOCQUET L.,BARRAT J.L.Flow boundary conditions from nano-to micro-scales[J].Soft Matter,2007,3(6):685-693.
[7]WANG C.Y.The effect of slip on the flow in a rotating channel[J].Chemical Engineering Communications,2013,200(4):587-594.
[8]NANDY S.K.Unsteady flow of Maxwell fluid in the presence of nanoparticles toward a permeable shrinking surface with Navier slip[J].Journal of the Taiwan Institute of Chemical Engineers,2015,52:22-30.
[9]IBá?EZ G.Entropy generation in MHD porous channel with hydrodynamic slip and convective boundary conditions[J].International Journal of Heat and Mass Transfer,2015,80:274-280.
[10]BéG O.A.,UDDIN M.J.and RASHIDI M.M.et al.Double-diffusive radiative magnetic mixed convective slip flow with Biot and Richardson number effects[J].Journal of Engineering Thermophysics,2014,23(2):79-97.
[11]UNAL C.,BOHL W.R.and PASAMEHMETOGLU K.O.Modeling of heat and mass transfer in accelerator targets during postulated accidents[J].Nuclear Engineering and Design,2000,196(2):185-200.
[12]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[J].Proceedings of the Institution of Mechanical Engineers,Part N:Journal of Nanoengineering and Nanosystems,2013,227(2):77-99.
[13]ZUECO J.,BéG O.A.and TAKHAR H.S.et al.Thermophoretic hydromagnetic dissipative heat and mass transfer with lateral mass flux,heat source,Ohmic heating and thermal conductivity effects:Network simulation numerical study[J].Applied Thermal Engineering,2009,29(14):2808-2815.
[14]WU Z.,CHEN G.Q.Approach to transverse uniformity of concentration distribution of a solute in a solvent flowing along a straight pipe[J].Journal of Fluid Mechanics,2014,740:196-213.
[15]WU Z.,FU X.and WANG G.Concentration distribution of contaminant transport in wetland flows[J].Journal of Hydrology,2015,525:335-344.
[16]MAHMOUD M.A.Variable fluid properties and thermal radiation effects on mixed convection flow over a horizontal surface[J].International Journal for Computational Methods in Engineering Science and Mechanics,2010,11(5):299-303.
[17]GUPTA D.,KUMAR L.and BéG O.A.et al.Finite element simulation of mixed convection flow of micropolar fluid over a shrinking sheet with thermal radiation[J].Proceedings of the Institution of Mechanical Engineers,Part E:Journal of Process Mechanical Engineering,2014,228(1):61-72.
[18]KHAN W.A.,UDDIN M.J.and ISMAIL A.I.M.Effects of radiation on Blasius slip flow of oxide nanofluids with Merkin boundary condition[J].Proceedings of the Institution of Mechanical Engineers,Part N:Journal of Nanomaterials Nanoengineering and Nanosystems,2013,227(1):3-9.
[19]BEJAN A.Convection heat transfer(Chapter 4)[M].4th Edition,New York,USA:Wiley,2013.
[20]KARNIADAKIS G.,BESKOK A.and ALURU N.Microflows and nanoflows fundamentals and simulation[M].New York,USA:Springer Science,2005.
[21]UDDIN M.J.,BéG O.A.and AZIZ A.et al.Group analysis of free convection flow of a magnetic nanofluid with chemical reaction[J].Mathematical Problems in Engineering,2015,2015:ID621503.
[22]OSTRACH S.An analysis of laminar free-convection flow and heat transfer about a flat plate parallel to the direction of the generating body force[R].National Advisory Committee for Aeronautics,Report No.NACA-TR-1111,1953,63-79.
[23]TRIPATHI D.,BéG O.A.A numerical study of oscillating peristaltic flow of generalized Maxwell viscoelastic fluids through a porous medium[J].Transport in Porous Media,2012,95(2):337-348.