Narrow Results

This paper intends to build a mathematical model of a two-dimensional Williamson nanofluid flow due to the stretching of a sheet linearly. The flow geometry is influenced by the magnetic field that is applied externally to the system. The induced magnetic field is infinitesimal and hence neglected. However, the flow structure is incorporated with the Brownian motion and thermophoresis effects as it alter the physics of the flow. The equations that model the flow comprise the highly nonlinear coupled simultaneous system. Thus, a numerical technique namely finite difference accompanied with the Thomas algorithm is adopted to approach the flow system. The motion, temperature, and concentration of the Williamson nanofluid flow are studied for the different flow controlling parameters. The co-efficient of skin-friction, heat, and mass transfer rates is also computed. The streamlines, isotherms, and iso-concentration are plotted to picturise the flow phenomena in the complete domain. The study reveals that the temperature of the flow raises with the Brownian motion of the nanoparticles and the trend is opposite with the concentration. The strength of the streamlines, isotherms, and the concentration contour is identified to be high for the least magnitude of Weissenberg number. The Brownian motion raises the heat transfer rate and slows down the mass transfer rate.

In this research, a novel design stochastic numerical technique is presented to investigate the unsteady form magnetohydrodynamic (MHD) slip flow along the boundary layer to analyze the transportation and heat transfer in a solar collector through nano liquids which is a revolution in the field of neurocomputing. Thermal conductivity in variable form is dependent on temperature and wall slips are assumed over the boundary. For mathematical modeling, the solar collector is assumed in the form of a nonlinear stretching sheet and a quite new artificial neural networks (ANNs) based approach is used to solve the current problem in which inverse multiquadric radial basis (IMRB) kernel is sandwiched between a global search solver named genetic algorithms (GAs) and a highly effective local solver named sequential quadratic programming (SQP) i.e. IMRB-GASQP solver. The governing boundary value problem is altered in the form of a system of nonlinear ordinary differential equations (ODEs) through the utilization of similarity transformation and then the obtained system of ODEs is solved using IMRB-GASQP solver by altering the values of distinguished parameters involved in it to observe the fluctuation in the velocity and temperature profiles of nanofluid. The obtained results are effectively compared with the reference solutions using the Adams numerical technique in graphical and tabulated form. An exhaustive error analysis using performance operators is presented while the efficacy of the designed solver using various statistical operators is also part of this research.

A numerical solution for steady-state, incompressible, laminar Casson fluid flow and heat transfer in the combined region of a boundary layer is presented for the case of mixed convection and slip velocity. Before introducing the present technique of non-Newtonian Casson model, reviewing the literature has been carefully performed, an improved technique for this model is studied, which has not been previously reported. The presented analysis involves the harness of a magnetic field, viscous dissipation, internal heat generation/absorption and the slip velocity. Finite difference method (FDM) has been used to get an accurate and complete numerical solution. In this novel study, it is proved by means of a finite difference technique, that the velocity and the thermal field may be influenced with the presence of mixed convection phenomenon. The results show that both the fluid velocity and temperature may be predicted from the values of the controlling parameters. Finally, the graphical output reveals that the fluid velocity is diminished by strengthening both the Hartman number and the Casson parameter while the reverse characteristics are observed for the Grashof number.

The nanofluids are a recent challenging task in a nanotechnology field used in heat transfer enhancement for base fluids. The major purpose of this research is to examine the influences of Hall current on the non-Newtonian power-law nanofluid on an exponentially extending surface. Implementation in the Cattaneo–Christov heat flux and the free stream is performed to analyze the thermal relaxation features. Entropy generation evaluation and Bejan number during the convection flow are investigated. The Runge–Kutta–Fehlberg method is employed to resolve the transformed governing nonlinear equations. The impacts of the key physical factors on the profiles of primary and secondary velocities, temperature and entropy generation are discussed across the graphs. The local skin-friction coefficients, Nusselt and Sherwood numbers are demonstrated in a tabular form under the impacts of key physical parameters. Two different types of power-law indicators including pseudoplastic fluid $(n=0.7)$ and dilatant fluid $(n=1.2)$ are conducted. The results indicated that the flow speed decreases at dilatant fluid compared to pseudoplastic fluid due to higher viscosity. Increasing Hall current parameter powers the axial and secondary velocity profiles. Thermophoresis parameter powers the profiles of the temperature, nanoparticle volume fraction and local entropy generation. The dilatant fluid $(n=1.2)$ gives higher values of $C_{fx},C_{fz},{\mathrm{\text{Nu}}}_x$ and ${\mathrm{\text{Sh}}}_x$ compared to the pseudoplastic fluid $(n=0.7)$.

In this paper we investigate the average frequency of a certain positive slope which is produced when the velocity and magnetic fields V_y and B_x are crossed by the level in the magnetohydrodynamic equation. This level crossing analysis is in the inviscid limit where υ→0 and of course before the appearance of the shocks. The main goal of this paper is to show that this quantity, , is a good measure for the fluctuations of the velocity and magnetic fields in the magnetohydrodynamic turbulence.

The objective of this work is to explore the flow features and thermal radiation properties of the 2-D Magnetohydrodynamic (MHD) Carreau nanofluid model over an impenetrable stretching surface by utilizing the supervised learning strength of Levenberg–Marquardt backpropagation neural networking technique (LMBNNT). The mathematical formulation for MHD Carreau nanofluid flow model (MHDCNFM) in terms of partial differential equations (PDEs) is transformed into equivalent nonlinear ordinary differential equations (ODEs) by utilizing the similarity transformation and dimensional parameters. A reference dataset of proposed LMBNNT is made for Carreau nanofluid flow model exploiting the strength of Lobatto IIIA technique through the variations of different parameters against the velocity, temperature profile and concentration. These reference datasets are placed for validation, training and testing by LMBNNT and obtained outcomes are compared with reference results to check the accuracy of the designed methodology. The validation of the proposed solution methodology is obtained through the mean square error (MSE), error histogram error profile, regression p lot and fitness plot. MSE values’ accuracy is upto ${10}^{-10}$ which establish the reliability of the LMBNNT. Moreover, due to an increase in Weissenberg number, fluid velocity decays in case of shear thinning liquid and higher values of Biot number enhance the temperature profile and improves the rate of heat transfer. Moreover, the increment in Hartman number reduces the surface drag force and large values of Prandtl number reduce the heat transfer process. These results of all these parameters are expressed in well-organized numerical and graphical forms.

In this paper, an investigation into Williamson nanofluid stagnation point flow of nano-biofilm over a stretching/ shrinking sheet with chemical reaction is performed. Moreover, the impact of cylindrical-shaped nanoparticles, activation energy, and bioconvection has been considered. The fluid’s fluctuating transport properties (dynamic viscosity, heat conductivity, nanoparticle mass diffusivity) and microorganism diffusivity are evaluated. The nonlinear systems of partial differential equations are transformed into nonlinear differential equations via the implementation of similarity transformations. The shooting approach and RK-4 technique are used for this investigation. The impacts of various fluid transport characteristics and various factors on patterns of velocity, temperature, the concentration of nanoparticles, and motile density are described. The Brownian motion, heat source and thermophoresis parameters all lead to a more consistent temperature profile being observed. It is seen that concentration-dependent properties decrease the velocity profile while the temperature, concentration, and motile density profiles increase. Also, the physical quantities decrease with the rising values of concentration-dependent properties.

In the past few years, many technical strategies, such as molding, condenser heat exchanger, liquefied metal filtration, fusion control and nuclear reactor coolant, that involve hydromagnetic fluxes and thermal intensification in porous media have been observed. This study investigates the Carreau nanofluid of nanobiofilm through stretching/shrinking sheet with a stagnant point flow, nanoparticles and convecting microbes. The orthogonal ($90^{\circ }$ impinge) coating stagnant point circulation of a medium is considered, although the sheet may be stretched/shrinked as the procedure utilized in industry. The variations in the fluid (dynamic viscosity, thermal conductivity, mass permeability) and microbes are utilized. The similarity transformation factors are used to transform the system of partial differential equations into a nonlinear system of ordinary differential equations. To find the solution of a system of equations, the Runge–Kutta method with shooting technique has been used. The flow rate, temperature and concentration, as well as the heat transfer rate, and the physical quantities have been discussed. The nanoparticle volume fraction increases with the increasing effect of activating energy as well as thermophoresis parameter, but it decreases with the enhancing effect of Lewis number (Le) and Brownian motion parameter (Nb). The graphs and tables display the illustration of the influence of different parameters.

This paper studies the mixed convective flow of a magnetohydrodynamic micropolar fluid over an extending sheet. The first-order velocity slip condition is taken to observe the slip flow of the fluid. The applications of solar radiation toward the micropolar fluid flow are analyzed in this paper. Furthermore, the Brownian motion, thermophoresis and Joule heating impacts are also studied. Also, the Cattaneo-Christov heat flux model, chemical reaction and activation energy are observed. The leading PDEs have been transformed to ODEs and then solved with the help of homotopy analysis technique. The impacts of different physical parameters have been evaluated theoretically. The outcomes exhibited that the material factors have augmented the microrotation and velocity profiles. Moreover, the velocity slip parameter has a reverse relation with velocity and microrotation profiles, while there is a direct relation of a velocity slip with the energy curve. The velocity profile has increased with higher thermal and mass Grashof numbers. With increasing Brownian motion parameter, the thermal profile is amplified while the concentration profile is declined. On the other hand, the thermal and mass profiles have been boosted with greater thermophoresis parameter. The velocity profile has decreased with higher magnetic parameter, whereas the temperature profile has augmented with higher magnetic parameter. The couple stress and skin friction have been augmented with material parameter, whereas the skin friction has been reduced with thermal and mass Grashof numbers.

The present investigation computes the heat transport phenomenon of the magnetohydrodynamic (MHD) flow of CuO-Ag/H₂O hybrid nanofluid over a spinning disc. The authors are confident that there is very less analysis covering the fluid flow containing silver and copper oxide nanoparticles over a rotating disk. Therefore, the authors are interested to consider the water-based nanoliquid flow over a spinning disk. Furthermore, the velocity slip and thermal convective conditions are taken into consideration. The formulation of the problem is made in the form of PDEs and is then converted into the nonlinear ODEs by employing suitable similarity transformations. The homotopic analysis approach is applied for the semi-analytical solution of these resulting equations. The convergence of homotopic approach has also revealed with the help of figure. The performance of the hybrid nanofluid flow velocities and temperature has been shown in a graphical form against distinct flow parameters. Also, the numerical results of skin friction coefficient and Nusselt number have been calculated in a tabular form. The outcomes of the current problem show that the increase in the skin friction of the water-based copper oxide nanofluid is greater than the water-based silver nanofluid at 4% of the nanoparticle volume fraction. Also, the skin friction of the hybrid nanofluid is increased by 8% compared to the silver nanofluid at 4% of the nanoparticle volume fraction. Furthermore, the heat transfer rate of the water-based copper oxide nanofluid is greater than the water-based silver nanofluid at 4% of the nanoparticle volume fraction. Also, the heat transfer rate of the hybrid nanofluid is 52% greater than that of silver nanofluid at 4% of the nanoparticle volume fraction. It is found that the Nusselt number of the hybrid nanofluid is highly affected by the embedded parameters as compared to nanofluids.

In this study, magnetohydrodynamic cross fluid model is used to formulate the 2D boundary layer equations of fluid moving on the parabolic surface. The surface is assumed to be in vertical shape due to the convection. The underlying effects of viscous dissipation and chemical reaction are modeled to observe the transportation of heat and mass rate. To understand fluid behavior, the thermophysical properties are considered as variable because they have huge influence in food processing, viscometers, lubricants and various industrial works. The assumed geometry of fluid flows is similar in shape of bullet, submarine, aircraft and car’s bonnet, namely paraboloid surface. The modeled equations of cross fluid with mentioned effects are obtained in form of PDEs and then converted these equations in form of ODEs by assuming set of scaling transformations. For the sake of numerical and graphical outcomes, the resulting equations are solved numerically on Matlab software via BVP4c method. Results achieved across velocity indicate that the decay happens by numerous values of Weissenberg number, power law index, viscosity parameter and Hartmann number. The temperature and concentration fields attained increasing influence by thermal conductivity coefficient, Eckert number and thermal diffusivity parameter.

The featured problem explores the impact of cross-diffusion on the two-dimensional electrically conducting flow of a viscous liquid over a nonlinearly stretching sheet through a permeable medium. An inclusion of radiative heat energizes the heat transport phenomenon whereas the solutal transfer enriches by the conjunction of the chemical reaction. To justify the behavior of electromagnetic radiation, the Rosseland approximation is used by considering nonlinear thermal radiation. Further, the convective boundary conditions also affect the flow properties. The approachable transformations are employed to get a suitable non-dimensional form of the governing equations for the formulated problem. Due to the complex nature of the distorted equations, the system of equations is solved using an in-built code bvp5c predefined in MATLAB. The computation is carried out for the involvement of the suitable values of contributing parameters on the flow characteristics and along with the simulations of the rate coefficients. Further, the assigned particular parameters present an outcome that validates with a good correlation. Finally, the important outcomes are — enhanced suction due to the permeability of the surface augments the fluid velocity whereas the trend is reversed in the case of injection. The augmentation in the fluid temperature is exhibited for the radiating heat but the reacting species attenuates the fluid concentration.

This study numerically investigates the magnetohydrodynamic (MHD) free convection of a fluid in a porous triangle cavity containing a circular obstacle subjected to various thermal configurations. The investigation is conducted using a penalty finite element technique. The inclined side walls are non-uniformly heated while the bottom is maintained cold isothermal. Three types of thermal configurations are considered at the obstacle boundary. The effects of various physical parameters on the MHD free convection have been studied. The temperature field, fluid flow and heat transfer are strongly dependent on the type of thermal boundary condition of the circular obstacle, Prandtl number and magnetic induction. The obtained results are verified with a grid sensitivity study and validated using existing results in literature. A comparison between the present results and ones existing in literature illustrates the reliability and dependability of this study.

This study investigates thin film’s drainage and lifting of a steady, non-isothermal-modified second-grade incompressible fluid. An approximate analytical technique The homotopy analysis method (HAM) is used to solve the developed governing equations for velocity and temperature fields together with boundary conditions. The expressions for velocity profile, average velocity, temperature distribution, shear stress, and volume flow rate are provided explicitly. The flow of the thin film is found to be substantially dependent on the flow behavior index $m$, magnetic field parameter, dimensionless numbers say stock number $S_t$, and Brinkman number $B_r$. The impact of the above-involved parameters on the fluid’s temperature and velocity is depicted numerically as well as graphically.

In this research, the dynamics of MHD Casson fluid flow has been discussed in the presence of non-Darcy Forchheimer porous medium. The investigation is focused on how thermal radiation, Soret–Dufour, and chemical reactions affect the incompressible Casson flow in a non-Darcy Forchheimer porous medium, taking account of pressure force. The mathematical model of the system is solved using the finite difference scheme followed by the shooting technique with bvp4c tool in MATLAB. The effects of physical parameters on velocity and transport (heat and mass) profile are illustrated through graphs. From the results, it is observed that Soret effect reduces the thermal boundary layer thickness which leads to the asymptotic increase in heat dissipation. The findings of the study on MHD Casson fluid model considering the non-Darcy Forchheimer porous medium are useful in engineering and science areas such as chemical machinery systems, geophysics, etc.

An investigation of the impacts of magnetic field, heat generation/absorption and thermal radiation on unsteady free convection dusty fluid flow over a non-isothermal vertical cone enclosed inside a porous medium is explored. The Crank–Nicolson approach is used to get the numerical solutions for these nonlinear, coupled partial differential equations (PDEs). The interaction of physical parameter range on temperature and velocity distribution is calculated and graphically presented. The results demonstrate that when the porosity, heat generation/absorption, and thermal radiation parameters are increased, the velocities rise, whereas the magnetic and mass concentration of particle phase parameters have an opposite effect. Furthermore, raising the fluid-particle interaction parameter causes a rise in dust phase velocity but a reduction in fluid phase velocity.

We use axisymmetric magnetohydrodynamic simulations to investigate the spinning-down of magnetars rotating in the propeller regime and moving supersonically through the interstellar medium. The simulations indicate that magnetars spin down rapidly due to this interaction, and faster than for the case of a non-moving star. We discuss this model with respect to soft gamma repeaters (SGRs) and the isolated neutron star candidates.

In this paper, we explore the self-similarity time evolution of a hot accretion flow around a compact object in the presence of a toroidal magnetic field. We focus on a simplified model which is axisymmetric, rotating, unsteady viscous-resistive under an advection-dominated stage. In this work, we suppose that both the kinematic viscosity and the magnetic diffusivity to be a result of turbulence in the accretion flow. To describe such a flow, we apply magneto-hydrodynamics equations in spherical coordinates, $(r,𝜃,\phi )$ and adopt unsteady self-similar solutions. By neglecting the latitudinal dependence of the flow, we obtain a set of one-dimensional differential equations governing the accretion system. In this research, we encounter two parameters related to the magnetic field; one of them is, $\beta$, defined as the ratio of the magnetic pressure to the gas pressure and the other one, ${\mathrm{\Gamma }}_0$ applied in the magnetic diffusivity definition. Our results show that $\beta$ is a function of position, and increases towards outer layers. On the other hand, we examine different strength of magnetic field by choosing different value of ${\beta }_0$ which is the value of $\beta$ at the inner edge of disc. We see that both ${\beta }_0$ and ${\mathrm{\Gamma }}_0$ have positive effect on growing the radial infall velocity but density and gas pressure decrease by larger values of these parameters. Moreover, the rotational velocity and temperature of accreting material reduce considerably under the influence of a stronger magnetic field. We also focus on the behavior of the mass accretion rate appearing as a descending function of position. Finally, our solutions confirm that the radial trend of the physical quantities in a dynamical accretion flow is different from the ones in a steady flow. However, the effect of various parameters on the physical quantities in our model is qualitatively consistent with similar steady models.

This paper explores the bioconvective Maxwell fluid flow over a horizontal stretching sheet. The Maxwell fluid flow is considered in the presence of gyrotactic microorganisms. The velocity slips and convection conditions are used in this investigation. Additionally, the Cattaneo–Christov heat and mass flux model, Brownian motion, thermophoresis, and activation energy are employed in the flow problem. The model formulation has been transferred to a dimension-free format using similarity variables and solved by the homotopy analysis approach. Figures have been sketched to depict the HAM convergence. The consequences of this study are that the velocity of Maxwell fluid flow reduces for higher Hartmann number, buoyancy ratio factor, and bioconvective Rayleigh number, whereas the increasing behavior in velocity profile is seen against Deborah number. The thermal characteristics of the Maxwell fluid flow diminish with developing values of the thermal relaxation factor and Prandtl number, while augmenting with the increasing Brownian motion, thermal and concentration Biot numbers and thermophoresis factor. The rate of thermal transmission of the Maxwell fluid flow enhances with the increasing Prandtl number, and mixed convective factor, while diminishing with the increasing buoyancy ratio factor, thermophoresis factor and Brownian motion factor.

Plasma edge rotations and magnetohydrodynamic behaviors have been studied during radial electric field variations in IR-T1 tokamak. An external positive limiter bias has been used as an external radial electric field. The profiles of radial electric field, floating potential, poloidal and toroidal rotation velocities and MHD activities have been studied during positive limiter bias. The poloidal and toroidal velocities reduced when the bias was applied and their fluctuations on the plasma edge became smoother furthermore. A significant excitation in dominant mode (4, 1) oscillation amplitude and a sharp decrease in magnetic island rotation frequency have been seen.