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Abstract
Polymeric enrobing flows are important in industrial manufacturing technology and process systems. Such flows are non-Newtonian. Motivated by such applications, in this article we investigate the nonlinear steady state boundary layer flow, heat, and mass transfer of an incompressible Jefferys non-Newtonian fluid past a vertical porous plate in a non-Darcy porous medium. The transformed conservation equations are solved numerically subject to physically appropriate boundary conditions using a versatile, implicit, Keller-box finite-difference technique. The numerical code is validated with previous studies. The influence of a number of emerging non-dimensional parameters, namely Deborah number (De), Darcy number (Da), Prandtl number (Pr), ratio of relaxation to retardation times (λ), Schmidt number (Sc), Forchheimer parameter (Λ), and dimensionless tangential coordinate (ξ) on velocity, temperature, and concentration evolution in the boundary layer regime are examined in detail. Furthermore, the effects of these parameters on surface heat transfer rate, mass transfer rate, and local skin friction are also investigated. It is found that the boundary layer flow is decelerated with increasing De and Forchheimer parameter, whereas temperature and concentration are elevated. Increasing λ and Da enhances the velocity but reduces the temperature and concentration. The heat transfer rate and mass transfer rates are found to be depressed with increasing De and enhanced with increasing λ. Local skin friction is found to be decreased with a rise in De, whereas it is elevated with increasing λ. An increasing Sc decreases the velocity and concentration but increases temperature.
NOMENCLATURE
| B0 | = | externally imposed magnetic field |
| C | = | concentration |
| Cf | = | skin friction coefficient |
| Da | = | Darcy number |
| De | = | Deborah number |
| Dm | = | mass (species) diffusivity |
| f | = | non-dimensional steam function |
| g | = | acceleration due to gravity |
| Gr | = | Grashof (free convection) number |
| K | = | thermal diffusivity |
| N | = | buoyancy ratio parameter |
| Nu | = | local Nusselt number |
| Pr | = | Prandtl number |
| T | = | temperature of the Jeffery fluid |
| S | = | Cauchy stress tensor |
| Sc | = | Schmidt number |
| Sh | = | Sherwood number |
| u, v | = | non-dimensional velocity components along the x- and y-directions, respectively |
| x | = | stream-wise coordinate |
| y | = | transverse coordinate |
Greek Symbols
| α | = | thermal diffusivity |
| β | = | coefficient of thermal expansion |
| β* | = | coefficient of concentration expansion |
| λ | = | ratio of relaxation to retardation times |
| λ1 | = | retardation time |
| η | = | dimensionless radial coordinate |
| μ | = | dynamic viscosity |
| v | = | kinematic viscosity |
| θ | = | non-dimensional temperature |
| φ | = | non-dimensional concentration |
| Γ | = | inertial drag coefficient |
| Λ | = | local inertial drag coefficient (Forchheimer parameter) |
| ρ | = | density of Jeffery fluid |
| ξ | = | dimensionless tangential coordinate |
| Ψ | = | dimensionless stream function |
Subscripts
| w | = | surface conditions on plate (wall) |
| ∞ | = | free stream conditions |