Coupled Effects of Surface Inclination and Magnetic Field on Free Convection Heat Transfer of Nanofluid over a Flat Plate in a Porous Medium in the Presence of Thermal Radiation
The present paper focuses on the impacts of stretching surface inclination, magnetic field and thermal radiation on natural convection heat transfer of nanofluids over a surface in a porous medium. The flow and heat transfer models are solved using multi-step differential transformation method. From the parametric study, the results show that the velocity of the nanofluid increases as the plate inclination increases while the temperature of the nanofluid decreases as the plate inclination increases. Also, the flow velocity of the fluid attains minimum value when the plate assumes horizontal position while it reaches maximum value when the plate is at vertical position. The velocity of the fluid decreases as the magnetic field parameter increases. However, the temperature gradient of the flow increases as the magnetic field parameter increases. The viscous and thermal boundary layers increase with the increase of thermal radiation parameter. The present study will help in the design of flow equipment in various industrial and engineering various applications.
E. Schmidt and W. Beckmann. Das temperatur-und geschwindigkeitsfeld vor einer wärme abgebenden senkrecher
platte bei natürelicher convention. Tech. Mech. U. Themodynamik, Bd. 1(10) (1930), 341-349; cont. Bd. 1(11) (1930),
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, NACA Report, 1111, 1953.
. E.M. Sparrow and J.L. Gregg, Laminar free convection from a vertical plate with uniform surface heat flux,
Trans. A.S.M.E. 78 (1956) 435-440.
. E.J. Lefevre, Laminar free convection from a vertical plane surface, 9th Intern. Congress on Applied
Mechanics, Brussels, paper I, 168 (1956).
. E.M. Sparrow and J.L. Gregg, Similar solutions for free convection from a nonisothermal vertical plate, Trans.
A.S.M.E. 80 (1958) 379-386.
. K. Stewartson and L.T. Jones, The heated vertical plate at high Prandtl number, J. Aeronautical Sciences 24
. H.K. Kuiken, An asymptotic solution for large Prandtl number free convection, J. Engng. Math. 2 (1968)
. H.K. Kuiken, Free convection at low Prandtl numbers, J. Fluid Mech. 37 (1969) 785-798.
. S. Eshghy, Free-convection layers at large Prandtl number, J. Applied Math. and Physics (ZAMP) 22 (1971)
. S. Roy, High Prandtl number free convection for uniform surface heat flux, Trans A.S.M.E.J. Heat Transfer
. H.K. Kuiken and Z. Rotem, Asymptotic solution for the plume at very large and small Prandtl numbers, J.
Fluid Mech. 45 (1971) 585-600.
T.Y. Na, I.S. Habib, Solution of the natural convection problem by parameter differentiation, Int. J. Heat Mass
Transfer 17 (1974) 457–459.
. J.H. Merkin, A note on the similarity solutions for free convection on a vertical plate, J. Engng. Math. 19
J.H. Merkin, I. Pop, Conjugate free convection on a vertical surface, Int. J. Heat Mass Transfer 39 (1996) 1527–
F. M. Ali, R. Nazar, and N. M. Arifin, “Numerical investigation of free convective boundary layer in a viscous
fluid,” The American Journal of Scientific Research, no. 5, pp. 13–19, 2009.
S. S. Motsa, S. Shateyi, and Z. Makukula, “Homotopy analysis of free convection boundary layer flow with heat
and mass transfer,” Chemical Engineering Communications, vol.198, no.6, pp. 783–795, 2011.
S. S. Motsa, Z. G. Makukula and S. Shateyi. Spectral Local Linearisation Approach for Natural Convection
Boundary Layer Flow. Hindawi Publishing Corporation Mathematical Problems in Engineering, Volume 2013 (2013),
Article ID 765013, 7 pages.
A.R. Ghotbi, H. Bararnia, G. Domairry, and A.Barari,“Investigation of a powerful analytical method into natural
convection boundary layer flow,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 5,
pp. 2222–2228, 2009. M. G. Sobamowo and A. A. Yinusa. Insight into the Boundary Layer Flows of Free Convection and Heat
Transfer of Nanofluids Over a Vertical Plate using Multi-Step Differential Transformation Method Iranian Journal
of Mechanical Engineering, 20(1), 1-42, 2019.