Soret and Dufour effects on unsteady MHD second-grade nanofluid flow across an exponentially stretching surface

Abstract

The unsteady energy and mass transport of magnetohydrodynamics (MHD) second grade nanofluid via an exponentially extending surface with Dufour and Soret effects are investigated in this study. Variable thermal conductivity and mixed convection effects are used to investigate the heat transfer mechanism. There are also new characteristics such as slip flow, viscous dissipation, Brownian motion, nonlinear thermal radiation, and thermophoresis. In the problem formulation, the boundary-layer approximation is used. Using the suitable transformations, the energy, momentum, and concentration equations are generated into non-linear ordinary differential equations (ODEs). The solution to the resultant problems was calculated via the Homotopy analysis method (HAM). The effects of environmental parameters on velocity, temperature, and concentration profiles are graphically depicted. When comparing the current results to the previous literature, there was also a satisfactory level of agreement. In comparison to a flow based on constant characteristics, the flow with variable thermal conductivity is shown to be significantly different and realistic. The temperature of the fluid grew in direct proportion to the thermophoresis motion, buoyancy ratio, and Brownian motion parameters. According to the findings, the slippery porous surface may be employed efficiently in chemical and mechanical sectors that deal with a variety of very viscous flows.

Figure 1

Flow geometry.

Figure 2

Variation of $f^{\prime }\left(\eta \right)$ for M.

Figure 3

Variation of $f^{\prime }\left(\eta \right)$ for $\alpha .$

Figure 4

Variation of $f^{\prime }\left(\eta \right)$ for Gr (a) and Gm (b).

Figure 5

Variation of (a)$f^{\prime }\left(\eta \right)$ and (b) $\theta \left(\eta \right)$ for $\beta .$

Figure 6

Variation of $\theta \left(\eta \right)$ for Nr (a) and $\theta w$ (b).

Figure 7

Variation of $\theta \left(\eta \right)$ for $Ec.$

Figure 8

Variation of $\theta \left(\eta \right)$ for Nt (a) and Nb (b).

Figure 9

Variation of $\theta \left(\eta \right)$ for Df (a) and δ (b).

Figure 10

Variation of $\varphi \left(\eta \right)$ for Sr (a) and Sc (b).

Figure 11

Impacts of M and $\alpha$ on $C_f.$

Figure 12

Impacts of Nt and $\mathit{Nb}$ on $C_f.$

Figure 13

Impacts of Nr and $\sigma$ on $N{u}_x.$

Figure 14

Impacts of Sc and $\mathit{Sr}$ on $S{h}_x.$