Numerical Study of Unsteady Mass Motion Flow of Power Law Fluid Along a Vertical Plate with the Effect of Viscous Dissipation and Low Magnetic Field
American Journal of Aerospace Engineering
Volume 4, Issue 4, August 2017, Pages: 38-53
Received: Dec. 10, 2017;
Accepted: Jan. 11, 2018;
Published: Jan. 30, 2018
Views 1224 Downloads 60
GM Fahad Bin Mostafa, Department of Applied Mathematics, University of Dhaka, Dhaka, Bangladesh
Md. Rakib Hossain, Department of Applied Mathematics, University of Dhaka, Dhaka, Bangladesh
Md. Abdus Samad, Department of Applied Mathematics, University of Dhaka, Dhaka, Bangladesh
The unsteady laminar boundary layer flow along a vertical stationary plate was investigated by taking into account the viscous dissipation of non- Newtonian fluid in case of free convection particularly. The governing non-linear partial differential equations are transformed into ordinary differential equations using a similarity transformation. Transformed equations have been discretized by finite difference approximation. The effects of viscous dissipation on velocity and temperature profile with unsteady case dimensionless numbers such as, Prandtl number (Pr), Eckert number (Ec), Grashof number (Gr) and magnetic parameter (M) have been depicted. It is observed that the interaction between the viscous heating and the buoyancy force has a significant influence on the results. Small effects have been found for Eckert number (Ec). Eventually, skin fiction coefficient (Cf) and heat transfer rate (Nu) are presented in tabular form for engineering studies.
GM Fahad Bin Mostafa,
Md. Rakib Hossain,
Md. Abdus Samad,
Numerical Study of Unsteady Mass Motion Flow of Power Law Fluid Along a Vertical Plate with the Effect of Viscous Dissipation and Low Magnetic Field, American Journal of Aerospace Engineering.
Vol. 4, No. 4,
2017, pp. 38-53.
Sakiadis. B. C, “Boundary-layer behavior on continuous solid surface on a continuous flat surface-I, The boundary layer on a continuous flat surface”, AICHE J., (1961a), pp. 26-28.
Sakiadis. B. C, “Boundary-layer behavior on continuous solid surface on a continuous flat surface-II, The boundary layer on a continuous flat surface”, AICHE J, (1961b), pp. 221-225.
Rajgopal K. R., T. Y. Na and A. S. Gupta, Flow of a viscoelastic fluid over a stretching sheet. Rheol. Acta, (1984.) pp. 213-215.
Dandapat, B. S. and A. S. Gupta, “Flow and heat transfer in a viscoelastic fluid over a stretching sheet”, Int. J. Non-Linear Mech., (1989) pp. 215-219.
Gupta P. S., Gupta A. S., “Heat and Mass Transfer on a Stretching Sheet with Suction or Blowing”, Can. J. Chem. Eng., (1977), pp. 744-746.
Afzal N., Varshney I. S., “The Cooling of a Low Heat Resistance Stretching Sheet Moving through a Fluid”, Warme Stoffubertrag, (1980), pp. 289-299.
Banks W. H. H., “Similarity Solutions of the Boundary Layer Equations for a Stretching Wall”, J. Mec. Theor. Appl., (1983), pp. 375-392.
Grubka L. J., Bobba K. M., “Heat Transfer Characteristics of a Continuous Stretching Surface with Variable Temperature”, ASME J. Heat Transfer, (1985), pp. 248-250.
Chen C. K., Char M. I., “Heat Transfer of a Continuous Stretching Surface with Suction or Blowing”, J. Math. Anal. Appl., (1988), pp. 568-580.
M. R. Haque., M. M. Alim, M. M. Ali, R. Karim., “Effects of viscous dissipation on natural convective flow over a sphere with temperature dependent thermal conductivity in presence of heat generation”. Elsever (2015) pp. 215-224.
Takhar, H. S., R. S. R. Glora and V. M. Soundalgekar, “Radiation effects on MHD free convection flow of radiating fluid past a semi-infinite vertical plate”, Int. J. Num. Methods Heat Fluid Flow, (1996) pp. 77-83.
Chamkha, A. J., H. S. Takhar and V. M. Soundalgekar, “Radiation effect on free convection flow past a semi-Infinite vertical plate with mass transfer. Chem. Eng. J., (2001) pp. 335-342.
Raptis, A. 1nd C. Perdikis, “Radiation and free convection flow past a moving plate”. App. Mech. Eng., (1999) pp. 817-821.
Kishan Naikoti, Shashidar Reddy Borra, “Quasi-linearization Approach to MHD Effects on Boundary Layer Flow of Power-Law Fluids Past A Semi Infinite Flat Plate with Thermal Dispersion”, Int. J. of Non-Linear Science, Vol. 11, (2011), pp. 301-311.
Mansour M. A. and Gorla R. S. R., “Mixed convection-radiation interaction in power- law fluids along a non-isothermal wedge embedded in a porous medium”, Transport in Porous Media, (1998), pp. 113-124.
Raptis A., “Flow of a micro polar fluid past a continuously moving plate by the presence of radiation”, Int. J. Heat Mass Transfer, (1998), pp. 2865-2866.
Sajid M. and Hayat T., “Influence of thermal radiation on the boundary layer flow due to an exponentially stretching sheet”, Int. J. Heat Mass Transfer, Vol. 35, (2008), pp. 347-356.
Sahoo B., Poncet S., “Flow an heat transfer of a third grade fluid past an exponentially stretching sheet with partial slip boundary condition”, Int. J. Heat Mass Transfer, (2011), pp. 5010-5050.
Kolar, A. K. and Sastri, V. M., “Free Convective Transpiration over a Vertical Plate”a Numerical Study”, J. Heat and Mass Transfer, (1988), pp. 327-336.
Camargo R., Luna E. and Trevino C., “Numerical Study of the Natural Convective Cooling of a Vertical Plate”, J. Heat and Mass Transfer, (1996), pp. 89-95.
M. A. Samad, M. M. Rahaman, M. A. Rahaman and M. Mohebujjaman, “Numerical Study of MHD Forced Convective Flow of a Micro polar Fluid past a non-linear Stretching Sheet with Variable Viscosity” Dhaka Univ J. Sci. (2009) 57 (2) pp. 243-248.
M. M. Alim, M. A. Alim and M. K. Chowdhury, “Effect of pressure stress work and viscous dissipation in natural convection flow along a vertical plate with heat conduction” J. Naval and Marine Eng. 3. (2006) pp. 69-76.
K. C. Saha, M. A. Samad and M. R. Hossain, “Effect of viscous dissipation on MHD Free Convection flow Heat and Mass Transfer of Non-Newtonian Fluids along a Continuously moving Stretching Sheet” Research J. of App. Sciences, Eng. And Tech., (2015), pp. 1058-1073.
Fahad B. Mostafa, M. A. Samad and M. R. Hossain. “Combined Effect of Viscous Dissipation and Radiation on Unsteady Free Convective Non-Newtonian Fluid along a Continuously Moving Vertically Stretched Surface with No-Slip Phenomena” American Journal of Computational and Applied Mathematics 2017 7 (3) pp. 71-79.