Unsteady Natural Convection Heat Transfer Past a Vertical Flat Plate Embedded in a Porous Medium Saturated With Fractional Oldroyd-B Fluid

Abstract

This paper investigates natural convection heat transfer of generalized Oldroyd-B fluid in a porous medium with modified fractional Darcy's law. Nonlinear coupled boundary layer governing equations are formulated with time–space fractional derivatives in the momentum equation. Numerical solutions are obtained by the newly developed finite difference method combined with L1-algorithm. The effects of involved parameters on velocity and temperature fields are presented graphically and analyzed in detail. Results indicate that, different from the classical result that Prandtl number only affects the heat transfer, it has remarkable influence on both the velocity and temperature boundary layers, the average Nusselt number rises dramatically in low Prandtl number, but increases slowly with the augment of Prandtl number. The maximum value of velocity profile and the thickness of momentum boundary layer increases with the augment of porosity and Darcy number. Moreover, the relaxation fractional derivative parameter accelerates the convection flow and weakens the elastic effect significantly, while the retardation fractional derivative parameter slows down the motion and strengthens the elastic effect.

Steady MHD mixed convection flow of a viscoelastic fluid over a magnetized convectively heated vertical surface with Hall current and induced magnetic field effects

“…where suction parameter S is assumed to be very small. Using Equations (19) and (20) in Equations (14) and (15) gives zeroth-and first-order perturbation equations, which are as follows: the zeroth-order equations are SINGH ET AL.…”

“…Thereafter, a series of investigations were performed by researchers to discuss the effect of external magnetic field on the flow characteristics of non‐Newtonian fluids. Some recent contributions to the topic are credited to Chamkha et al, 6 Shehzad et al, 7 Abbasbandy et al, 8 Ravikumar et al, 9 Sajid et al, 10 Khalid et al, 11 Nejad et al, 12 Gaffar et al, 13 Zhao et al, 14 Saqib et al, 15 Haung, 16 Amanulla et al, 17 Ali et al, 18 and Rehman et al 19 One of the subclasses of non‐Newtonian fluid is viscoelastic fluid. Analysis of the dynamics of the viscoelastic fluid in the presence of magnetic field is of great importance in practical point of view because of its tremendous applications in gas reservoirs, petroleum drilling, and production of complex multiphase products, such as paints, inks, and ceramic pastes.…”

Hall and ion-slip effects on MHD free convective flow of a viscoelastic fluid through porous regime in an inclined channel with moving magnetic field

“…Moreover, SAPUNKOV (1970), DJUKIC (1974) and COBBLE (1980) discussed the dynamics of non-Newtonian fluid in the presence of the magnetic field. Soon after, some eminent researchers (CHAMKHA et al, 2011;SHEHZAD et al, 2013;KHALID et al, 2015;NEJAD et al, 2015, ZHAO et al, 2017HUANG et al, 2018) discussed the influence of the magnetic field to the hydromagnetic flow of non-Newtonian fluids. Non-Newtonian fluids are divided into many categories, one of which is viscoelastic fluid.…”

Local and Nonlocal Differential Operators: A Comparative Study of Heat and Mass Transfers in MHD Oldroyd-B Fluid With Ramped Wall Temperature

“…25 Khan and Zaman 26 determined the solutions for velocity of OBF between two moving plates via Fourier and Laplace transformations. Zhao et al 27 evaluated the numerical solutions for fractional OBF in porous medium under the influence of heat transfer. Solutions for generalized OBF have been explored via fractional derivatives by Zheng et al [28][29][30] Zafar et al 31 studied an Oldroyd-B fluid for circular cylinders with noninteger-order derivatives.…”