MHD flow of time-fractional Casson nanofluid using generalized Fourier and Fick's laws over an inclined channel with applications of gold nanoparticles

Abstract

Gold nanoparticles are commonly used as a tracer in laboratories. They are biocompatible and can transport heat energy to tumor cells via a variety of clinical techniques. As cancer cells are tiny, properly sized nanoparticles were introduced into the circulation for invasion. As a result, gold nanoparticles are highly effective. Therefore, the current research investigates the magnetohydrodynamic free convection flow of Casson nanofluid in an inclined channel. The blood is considered as a base fluid, and gold nanoparticles are assumed to be uniformly dispersed in it. The above flow regime is formulated in terms of partial differential equations. The system of derived equations with imposed boundary conditions is non-dimensionalized using appropriate dimensionless variables. Fourier's and Fick's laws are used to fractionalize the classical dimensionless model. The Laplace and Fourier sine transformations with a new transformation are used for the closed-form solutions of the considered problem. Finally, the results are expressed in terms of a specific function known as the Mittag-Leffler function. Various figures and tables present the effect of various physical parameters on the achieved results. Graphical results conclude that the fractional Casson fluid model described a more realistic aspect of the fluid velocity profile, temperature, and concentration profile than the classical Casson fluid model. The heat transfer rate and Sherwood number are calculated and presented in tabular form. It is worth noting that increasing the volume percentage of gold nanoparticles from 0 to 0.04 percent resulted in an increase of up to 3.825% in the heat transfer rate.

Analytical Solution for MHD Casson Nanofluid Flow and Heat Transfer due to Stretching Sheet in Porous Medium

“…The obtained solutions are visually represented through the utilization of MATLAB software, and their characteristics are further scrutinized through an in-depth discussion. The analysis for velocity and temperature profiles are influenced by significant parameters on Casson fluid, porosity, magnetic field, nanoparticle volume fraction, and Prandtl number, which are varied within the range of 0.5 ≤ 𝛽 ≤ 2, 2 ≤ 𝐾 ≤ 8, 2 ≤ 𝑀 ≤ 8, 0.01 ≤ 𝜙 ≤ 0.04, and 1 ≤ Pr ≤ 6.2 [8,10,34]. All the computational in this study involves the dispersion of water based 𝐴𝑙 2 𝑂 3 and water based 𝑆𝑖𝑂 2 with their thermophysical characteristics is referred in Table 1.…”

Numerical insights of fractal–fractional modeling of magnetohydrodynamic Casson hybrid nanofluid with heat transfer enhancement

“…For t > 0, the left plate starts oscillations with velocity U 0 sin 𝜔t and the temperature of the left plate rises with Newtonian heating while the right plate is still stationary with surrounding temperature T a as given in Figure 1. By utilizing the Boussinseq's approximation [47] and Roseland approximations [48], the physical governing equations that govern the flow and partially coupled with the thermal field given as [30] 𝜌 hn𝑓 𝜕u 𝜕t…”

“…By utilizing the Boussinseq's approximation [47] and Roseland approximations [48], the physical governing equations that govern the flow and partially coupled with the thermal field given as [30] $$$$ {\rho}_{hnf}\frac{\partial u}{\partial t}={\mu}_{hnf}\left(1+\frac{1}{\eta}\right)\frac{\partial^2u}{\partial {y}^2}-{\sigma}_{hnf}{B}_0^2u-\frac{\mu_{hnf}{\phi}^{\ast }}{k_1}u+{\left(\rho {\beta}_T\right)}_{hnf}{g}_x\left(T-{T}_a\right), $$$$ $$$$ {\left(\rho {C}_p\right)}_{hnf}\frac{\partial T}{\partial t}={k}_{hnf}\frac{\partial T}{\partial {y}^2}+{\mu}_{hnf}\left(1+\frac{1}{\eta}\right){\left(\frac{\partial u}{\partial y}\right)}^2+{\sigma}_{hnf}{B}_0^2{u}&a...$$…”

“…For instance, Ramzan et al [29] studied the mixed convective fluid flow of Casson fluid through an inclined plate with chemical reaction and thermal radiation along a perpendicular magnetic field. Shah et al [30] examined the Casson fluid flow between two parallel plates through fractional derivatives of singular power law kernel with the use of gold nanoparticles. Dash et al [31] analyzed the Casson fluid flow through a pipe which is filled with porous material by considering blood as a base fluid.…”

The Generalized Similarity Measures Based on Complex Interval-Valued Hesitant Fuzzy Sets and Their Applications in Pattern Recognition and Medical Diagnosis

“…Mu et al [12] investigated multi-attribute DM (MADM) relying on interval-valued Pythagorean FS. Researchers can expand the theory of FS, IvFS to various other theories such as [13][14][15][16].…”