Existence of boundary layer nanofluid flow through a divergent channel in porous medium with mass suction/injection

Abstract

The steady two-dimensional, laminar, viscous, incompressible boundary layer flow of Cu/Ag-H₂O nanofluid in a diverging channel formed by two non-parallel walls in a Darcian porous medium is numerically studied in the presence of mass suction/injection of equal magnitude on both the walls. Here, divergent flow is generated by a line source of fluid volume at the intersection of channel walls. Using similarity transformations, the non-linear governing PDEs are transformed into self-similar coupled non-linear ODEs and they are solved numerically with the help of MATLAB-built solver “bvp4c”. The conditions for the existence of boundary layer flow structure for nanofluid through divergent channel in porous medium are obtained. The analysis reveals that when the permeability parameter $K$ and nanofluid-volume-fraction-related parameter $\phi_{1}$ are chosen in a specific manner such that they satisfy the condition $K > 2\phi_{1}$ then boundary layer flow exists, preventing separation for any mass suction/injection or even in the absence of mass suction/injection. A similar velocity field rises with permeability parameter, which exhibits opposite behavior with nanoparticle volume fraction. Also temperature increases with nanoparticle volume fraction, permeability parameter, and Eckert number, and decreases with power-law exponent (related to variable wall temperature). Skin-friction coefficient and heat transfer rate for Cu-water nanofluid are stronger when compared with Ag-water nanofluid.

Abbreviations

$A_{1}$ :

Nanoparticle parameter

$C_{f}$ :

Skin-friction coefficient

Ec :

Eckert number

$f$ :

Dimensionless velocity

$k$ :

Variable permeability

$k_{0}$ :

A constant

$K$ :

Permeability parameter

$L$ :

Characteristic length

$n$ :

Power-law exponent

$Nu_{x}$ :

Local Nusselt number

p :

Pressure

$\Pr$ :

Prandtl number

$Q$ :

Volume flow rate

$q_{w}$ :

Wall heat flux

${\text{Re}}_{x}$ :

Local Reynolds number

$S$ :

Suction/injection parameter

$T$ :

Temperature

$T_{0}$ :

Constant depending upon thermal properties

$T_{w}$ :

Temperature at the surface

$T_{\infty }$ :

Ambient temperature

$u$,$v$:

Velocity components along, respectively, x- and y-axes

$U$ :

Free-stream velocity

$U_{0}$ :

Characteristic velocity

$v_{w}$ :

Suction/injection velocity

x, y:

Cartesian coordinate measured along the surface and normal to it, respectively