Thermal Marangoni flow past a permeable stretching/shrinking sheet in a hybrid Cu-Al2O3/water nanofluid

The present study accentuates the Marangoni convection flow and heat transfer characteristics of a hybrid Cu-Al2O3/water nanofluid past a stretching/shrinking sheet. The presence of surface tension due to an imposed temperature gradient at the wall surface induces the thermal Marangoni convection. A suitable transformation is employed to convert the boundary layer flow and energy equations into a nonlinear set of ordinary (similarity) differential equations. The bvp4c solver in MATLAB software is utilized to solve the transformed system. The change in velocity and temperature, as well as the Nusselt number with the accretion of the dimensionless Marangoni, nanoparticles volume fraction and suction parameters, are discussed and manifested in the graph forms. The presence of two solutions for both stretching and shrinking flow cases are noticeable with the imposition of wall mass suction parameter. The adoption of stability analysis proves that the first solution is the real solution. Meanwhile, the heat transfer rate significantly augments with an upsurge of the Cu volume fraction (shrinking flow case) and Marangoni parameter (stretching flow case). Both Marangoni and Cu volume fraction parameters also can decelerate the boundary layer separation process

Radiative flow of magnetic nanofluids over a moving surface with convective boundary condition

The influence of convective boundary conditions and heat radiation on magnetic nanofluids (MNFs) flowing through a permeable moving plate is investigated numerically in this study. The governing partial differential equations (PDEs) are transformed into ordinary differential equations (ODEs) using suitable similarity variables. The ODEs are solved by implementing the built-in solver in Matlab called bvp4c. The stability analysis has supported our initial presumption that only the first solution is stable. The thermal performance between cobalt ferrite nanofluid and manganese-zinc ferrite nanofluid is compared, and it appears that cobalt ferrite nanofluid has a slightly better performance in heat transportation compared to manganese-zinc ferrite nanofluid. We also considered a higher amount of thermal radiation and Biot number to scrutinize the heat transfer performance of MNF, and we found out that a greater amount of these parameters are effective in improving the heat transfer rate

Thermal Marangoni flow past a permeable stretching/shrinking sheet in a hybrid Cu-Al2O3/water nanofluid

The present study accentuates the Marangoni convection flow and heat transfer characteristics of a hybrid Cu-Al2O3/water nanofluid past a stretching/shrinking sheet. The presence of surface tension due to an imposed temperature gradient at the wall surface induces the thermal Marangoni convection. A suitable transformation is employed to convert the boundary layer flow and energy equations into a nonlinear set of ordinary (similarity) differential equations. The bvp4c solver in MATLAB software is utilized to solve the transformed system. The change in velocity and temperature, as well as the Nusselt number with the accretion of the dimensionless Marangoni, nanoparticles volume fraction and suction parameters, are discussed and manifested in the graph forms. The presence of two solutions for both stretching and shrinking flow cases are noticeable with the imposition of wall mass suction parameter. The adoption of stability analysis proves that the first solution is the real solution. Meanwhile, the heat transfer rate significantly augments with an upsurge of the Cu volume fraction (shrinking flow case) and Marangoni parameter (stretching flow case). Both Marangoni and Cu volume fraction parameters also can decelerate the boundary layer separation process

MHD flow of hybrid nanofluid past a stretching sheet: double stratification and multiple slips effects

Studies of hybrid nanofluids flowing over various physical geometries and conditions are popular among researchers to understand the behavior of these fluids. Thenceforth, the numerical solutions for hybrid Ag-CuO/H2 O nanofluid flow over a stretching sheet with suction, magnetic field, double stratification, and multiple slips effects are analyzed in the present study. Governing equations and boundary conditions are introduced to describe the flow problem. Then, similarity variables are applied to transform the equations into non-linear ordinary differential equations and boundary conditions. The numerical com-putation for the problem is done in Matlab (bvp4c solver), and the results are presented in tables and graphs. It is found that the rise in solutal slip and stratification parameters reduces the Sherwood number. Meanwhile, the increase in thermal slip and stratification parameters lowers the Nusselt number. The skin friction coefficient is observed to increase with the augmentation of the hydrodynamic slip parameter

Hybrid nanofluid stagnation point flow past a slip shrinking Riga plate

Magnetic nanofluids cover many of uses since their characteristics are externally controllable, and their physical properties may vary with the nanoparticle volume fraction and magnetic field strength. Hybrid nanofluid also has been commercialized as the advancement of traditional nanofluid. The preliminary research on hybrid magnetic nanofluids inspired the present study to discover the stagnation-point flow of hybrid magnetite-cobalt ferrite/water nanofluid towards a shrinking Riga plate with the presence of velocity slip. The complex governing model of the flow is simplified by implementing the similarity transformation. A well-established numerical package, namely bvp4c in MATLAB, is used for numerical calculation as well as stability analysis. Two solutions are found due to the opposing flow from the shrinking Riga plate. From the stability analysis, the first solution which fulfills the boundary condition is the physically stable solution. The rising values of electromagnetohydrodynamic (EMHD) parameter and cobalt ferrite concentration augment the skin friction coefficient. Specifically, the critical point is lessened by 3% when the EMHD parameter is augmented from 0.3 to 0.5 and 0.5 to 0.7, which concludes that a suitably higher EMHD parameter could prevent the separation of the boundary layer. The heat transfer progress is actively performed with the enhancement of EMHD and velocity slip parameters which conclusively shows the suitability of these parameters in developing the cooling heat transfer fluid

Impact of suction and thermal radiation on unsteady ternary hybrid nanofluid flow over a biaxial shrinking sheet

The use of hybrid nanofluids in practical applications is pivotal for enhanced heat transfer efficiency especially for electronics cooling, and manufacturing processes. This study delves into numerically investigating the unsteady water-based (alumina+copper+titanium dioxide) ternary hybrid nanofluid flow over a permeable biaxial shrinking sheet, considering the influence of thermal radiation. The model, initially formulated as partial differential equations (PDEs), is adeptly transformed into ordinary differential equations (ODEs) via established similarity transformations. Subsequently, a numerical solution employing the finite difference scheme in bvp4c MATLAB unravels the behaviors of crucial physical quantities—across various parameter configurations. Remarkably, this study reveals the presence of two potential solutions, among which only one exhibits physical stability. Notably, the findings underscore the efficacy of enlarging the boundary suction parameter and diminishing thermal radiation for augmenting heat transfer within the specified conditions of ternary hybrid nanofluid. A noteworthy finding of this study reveals that an increase in the boundary suction parameter by 4% leads to a remarkable 9% delay in the boundary layer separation of the ternary hybrid nanofluid, thus maintaining the laminar phase flow. This study offers crucial guidance and insights for researchers and practitioners delving into the mathematical or experimental aspects of ternary hybrid nanofluid dynamics

Magnetohydrodynamic and viscous dissipation effects on radiative heat transfer of non-newtonian fluid flow past a nonlinearly shrinking sheet: Reiner–Philippoff model

Heat transfer is an important process in many engineering, industrial, residential, and commercial buildings. Thus, this study aims to analyse the effect of MHD and viscous dissipation on radiative heat transfer of Reiner–Philippoff fluid flow over a nonlinearly shrinking sheet. By adopting appropriate similarity transformations, the partial derivatives of multivariable differential equations are transformed into the similarity equations of a particular form. The resulting mathematical model is elucidated in MATLAB software using the bvp4c technique. To determine the impact of physical parameters supplied into the problem, the results are shown in the form of tables and graphs. The findings reveal that the heat transfer rate reduces as the Eckert number and radiation parameter are introduced in the operating fluid. However, increasing the magnetic parameter raises both the skin friction coefficient and the local Nusselt number, which impulsively improves the heat transfer performance. The suction effect has a noticeable influence on the Reiner–Philippoff fluid, since increasing the suction parameter's value is seen to enhance the skin friction coefficient and the heat transfer performance. The dual solutions are established, leading to the stability analysis that supports the first solution's validity

A Stability Analysis For Magnetohydrodynamics Stagnation Point Flow With Zero Nanoparticles Flux Condition And Anisotropic Slip

The numerical study of nanofluid stagnation point flow coupled with heat and mass transfer on a moving sheet with bi-directional slip velocities is emphasized. A magnetic field is considered normal to the moving sheet. Buongiorno’s model is utilized to assimilate the mixed effects of thermophoresis and Brownian motion due to the nanoparticles. Zero nanoparticles’ flux condition at the surface is employed, which indicates that the nanoparticles’ fraction are passively controlled. This condition makes the model more practical for certain engineering applications. The continuity, momentum, energy and concentration equations are transformed into a set of nonlinear ordinary (similarity) differential equations. Using bvp4c code in MATLAB software, the similarity solutions are graphically demonstrated for considerable parameters such as thermophoresis, Brownian motion and slips on the velocity, nanoparticles volume fraction and temperature profiles. The rate of heat transfer is reduced with the intensification of the anisotropic slip (difference of two-directional slip velocities) and the thermophoresis parameter, while the opposite result is obtained for the mass transfer rate. The study also revealed the existence of non-unique solutions on all the profiles, but, surprisingly, dual solutions exist boundlessly for any positive value of the control parameters. A stability analysis is implemented to assert the reliability and acceptability of the first solution as the physical solution

Flow and heat transfer of hybrid nanofluid induced by an exponentially stretching/shrinking curved surface

The efficient performance of heat transfer fluid in terms of thermal conductivity plays a significant role in thermal engineering activities. In this work, the flow of boundary layer and heat transfer of hybrid nanofluid induced by an exponentially permeable stretching/shrinking curved surface is modelled and scrutinized numerically. Facilitated by bvp4c function, the ordinary differential equations are being solved. The implications of some intended parameters towards the physical quantities are plotted, while the comparison of results for the validation purpose is also tabulated. We found out that the boundary layer separation is deferred as copper volume fraction and curvature parameters increased. The stability analysis for the flow is conducted as the dual solutions are visible. The first (second) solution of the hybrid nanofluid flow is observed to be stable (unstable). For the physical solution, the increment in copper volume fraction leads to the accretion of the skin friction coefficient at the shrinking surface but has reduced the local Nusselt number. The presence of hybrid nanofluid has enhanced the velocity and temperature profiles. Generally, this study provides the initial prediction for the scientist and engineers in controlling the parameters to achieve the optimum desires for the related practical applications

Brownian and thermophoresis diffusion effects on magnetohydrodynamic Reiner–Philippoff nanofluid flow past a shrinking sheet

The aim of this paper is to highlight the output of the investigation on the MHD and radiative flow and thermal characteristics of a non-Newtonian Reiner–Philippoff nanofluid with Brownian and thermophoresis diffusion effects. The model studied is embedded in the Buongiorno theory. This unique model is designed to observe both shear thickening and shear thinning properties on that particular fluid with embedded Brownian and thermophoresis diffusion implications. The proposed model consists of continuity, momentum, energy, and concentration equations constructed using the theoretical assumptions and are reduced to a set of ordinary differential equations (ODEs) before solving it using the bvp4c function in MATLAB software. Two solutions are observed, and their physical significance is justified using the temporal stability analysis. From the standpoint of the Reiner–Philippoff fluid parameter, the skin friction coefficient as well as the heat and mass transfer rates are at maximum for the shear-thickening fluid followed by the Newtonian and shear-thinning fluids. The thermophoresis parameter is noticed to decline the heat and mass transfer rate whereas the Brownian motion parameter boosts the mass transfer rate but decreases the heat transfer rate