Investigation of Velocity Profile in Time Dependent Boundary Layer Flow of a Modified Power-Law Fluid of Fourth Grade
More details
Hide details
Department of Mechanical Engineering, Afyon Kocatepe University 03200, Afyonkarahisar, Turkey
Online publication date: 2020-06-05
Publication date: 2020-06-01
International Journal of Applied Mechanics and Engineering 2020;25(2):176-191
This paper deals with the investigation of time dependent boundary layer flow of a modified power-law fluid of fourth grade on a stretched surface with an injection or suction boundary condition. The fluid model is a mixture of fourth grade and power-law fluids in which the fluid may display shear thickening, shear thinning or normal stress textures. By using the scaling and translation transformations which is a type of Lie Group transformation, time dependent boundary layer equations are reduced into two alternative ordinary differential equations systems (ODEs) with boundary conditions. During this reduction, special Lie Group transformations are used for translation, scaling and combined transformation. Numerical solutions have been carried out for the ordinary differential equations for various fluids and boundary condition parameters. As a result of numerical analysis, it is observed that the boundary layer thickness decreases as the power-law index value increases. It was also observed that for the fourth-grade fluid parameter, as the parameter increases, the boundary layer thickness decreases while the velocity in the y direction increases.
Pakdemirli M. and Suhubi E.S. (1992): Similarity solutions of boundary layer equations for second order fluids. − Int. J. Engng Sci., vol.30, pp.611-629.
Pakdemirli M. (1992): The boundary layer equations of third grade fluids. − Int. J. Non-Linear Mech., vol.27, pp.785-793.
Yürüsoy M. and Pakdemirli M. (1997): Symmetry reductions of unsteady three dimensional boundary layers of some non-Newtonian fluids. − Int. J. Engng Sci., vol.35, pp.731-740.
Yürüsoy M. (2006): Unsteady boundary layer flow of power-law fluid on stretching sheet surface. − Int. J. Engng Sci., vol.44, pp.325-332.
Keçebaş A. and Yürüsoy M. (2006): Similarity solutions of unsteady boundary layer equations of a special third grade fluid. − Int. J. Engng Sci., vol.44, pp.721-729.
Pakdemirli M., Aksoy Y., Yürüsoy M. and Khalique C.M. (2008): Symmetries of boundary layer equations of power-law fluids of second grade. − Acta Mech Sin., vol.24, pp.661-670.
Abbasbandy S., Yürüsoy M. and Pakdemirli M. (2008): The analysis approach of boundary layer equations of power-law fluids of second grade. − Z. Naturforsch., vol.63a, pp.564-570.
Pakdemirli M., Hayat T., Yürüsoy M., Abbasbandy S. and Asghar S. (2011): Perturbation analysis of a modified second grade fluid over a porous plate. − Nonlinear Analysis: Real World Applications, vol.12, pp.1774-1785.
Khan M., Salahuddin T. and Malik M.Y. (2018): An immediate change in viscosity of Carreau nanofluid due to double stratified medium: application of Fourier’s and Fick’s laws. − Journal of the Brazilian Society of Mechanical Sciences and Engineering, vol.40, pp.457-.
Khan M., Shahid A., Malik M.Y. and Salahuddin T. (2018): Thermal and concentration diffusion in Jeffery nanofluid flow over an inclined stretching sheet: A generalized Fourier’s and Fick’s perspective. − Journal of Molecular Liquids, vol.251, pp.7-14.
Khan M., Shahid A., Salahuddin T., Malik M.Y. and Mushtaq M. (2018): Heat and mass diffusions for Casson nanofluid flow over a stretching surface with variable viscosity and convective boundary conditions. − Journal of the Brazilian Society of Mechanical Sciences and Engineering, vol.40, pp.533.
Khan M., Malik M.Y., Salahuddin T. and Khan F. (2019):, Generalized diffusion effects on Maxwell nanofuid stagnation point flow over a stretching sheet with slip conditions and chemical reaction. − Journal of the Brazilian Society of Mechanical Sciences and Engineering, vol.41, pp.138.
Khan M., Salahuddin T., Tanveer A., Malik M.Y. and Hussain A. (2018): Change in internal energy of thermal diffusion stagnation point Maxwell nanofluid flow along with solar radiation and thermal conductivity. − Chinese Journal of Chemical Engineering, vol.27, pp.2352-2358.
Yürüsoy M. and Pakdemirli M. (1996): Group-theoretic approach to unsteady boundary-layer equations of some non-Newtonian fluids. − Modern Group Analysis VI, Johennesburg, South Africa.
Ibragimov N.H. (1994): CRC Handbook of lie Group analysis of Differential Equations. − Volume 1, CRC Press, Boca Raton.
Bluman G.W. and Kumei S. (1989): Symmetries and Differential Equations. − New York: Springer-Verlag.
Journals System - logo
Scroll to top