Computational study of magneto-convective non-Newtonian nanofluid slip flow over a stretching/shrinking sheet embedded in a porous medium

Abstract

A Steady flow of two-dimensional magnetohydrodynamic non-Newtonian fluid over a stretching/shrinking sheet in the presence of nanoparticles is exemplified theoretically and numerically. In this problem, we have considered the thermal radiation and adjust the hot fluid along with the lower surface of the wall namely convective boundary-layer slip. To the best of the authors' knowledge, this parameter was here incorporated for the first time in such field of magnetofluid dynamic characteristics of conducting bio-nanofluids embedded in a porous medium. The solution of governing dimensionless problem is executed by Legendre-based collocation method (LBCM). It is vital to remark that the account for the velocity slip in the boundary conditions increases the velocity component. Also, the liquid acts as a Newtonian fluid when the Casson parameter increases. Consequently, those parameters contribute to the cooling plate, while others have the opposite effect. Thus, by selecting the appropriate fluid model and adjusting the governing parameters, the cooling/heating mechanism can be created. These results will assist the engineers in designing applications that require high-temperature nanomaterials processing operations.

Introduction

Non-Newtonian fluids have been extensively studied in recent years by several researchers and scientists due to their applications in a wide range of human endeavors, including sciences, technology, chemical, and engineering practices, as well as manufacturing and industrial processes. It is well established that the local strain rate is directly proportional to the viscous stresses induced by Newtonian fluid flow. This means that the relationship between viscous stresses caused by flow is not linear or time-dependent. Examples of Non-Newtonian fluids include blood, cosmetics, toothpaste, ketchup, food, soaps, and pharmaceuticals. Non-Newtonian liquids are classified into 3 groups: viscoelastic, time-independent, and time-dependent. The temperature, shear rate, and time all influence the viscosity of time-dependent non-Newtonian fluids. Non-Newtonian fluids that are time-independent are those in which only the shear rates at a given time are affected by stress. Among these fluid models, Casson Fluid (CF) is known as non-Newtonian due to its rheological characteristics in connection with shear stress. Casson fluid (CF) has received significant attention in many fields including science, engineering, and food processing. Oil, honey, jelly, and paint are common examples of common commodities exhibiting CF properties [1]. It acts like an elastic solid at low shear stress; also, it acts like a Newtonian fluid above the critical stress value [2], [3]. The pioneering work regarding the CF model was the work of Casson which defines the pigment-oil suspension prediction flow [4]. The boundary layer flow of CF over a dissipated stretched cylinder was investigated by [5]. The authors demonstrated that the increasing Casson parameter reduces the yield stress factor which in turn decreases the fluid flow and the boundary layer thickness The effect of Dufour and Soret on magnetohydrodynamic (MHD) flow of Casson fluid was solved analytically by [6]. They found that the parameter Casson decreases both the speed and thickness of the boundaries layer flow. The Computational simulation of Non-Newtonian CF flow over a variable chemical reaction and linear stratification Riga plate has been investigated by [7]. Meanwhile, the work of Iqbal and Azha examined the Non-Newtonian CF on the Riga plate of stagnation point boundary layer flow [8]. So far, many researchers are making important contributions to non-Newtonian fluid dynamics studies [9], [10], [11], [12], [13].

Magnetic nanofluid technologies are becoming more attractive in industries due to a variety of applications in biomaterials for wound treatment [14], gastrointestinal drugs [15], [16], sterilizing devices [17], [18], and other related fields. However, magnetic fields are known to be utilized for the regulation of electrically conducting nanofluids that can be orchestrated to accomplish the intended results in applications. Several studies have revealed that magnetic nanofluids suspensions have exceptional performance in which nanoparticles have the same magnitude order as DNA or protein [19], [20]. The Bio suspensions based on magnetic nanoparticles have recently been used in targeted drug release, magnetic resonance imaging (MRI), and asthma treatment with magnetic nano-suspensions. The motivation for this new kind of nanofluid is to understand the magnetofluid dynamic properties of conducting bio-nanofluids as well as thermophysical properties due to its practical utilization in wide applications such as tribology, drug, delivery, propulsion, burn injury treatment, etc. In brief, we intend to investigate the slip-controlled electrically conducting flow of bio-nano-polymers passing through a shrinking or stretching sheet under a transverse magnetic field. The key characteristics revealed are Brownian motion and thermophoresis, which are regarded as the key mechanisms that improve thermal conductivity (the primary advantage of nanofluids). Uddin et al. [21] utilized the model of bio-nano-materials processing to investigate the effect of the Magnetic field on convective boundary layer flow and observed that the velocity reduces due to rising in Magnetic field parameter. Crainic et al. [22] exhibited that the utilizing of Magnetic fields and nanomagnetic fluids increase the performance of (Nanomagnetic Fluids) MNF and RTM–Resin Transfer Molding (RTM). While Sheikholeslami et al. [23] discussed the significance of Magnetic field on Cupper–water nanofluid Flow using the control volume finite element method (CVFEM). Obalalu et al. [24] studied the thermodynamics process with heat transfer of electrical conducting fluid for an unsteady vertical porous channel fluid flow with an external magnetic field. The Magnetohydrodynamic micropolar nanofluid past a permeable stretching/shrinking sheet with Newtonian heating were investigate by [25]. The effect of thermal radiation on engine oil nanofluid flow over a permeable wedge under convective heating: Keller box method were study via [26]. The Internal heat generation on bioconvection of an MHD nanofluid flow due to gyrotactic microorganisms were investigate via [27]. The Nodal/Saddle stagnation point slip flow of an aqueous convectional magnesium oxide–gold hybrid nanofluid with viscous dissipation were study via [28]. The MHD rotating flow of a Maxwell fluid with Arrhenius activation energy and non-Fourier heat flux model were study via [29].

Since then, numerous scientists have studied the numerical modeling of bio-nano-materials processing on heat and mass transfer with the inclusion of multiple slip boundary conditions either feature first and second-order velocity slip condition, thermal convective heating, Temperature jump, prescribed surface heat flux, and mass slip. However, the generalization of Temperature jump and prescribed surface heat flux is thermal convective heating. Generally, the Knudsen number is typically utilized as a parameter in this research, and the conventional no-slip condition is obtained when this value is zero. Therefore, for a Knudsen number smaller than 0.001 the continuum flow hypothesis remains true. The Slip flow is defined as a flow that has a Knudsen number of 0.001 to 0.1. However, the performance of the slip flow regime with the fluid velocity substantially differs from the conventional no slip-flow [30]. nevertheless, the Navier-Stokes equations still compile to the flow of the slip system due to the micro-scale dimensions. The slip flow in the literature was studied for various flow configurations. Amongst these articles, the experimental and theoretical slips model of the gas microflow were studied by [31]. Andersson [32] examined the slip fluid over an impermeable stretching surface. In many engineering processes [35], [36], convective heating occurs such as thermal energy storage, and nuclear plants. Recently, [33] utilized the model of non-Newtonian Casson fluid to study the thermodynamics process of thermal radiation and with convective boundary conditions. Akbar et al. [34] revealed that the utilizing of Convective heating and thermal radiation parameter enhanced the behavior of the heat transfer fluids. The thermal conductivity of natural convective of entropy production induced by a stretching surface with convective surface boundary conditions and velocity slip using Optimal Homotopy Analysis Method (OHAM) were investigated by [34]. The bioconvection in a convectional nanofluid flow containing gyrotactic microorganisms over an isothermal vertical cone embedded in a porous surface with chemical reactive species were investigated by [35].

Based on the discussions above, the objective of this current exploration focuses on Slip Effects and magnetic field on convective non-Darcy MHD Casson(non-Newtonian) bio-nanofluid flow over a shrinking or stretching sheet. The consequence of the bio-nano materials and hydromagnetic Casson (non-Newtonian) fluid needs more attention on this topic. However, it is observed that these present models are the synthesis of bio-magnetic nanofluids of potential interest in wound treatments, skin repair, and smart coatings for biological devices. The Legendre-based collocation method and MATHEMATICAL 11.0 software are employed to achieve an approximate solution of the flow distributions and characteristics.