Couple Stress Sodium Alginate-Based Casson Nanofluid Analysis through Fick’s and Fourier’s Laws with Inclined Microchannel

Abstract

Casson nanofluid plays a vital role in food industries with sodium alginate nanoparticles. That is why many researchers used Casson nanofluid in their study. Due to this, the main objective of this study is to investigate the inclined microchannel flow of a Casson nanofluid based on sodium alginate (SA) under a few stresses. Because the plate at $y=d$ is stationary and the plate at $y=0$ is in motion, the fluid flows. Physically existent things utilize partial differential equations as a method of derivation. By using dimensionless variables, the underlying PDEs are dimensionless. Applying Fourier’s and Fick’s laws to the time-fractional model makes the classical model dimensionally stable by generalization. A generalized fractional model is solved using the Laplace and Fourier integral transformations. In addition, the parametric influence of other physical elements, such as the Casson parameter, coupling velocity, temperature, and stress parameters, is considered (Grashof, Schmidt, and Prandtl numbers). Concentration distributions are shown using graphs and discussed with accompanying text. We compute and describe the Sherwood number, rate of heat transfer, and skin friction. It is concluded that skin friction and Nusselt number can be enhanced by adding nanoparticle. Also, the fractional derivative makes the study more realistic by incorporating Fick’s and Fourier’s laws as compared to the classical one.