Effects of Thermophoresis on Unsteady MHD Free Convective Heat and Mass Transfer along an Inclined Porous Plate with Heat Generation in Presence of Magnetic Field

Affiliation(s)

Department of Natural Sciences, Daffodil International University, Dhaka, Bangladesh.

Department of Mathematics, Comilla University, Comilla, Bangladesh.

Department of Natural Sciences, Daffodil International University, Dhaka, Bangladesh.

Department of Mathematics, Comilla University, Comilla, Bangladesh.

ABSTRACT

An analysis of Thermophoresis effect on unsteady magneto-hydrodynamic free convection flow over an inclined porous plate with time dependent suction in presence of magnetic field with heat generation has been considered by employing Nachtsheim-Swigert shooting iteration technique along with sixth order Runge-Kutta integration scheme. Resulting non-dimensional velocity, temperature and concentration profiles are then presented graphically for different values of the parameters entering into the problem. Finally, the effects of the pertinent parameters on the skin-friction coefficient, the rate of heat transfer (Nusselt number) and wall deposition flux (Stanton number), which are of physical interest, are exhibited in tabular form.

An analysis of Thermophoresis effect on unsteady magneto-hydrodynamic free convection flow over an inclined porous plate with time dependent suction in presence of magnetic field with heat generation has been considered by employing Nachtsheim-Swigert shooting iteration technique along with sixth order Runge-Kutta integration scheme. Resulting non-dimensional velocity, temperature and concentration profiles are then presented graphically for different values of the parameters entering into the problem. Finally, the effects of the pertinent parameters on the skin-friction coefficient, the rate of heat transfer (Nusselt number) and wall deposition flux (Stanton number), which are of physical interest, are exhibited in tabular form.

Cite this paper

M. Kabir and M. Mahbub, "Effects of Thermophoresis on Unsteady MHD Free Convective Heat and Mass Transfer along an Inclined Porous Plate with Heat Generation in Presence of Magnetic Field,"*Open Journal of Fluid Dynamics*, Vol. 2 No. 4, 2012, pp. 120-129. doi: 10.4236/ojfd.2012.24012.

M. Kabir and M. Mahbub, "Effects of Thermophoresis on Unsteady MHD Free Convective Heat and Mass Transfer along an Inclined Porous Plate with Heat Generation in Presence of Magnetic Field,"

References

[1] S. Ostrach, “An Analysis of Laminar Free-Convection Flow and Heat Transfer about a Flat Plate Parallel to the Direction of the Generating Body Force,” Technical Note, NACA Report, Washington, 1952.

[2] B. C. Sakiadis, “Boundary-Layer Behavior on Continuous Solid Surfaces: I. Boundary-Layer Equations for Two-Dimensional and Axisymmetric Flow,” AIChE Journal, Vol. 7, No. 1, 1961, pp. 26-28. Hdoi:10.1002/aic.690070108

[3] L. E. Erickson, L. T. Fan and V. G. Fox, “Heat and Mass Transfer on a Moving Continuous Flat Plate with Suction or Injection,” Industrial Engineering and Chemical Fundamentals, Vol. 5, No. 1, 1966, pp. 19-25. Hdoi:10.1021/i160017a004

[4] S. L. Goren, “Thermophoresis of Aerosol Particles in Laminar Boundary Layer on Flat Plate,” Journal of Colloid Interface Science, Vol. 61, No. 1, 1977, pp. 77-85. Hdoi:10.1016/0021-9797(77)90416-7

[5] E. M. Sparrow, “Radiation Heat Transfer,” Augmented Edition, Hemisphere Publishing Corp., Washington DC, 1978.

[6] R. S. R. Gorla, “Unsteady Mass Transfer in the Boundary Layer on a Continuous Moving Sheet Electrod,” Journal of the Electrochemical Society, Vol. 125, No. 6, 1978, pp. 865-869. Hdoi:10.1149/1.2131569

[7] G. M. Homsy, F. T. Geyling and K. L. Walker, “Blasius Series for Thermophoretic Deposition of Small Particles,” Journal of Colloid Interface Science, Vol. 83, No. 2, 1981, pp. 495-501. Hdoi:10.1016/0021-9797(81)90345-3

[8] A. Raptis and C. Perdikis, “Unsteady Flow through a Porous Medium in the Presence of Free Convection,” International Communications in Heat and Mass Transfer, Vol. 12, No. 6, 1985, pp. 697-704. Hdoi:10.1016/0735-1933(85)90022-3

[9] M. Epstein, G. M. Hauser and R. E. Henry, “Thermophoretic Deposition of Particles In Natural Convection Flow from a Vertical Plate,” Journal of Heat Transfer, Vol. 107, No. 2, 1985, pp. 272-276. Hdoi:10.1115/1.3247410

[10] M. A. Alabraba, A. R. Bestman and A. Ogulu, “Laminar Convection in Binary Mixed of Hydromagnetic Flow with Radiative Heat Transfer-I, II,” Astrophysics and Space Science, Vol. 195, No. 2, 1992, pp. 431-439, 441-445. Hdoi:10.1007/BF00646774

[11] A. Sattar and M. Hossain, “Unsteady Hydromagnetic Free Convection Flow with Hall Current and Mass Transfer along an Accelerated Porous Plate with Time Dependent Temperature and Concentration,” Canadian Journal of Physics, Vol. 70, No. 5, 1992, pp. 369-375. Hdoi:10.1139/p92-061

[12] M. A. Hossain and H. S. Takhar, “Radiation Effect on Mixed Convection along a Vertical Plate with Uniform Surface Temperature,” Heat and Mass Transfer, Vol. 31, No. 4, 1996, pp. 243-248. Hdoi:10.1007/BF02328616

[13] J.-S. Lin, C.-J. Tsai and C.-P. Chang, “Suppression of Particle Deposition in Tube Flow by Thermophoresis,” Journal of Aerosol Science, Vol. 35, No. 2004, pp. 1235-1250. Hdoi:10.1016/j.jaerosci.2004.05.007

[14] M. A. Seddek, “Finite-Element Method for the Effects of Chemical Reaction, Variable Viscosity, Thermophoresis and Heat Generation/Absorption on a Boundary-Layer Hydromagnetic Flow with Heat and Mass Transfer over a Heat Surface,” Journal of Acta Machanica, Vol. 177, No. 2005, pp. 1-18.

[15] M. S. Alam, M. M. Rahman and M. A. Sattar, “Similarity Solutions for Hydromagnetic Free Convective Heat and Mass Transfer Flow along a Semi-Infinite Permeable Inclined Flat Plate with Heat Generation and Thermophoresis,” Nonlinear Analysis: Modelling and Control., Vol. 12, No. 4, 2007, pp. 433-445.

[16] M. A. Samad and M. E. Karim, “Thermal Radiation Interaction with Unsteady MHD Flow past a Vertical Flat Plate with Time Dependent Suction,” Dhaka University Journal of Science, Vol. 57, No. 1, 2009, pp. 113-118.

[17] M. A. A. Mahmoud, “Thermal Radiation Effect on Unsteady MHD Free Convection Flow Past a Vertical Plate with Temperature Dependent Viscosity,” Canadian Journal of Chemical Engineering, Vol. 87, No. 1, 2009, pp. 47-52. Hdoi:10.1002/cjce.20135

[18] M. A. Samad, M. E. Karim and D. Mohammad, “Free Convection Flow through a Porous Medium with Thermal Radiation, Viscous Dissipation and Variable Suction in Presence of Magnetic Field,” Bangladesh Journal of Scientific Research, Vol. 23, No. 1, 2010, pp. 61-72.

[19] P. Loganathan and P. P. Arasu, “Thermophoresis Effects on Non-Darcy MHD Mixed Convective Heat and Mass Transfer past a Porous Wedge in The Presence of Suction/Injection,” Theoretic Applied Mechanics, Vol. 37, No. 3, 2010, pp. 203-227. Hdoi:10.2298/TAM1003203L

[20] M. Ferdows, Nazmul and M. Ota, “Thermophoresis and Chemical Reaction Effects on MHD Natural Convective Heat and Mass Transfer Flow in a Rotating Fluid Considering Heat and Mass Fluxes,” Canadian Journal on Science and Engineering Mathematics, Vol. 2, No. 3, 2011, pp. 114-139.

[21] O. D. Makinde and P. O. Olanrewaju, “Unsteady Mixed Convection with Soret and Dufour Effects past a Porous Plate Moving through a Binary Mixture of Chemical Reacting Fluid,” Chemical Engineering Communications, Vol. 198, No. 7, 2011, pp. 920-938. Hdoi:10.1080/00986445.2011.545296

[22] N. Ghara, S. L. Maji, S. Das, R. Jana and S. K. Ghosh, “Effects of Hall Current and Ion-Slip on Unsteady MHD Couette Flow,” Open Journal of Fluid Dynamics, Vol. 2, No. 1, 2012, pp. 1-13. Hdoi:10.4236/ojfd.2012.21001

[23] G. K. Batchelor and C. Shen, “Thermophoretic Deposition of Particles in Gas ?owing over Cold Surface,” Journal of Colloid Interface Science, Vol. 107, No. 1, 1985, pp. 21-37. Hdoi:10.1016/0021-9797(85)90145-6

[24] L. Talbot, R. K. Cheng, A. W. Schefer and D. R. Wills, “Thermophoresis of Particles in a Heated Boundary Layer,” Journal of Fluid Mechanics, Vol. 101, No. 4, 1980, pp. 737-758. Hdoi:10.1017/S0022112080001905

[25] A. F. Mills, X. Hang and F. Ayazi, “The Effect of Wall Suction and Thermophoresis on Aerosol-Particle Deposition from a Laminar Boundary Layer on a ?at Plate,” International Jornal of Heat and Mass Transfer, Vol. 27, No. 7, 1984, pp. 1110-1114. Hdoi:10.1016/0017-9310(84)90127-3

[26] R. Tsai, “A Simple Approach for Evaluating the Effect of Wall Suction and Thermophoresis on Aerosol Particle Deposition Froma Laminar ?ow over A?at Plate,” International Communications in Heat and Mass Transfer, Vol. 26, No. 2, 1999, pp. 249-257. Hdoi:10.1016/S0735-1933(99)00011-1

[27] M. A. Samad and M. M. Rahman, “Thermal Radiation Interaction with Unsteady MHD Flow past a Vertical Porous Plate Immersed in a Porous Medium,” Journal of Naval Architechture and Marine Engineering, Vol. 3, No. 2, 2006, pp. 7-14.

[28] P. R. Nachtsheim and P. Swigert, “Satisfaction of the Asymptotic Boundary Conditions in Numerical Solution of the Systems of Non-Linear Equations of Boundary Layer Type,” Ph.D. Thesis, NASA TN D-3004, Washington DC, 1965.

[1] S. Ostrach, “An Analysis of Laminar Free-Convection Flow and Heat Transfer about a Flat Plate Parallel to the Direction of the Generating Body Force,” Technical Note, NACA Report, Washington, 1952.

[2] B. C. Sakiadis, “Boundary-Layer Behavior on Continuous Solid Surfaces: I. Boundary-Layer Equations for Two-Dimensional and Axisymmetric Flow,” AIChE Journal, Vol. 7, No. 1, 1961, pp. 26-28. Hdoi:10.1002/aic.690070108

[3] L. E. Erickson, L. T. Fan and V. G. Fox, “Heat and Mass Transfer on a Moving Continuous Flat Plate with Suction or Injection,” Industrial Engineering and Chemical Fundamentals, Vol. 5, No. 1, 1966, pp. 19-25. Hdoi:10.1021/i160017a004

[4] S. L. Goren, “Thermophoresis of Aerosol Particles in Laminar Boundary Layer on Flat Plate,” Journal of Colloid Interface Science, Vol. 61, No. 1, 1977, pp. 77-85. Hdoi:10.1016/0021-9797(77)90416-7

[5] E. M. Sparrow, “Radiation Heat Transfer,” Augmented Edition, Hemisphere Publishing Corp., Washington DC, 1978.

[6] R. S. R. Gorla, “Unsteady Mass Transfer in the Boundary Layer on a Continuous Moving Sheet Electrod,” Journal of the Electrochemical Society, Vol. 125, No. 6, 1978, pp. 865-869. Hdoi:10.1149/1.2131569

[7] G. M. Homsy, F. T. Geyling and K. L. Walker, “Blasius Series for Thermophoretic Deposition of Small Particles,” Journal of Colloid Interface Science, Vol. 83, No. 2, 1981, pp. 495-501. Hdoi:10.1016/0021-9797(81)90345-3

[8] A. Raptis and C. Perdikis, “Unsteady Flow through a Porous Medium in the Presence of Free Convection,” International Communications in Heat and Mass Transfer, Vol. 12, No. 6, 1985, pp. 697-704. Hdoi:10.1016/0735-1933(85)90022-3

[9] M. Epstein, G. M. Hauser and R. E. Henry, “Thermophoretic Deposition of Particles In Natural Convection Flow from a Vertical Plate,” Journal of Heat Transfer, Vol. 107, No. 2, 1985, pp. 272-276. Hdoi:10.1115/1.3247410

[10] M. A. Alabraba, A. R. Bestman and A. Ogulu, “Laminar Convection in Binary Mixed of Hydromagnetic Flow with Radiative Heat Transfer-I, II,” Astrophysics and Space Science, Vol. 195, No. 2, 1992, pp. 431-439, 441-445. Hdoi:10.1007/BF00646774

[11] A. Sattar and M. Hossain, “Unsteady Hydromagnetic Free Convection Flow with Hall Current and Mass Transfer along an Accelerated Porous Plate with Time Dependent Temperature and Concentration,” Canadian Journal of Physics, Vol. 70, No. 5, 1992, pp. 369-375. Hdoi:10.1139/p92-061

[12] M. A. Hossain and H. S. Takhar, “Radiation Effect on Mixed Convection along a Vertical Plate with Uniform Surface Temperature,” Heat and Mass Transfer, Vol. 31, No. 4, 1996, pp. 243-248. Hdoi:10.1007/BF02328616

[13] J.-S. Lin, C.-J. Tsai and C.-P. Chang, “Suppression of Particle Deposition in Tube Flow by Thermophoresis,” Journal of Aerosol Science, Vol. 35, No. 2004, pp. 1235-1250. Hdoi:10.1016/j.jaerosci.2004.05.007

[14] M. A. Seddek, “Finite-Element Method for the Effects of Chemical Reaction, Variable Viscosity, Thermophoresis and Heat Generation/Absorption on a Boundary-Layer Hydromagnetic Flow with Heat and Mass Transfer over a Heat Surface,” Journal of Acta Machanica, Vol. 177, No. 2005, pp. 1-18.

[15] M. S. Alam, M. M. Rahman and M. A. Sattar, “Similarity Solutions for Hydromagnetic Free Convective Heat and Mass Transfer Flow along a Semi-Infinite Permeable Inclined Flat Plate with Heat Generation and Thermophoresis,” Nonlinear Analysis: Modelling and Control., Vol. 12, No. 4, 2007, pp. 433-445.

[16] M. A. Samad and M. E. Karim, “Thermal Radiation Interaction with Unsteady MHD Flow past a Vertical Flat Plate with Time Dependent Suction,” Dhaka University Journal of Science, Vol. 57, No. 1, 2009, pp. 113-118.

[17] M. A. A. Mahmoud, “Thermal Radiation Effect on Unsteady MHD Free Convection Flow Past a Vertical Plate with Temperature Dependent Viscosity,” Canadian Journal of Chemical Engineering, Vol. 87, No. 1, 2009, pp. 47-52. Hdoi:10.1002/cjce.20135

[18] M. A. Samad, M. E. Karim and D. Mohammad, “Free Convection Flow through a Porous Medium with Thermal Radiation, Viscous Dissipation and Variable Suction in Presence of Magnetic Field,” Bangladesh Journal of Scientific Research, Vol. 23, No. 1, 2010, pp. 61-72.

[19] P. Loganathan and P. P. Arasu, “Thermophoresis Effects on Non-Darcy MHD Mixed Convective Heat and Mass Transfer past a Porous Wedge in The Presence of Suction/Injection,” Theoretic Applied Mechanics, Vol. 37, No. 3, 2010, pp. 203-227. Hdoi:10.2298/TAM1003203L

[20] M. Ferdows, Nazmul and M. Ota, “Thermophoresis and Chemical Reaction Effects on MHD Natural Convective Heat and Mass Transfer Flow in a Rotating Fluid Considering Heat and Mass Fluxes,” Canadian Journal on Science and Engineering Mathematics, Vol. 2, No. 3, 2011, pp. 114-139.

[21] O. D. Makinde and P. O. Olanrewaju, “Unsteady Mixed Convection with Soret and Dufour Effects past a Porous Plate Moving through a Binary Mixture of Chemical Reacting Fluid,” Chemical Engineering Communications, Vol. 198, No. 7, 2011, pp. 920-938. Hdoi:10.1080/00986445.2011.545296

[22] N. Ghara, S. L. Maji, S. Das, R. Jana and S. K. Ghosh, “Effects of Hall Current and Ion-Slip on Unsteady MHD Couette Flow,” Open Journal of Fluid Dynamics, Vol. 2, No. 1, 2012, pp. 1-13. Hdoi:10.4236/ojfd.2012.21001

[23] G. K. Batchelor and C. Shen, “Thermophoretic Deposition of Particles in Gas ?owing over Cold Surface,” Journal of Colloid Interface Science, Vol. 107, No. 1, 1985, pp. 21-37. Hdoi:10.1016/0021-9797(85)90145-6

[24] L. Talbot, R. K. Cheng, A. W. Schefer and D. R. Wills, “Thermophoresis of Particles in a Heated Boundary Layer,” Journal of Fluid Mechanics, Vol. 101, No. 4, 1980, pp. 737-758. Hdoi:10.1017/S0022112080001905

[25] A. F. Mills, X. Hang and F. Ayazi, “The Effect of Wall Suction and Thermophoresis on Aerosol-Particle Deposition from a Laminar Boundary Layer on a ?at Plate,” International Jornal of Heat and Mass Transfer, Vol. 27, No. 7, 1984, pp. 1110-1114. Hdoi:10.1016/0017-9310(84)90127-3

[26] R. Tsai, “A Simple Approach for Evaluating the Effect of Wall Suction and Thermophoresis on Aerosol Particle Deposition Froma Laminar ?ow over A?at Plate,” International Communications in Heat and Mass Transfer, Vol. 26, No. 2, 1999, pp. 249-257. Hdoi:10.1016/S0735-1933(99)00011-1

[27] M. A. Samad and M. M. Rahman, “Thermal Radiation Interaction with Unsteady MHD Flow past a Vertical Porous Plate Immersed in a Porous Medium,” Journal of Naval Architechture and Marine Engineering, Vol. 3, No. 2, 2006, pp. 7-14.

[28] P. R. Nachtsheim and P. Swigert, “Satisfaction of the Asymptotic Boundary Conditions in Numerical Solution of the Systems of Non-Linear Equations of Boundary Layer Type,” Ph.D. Thesis, NASA TN D-3004, Washington DC, 1965.