Entropy analysis of unsteady MHD three-dimensional flow of Williamson nanofluid over a convectively heated stretching sheet

This article addresses an investigation of the entropy analysis of Williamson nanofluid flow in the presence of gyrotactic microorganisms by considering variable viscosity and thermal conductivity over a convectively heated bidirectionally stretchable surface. Heat and mass transfer phenomena have been incorporated by taking into account the thermal radiation, heat source or sink, viscous dissipation, Brownian motion, and thermophoretic effects. The representing equations are nonlinear coupled partial differential equations and these equations are shaped into a set of ordinary differential equations via a suitable similarity transformation. The arising set of ordinary differential equations was then worked out by adopting a well-known scheme, namely the shooting method along with the Runge-Kutta-Felberge integration technique. The effects of flow and heat transfer controlling parameters on the solution variables are depicted and analyzed through the graphical presentation. The survey finds that magnifying viscosity parameter, Weissenberg number representing the non-Newtonian Williamson parameter cause to retard the velocity field in both the directions and thermal conductivity parameter causes to reduce fluid temperature. The study also recognizes that enhancing magnetic parameters and thermal conductivity parameters slow down the heat transfer rate. The entropy production of the system is estimated through the Bejan number. It is noticeable that the Bejan number is eminently dependent on the heat generation parameter, thermal radiation parameter, viscosity parameter, thermal conductivity parameter, and Biot number. The skillful accomplishment of the present heat and mass transfer system is achieved through the exteriorized choice of the pertinent parameters.     

MHD mixed convection of a Cu–water nanofluid flow through a channel with an open trapezoidal cavity and an elliptical obstacle

In the current work, numerical simulations are achieved to study the properties and the characteristics of fluid flow and heat transfer of (Cu–water) nanofluid under the magnetohydrodynamic effects in a horizontal rectangular canal with an open trapezoidal enclosure and an elliptical obstacle. The cavity lower wall is grooved and represents the heat source while the obstacle represents a stationary cold wall. On the other hand, the rest of the walls are considered adiabatic. The governing equations for this investigation are formulated, nondimensionalized, and then solved by Galerkin finite element approach. The numerical findings were examined across a wide range of Richardson number (0.1 ≤ Ri ≤ 10), Reynolds number (1 ≤ Re ≤ 125), Hartmann number (0 ≤ Ha ≤ 100), and volume fraction of nanofluid (0 ≤ φ ≤ 0.05). The current study's findings demonstrate that the flow strength increases inversely as the Reynolds number rises, which pushes the isotherms down to the lower part of the trapezoidal cavity. The Nu_avg rises as the Ri rise, the maximum Nu_avg = 10.345 at Ri = 10, Re = 50, ϕ = 0.05, and Ha = 0; however, it reduces with increasing Hartmann number. Also, it increase by increasing ϕ, at Ri = 10, the Nu_avg increased by 8.44% when the volume fraction of nanofluid increased from (ϕ = 0–0.05).     

Cubic B-splines method for Hall and ion slip impacts on unsteady MHD rotating flow past a vertical moving porous plate

The heat and mass transfer of unsteady magnetohydrodynamic (MHD) flow of Newtonian fluid with Hall current and ion-slip currents due to vast possible engineering applications is very important in areas like power generators, MHD accelerators, refrigeration coils, electric transformers, and heating elements. A quality-based research on Hall and ion-slip consequences on the rotating unsteady MHD flow past an infinite perpendicular moving absorbent plate have not been performed. Therefore, the Hall and ion-slip consequences on rotating unsteady MHD flow past an infinite perpendicular moving absorbent plate have not been performed. The similarity transformations are engaged to transfer the governing partial differential equations within favor of the scheme of nonlinear ordinary differential equations and elucidated numerically making use of cubic B-splines collocation mechanism. The influences of felicitous parameters on basic equations are remarked on through graphical profiles. Even though the computational estimations of frictional forces, Nusselt number, and Sherwood number for various parameters are distributed in tabular format and exchanged of views comparatively.     

Unconditional stability and error estimates of the modified characteristics FEMs for the time-dependent incompressible MHD equations

This paper focuses on the unconditional stability and convergence of characteristics type methods for the time-dependent incompressible MHD equations. For this purpose, we introduce a new characteristics time-discrete system. The optimal error estimates in $L^2$ and $H^1$ norms for the typical modified characteristics finite element method unconditionally can be deduced, while the whole previous works require certain time-step restrictions. Some numerical experiments document performance of the characteristics type methods for the time-dependent incompressible MHD equations.     

Effect of nonlinear thermal radiation on 3D magneto slip flow of Eyring-Powell nanofluid flow over a slendering sheet with binary chemical reaction and Arrhenius activation energy

An analysis is performed to study the combined effects of nonlinear thermal radiation, Arrhenius activation energy, chemical reaction and heat generation/absorption on the steady three-dimensional magnetohydrodynamic flow of Eyring-Powell nanofluid flow over a slendering stretchable sheet with velocity, thermal and solutal slips. The prevailing partial differential equations are transmuted into coupled non-linear ordinary differential equations via with the suitable similarity transformations. The resultant non-linear coupled differential equations are solved numerically by using the R-K 4^th order method along with shooting scheme. The results are calculated to measure the influence of sundry parameters on velocity, temperature, concentration, shear stress, temperature gradient and concentration gradient are presented graphically and in tabular form. It is noticed that the temperature is more impactable for higher values of radiative heat transport. The local Sherwood number decays exponentially for all the values of the chemical reaction parameter. We compared the present results for the limiting cases with previously published results, which has shown reliability and efficiency.     

Adomian decomposition method for the MHD flow of a viscous fluid with the influence of dissipative heat energy

An investigation is carried out on the effect of dissipative heat energy on the flow of an electrically conducting viscous fluid past a shrinking sheet. Both viscous and Joule dissipation effects are considered along with heat generation/absorption for the enhancement of heat transfer properties. The governing nonlinear coupled partial differential equations are transformed into nonlinear ordinary differential equations by a suitable choice of similarity transformations. However, the complex transformed equations are solved by an approximate analytical method known as the Adomian decomposition method with a suitable initial guess solution assumed from the known initial conditions. Moreover, the behavior of several parameters characterizing the flow phenomena are studied via graphs and the numerical computations for the engineering coefficients are obtained and presented through tables. However, the major outcomes of the results are that a higher suction is required to resist the fluid temperature and sinks as well as the dissipative heat energy favors enhancing the fluid temperature at all points in the flow domain.     

3D MHD cross flow over an exponential stretching porous surface

The present study aims to investigate the effects of thermal‐diffusion and diffusion‐thermo onan magnetohydrodynamic convective flow of viscous fluids over an exponentially stretching sheet. Thermal radiation effects are also considered in the study. This analysis is carried out in three dimensions and a similarity transformation is adopted to get a set of ordinary differential equations from a set of partial differential equations. And the Fourth‐order Runge‐Kutta method and shooting technique along with the secant method are employed to find out an iterative solution. We also analyze here the influence of the variable magnetic field, nonuniform permeability and variable chemical reaction on the fluid flow. The impact of various pertinent parameters of interest has extensively been explored through graphs and tables. The major findings of the present study are that resistive Lorentz force diminishes the fluid velocity and uplifts the thermal as well as concentration fields. Inclusion of porous matrix improves the viscous drag force which in turn augments wall shear stresses and peters out the heat and mass transfer rates from the sheet. In addition, the thermal expansion coefficient has an inverse relation with temperature.     

Numerical study of hydrodynamic flow of a Casson nanomaterial past an inclined sheet under porous medium

The main aim of the current paper is to investigate the mass and heat transportation of a Casson nanomaterial generated by the inclination of the surface. The magnetic field effect along with suction or injection are considered. The working nanomaterial is taken into consideration based on the concept of the Buongiorno nanofluid theory, which explores the thermal efficiencies of liquid flows under movement of Brownian and thermophoretic phenomena. The emergent system of differential expressions is converted to dimensionless form with the help of the appropriate transformations. This system is numerically executed by the implementation of Keller–Box and Newton's schemes. A good agreement of results can be found with the previous data in a limiting approach. The behavior of the physical quantities under concern, including energy exchange, Sherwood number, and wall shear stress are portrayed through graphs and in tabular form. The Nusselt number and Sherwood number are found to diminish against the altered magnitudes of Brownian motion and the inclination parameter. Moreover, the velocity profile decreases with the growth of the inclination effect. In the same vein, the buoyancy force and solutal buoyancy effects show a direct relation with the velocity field. The outcomes have promising technological uses in liquid‐based systems related to stretchable constituents.     

Stagnation flow of hybrid nanoparticles with MHD and slip effects

The flow of hybrid nanoparticles with significant physical parameters with different base fluids in the presence of Biot number, velocity slip, and MHD effects has not been explored so far, particularly for a circular cylinder. Therefore, the current report is presented to offer a numerical solution for hybrid nanoparticles with base fluids (water and ethylene glycerol) via a circular cylinder. The physical situation is interpreted in terms of partial differential equations and is converted into ordinary differential equations after applying the similarity transformation. The results are presented in both tabular and graphical forms. The impact of physical parameters on velocity distribution is examined through graphs. The comparative results of hybrid nanoparticles for distinct base fluids as ethylene glycol and water are proposed and the hybrid nanoparticles with base fluid water seems to be greater than that of the hybrid nanoparticles with base fluid EG. The temperature profile of hybrid nanoparticles is found to be a decreasing function with growth in velocity slip parameter but an opposite trend is noted in case of nanoparticles . The skin friction and Nusselt number augmented for the increase in magnetic field, velocity slip, and nanoparticle while it shows a decreasing trend toward thermal slip parameter. For the both cases, improvement in Biot number helps enhance the heat transfer constantly.     

Steady MHD Casson Ohmic heating and viscous dissipative fluid flow past an infinite vertical porous plate in the presence of Soret,Hall, and ion‐slip current

In the present study, the influence of Hall and ion‐slip current on steady magnetohydrodynamics mixed convective, Ohmic heating, and viscous dissipative Casson fluid flow over an infinite vertical porous plate in the presence of Soret effect and chemical reaction are investigated. The modeling equations are transformed into dimensionless equations and then solved analytically through the multiple regular perturbation law. Computations are performed graphically to analyze the behavior of fluid velocity, temperature, concentration, skin friction, Nusselt number, and Sherwood number on the vertical plate with the difference of emerging physical parameters. This study reflects that the incremental values of Casson fluid parameter and Schmidt number lead to reduction in velocity. However, fluid velocity rises due to enhancement of ion‐slip parameter but an opposite effect is observed in case of Hall parameter. In addition, the Sherwood number declines with enhancing dissimilar estimators of the chemical reaction, Schmidt number, as well as Soret number.