Time–space dependent fractional boundary layer flow of Maxwell fluid over an unsteady stretching surface

A Chebyshev Spectral Method for Heat and Mass Transfer in MHD Nanofluid Flow With Space Fractional Constitutive Model

“…In the aforementioned study, the case < α < 1 was proposed to describe shear thickening fluids, 2 > α > 1 model shear thinning fluids and α = 1, viscous fluids. The partially coupled system of equations describing the transport processes is given as (Chen et al, 2015;Khan and Pop, 2010) ∂u ∂x…”

“…They conducted a theoretical analysis of a steady pipe flow of a laminar incompressible flow, obtaining the frictional head loss, velocity profile and yield stress in terms of the fractional Reynolds number. Chen et al (2015) investigated the fractional boundary layer flow of a Maxwell fluid on an unsteady stretching surface. The constitutive equation was recast so as to introduce space-time dependent fractional derivatives.…”

A space fractional constitutive equation model for non-Newtonian fluid flow

“…For example, the critical Reynolds number of expansion fluid (0 < α < 1) is larger than the pseudoplastic fluid (1 < α < 2), when the diameter of the pipe is D = 1.0 m. Another interesting result is that the diameter D plays a more important role in determining the fractional Reynolds number, in comparison with Newtonian fluid. Extensive experiments are required in a future study to determine the feasibility of the generalized, fractional Reynolds number (21) in distinguishing flow patters of various non-Newtonian fluids.…”

“…For example, Ochoa-Tapia et al [15] provided a brief mathematical derivation of fractional Newton's law for viscosity based on Taylor series, to obtain a fractional-order Darcy's law for describing shear stress phenomena in non-homogeneous porous media. Chen et al [21] investigated the effects of model parameters to simulate the boundary layer flow of Maxwell fluids on an unsteady stretching surface, using the time-space fractional Navier-Stokes equation built upon a fractional-derivative based constitutive equation. However, the physical analysis and description of non-Newtonian fluid flow based on the fractional-derivative constitutive equation, which addresses the nonlocality of the velocity field (represented by a strong correlation between velocities), has not been investigated, hindering practical application of the space-fractional models.…”

MHD Maxwell Fluid Flow in Presence of Nano-Particle Through a Vertical Porous-Plate With Heat-Generation, Radiation Absorption and Chemical Reaction

“…Hayat and coauthors also considers Maxwell fluid flow in a rotating frame , over a stretching surface (Hayat et al 2009), effect of thermal radiation, thermophoresis and Joule heating on Maxwell fluid flow (Hayat and Qasim, 2010), channel flow of Maxwell fluid (Hayat et al 2011) in their investigation. Chen et al (2015) analysed hydrodynamics of Maxwell fluid flow over an unsteady stretching surface. The study of MHD Maxwell fluid flow over a stretching sheet with nanoparticles and presence of chemical reaction was reported by Afify and Elgazery …”