Nonlinear magnetohydrodynamic flow of nanofluids across a porous matrix over an extending sheet with mass transpiration and bioconvection

The consequences of the nonlinear magnetic field and radiative thermal energy are evaluated for bioconvective viscous flow across a porous matrix over a nonlinearly stretching sheet. The rationale of the study is to attain enhanced thermal transportation. The dilute dispersion of nanoentities and bioconvection of swimming microorganisms are taken into consideration. The coupled partial differential system of field equations is transformed into ordinary differential form. Finally, the numeric solution is obtained by utilizing the fourth-order Runge–Kutta method shooting technique, and results are validated through an acceptable accord with existing studies. The variation of influential parameters such as combined magnetic parameter, mass transpiration parameter, thermophoresis, Brownian motion, bioconvection Lewis numbers made notable impacts on fluid velocity, temperature, concentration of nanoentities, and distribution of microorganisms.     

Nanoscale energy transport of inclined magnetized 3D hybrid nanofluid with Lobatto IIIA scheme

Key developments in the field of nanotechnology have drawn the attention of many scholars toward the interaction of nanoparticles due to their capturing applications in solar energy systems and thermal engineering. Larger consumption of energy posed a challenge for thermal science, so thermal engineering is trying to solve this issue by increasing the thermal conductivity of the fluid. The thermal conductivity of conventional fluid is increased by incorporating the nanoparticles in the base fluid. Keeping this in mind, the present research project addresses the utilization of nanoparticles in a steady three-dimensional rotating flow of magnetohydrodynamic water-based hybrid fluid over an extending sheet. Nanoparticles of aluminum oxide (Al₂O₃) and silver (Ag) are being used with water (H₂O) as base fluid. The velocity of nanoparticles is being captured under the influence of an inclined magnetic field and the transport of heat is scrutinized through thermal radiation. The physical model generates partial differential equations and then transported into an equivalent set of a nonlinear ordinary differential equations. The purpose of numerical computation is made by the Lobatto IIIA method, which is a type of Matlab scheme bvp4c and based on the finite difference method. Geometry of velocity profile is explained with different parameters in presence and absence of magnetic field and energy of hybrid nanofluid is explained under the influence of the inclined and perpendicular magnetic field. Gradual increment in ϑ both f and g profiles because strengthen the magnetic field results lower velocity. An increment in nanoparticle concentration of Al₂O₃ and Ag gives a larger magnitude of velocity. The rotation parameter shows the rotation of nanoparticles; due to these rotations both linear and angular components of velocity increase in the presence and absence of a magnetic effect.     

On heated surface transport of heat bearing thermal radiation and MHD Cross flow with effects of nonuniform heat sink/source and buoyancy opposing/assisting flow

Heat transport subject to nonlinear thermal radiation has multiple applications in physics, industry, engineering field, and space technology, such as aerodynamic rockets, solar power technology, large open water reservoirs, and gas-cooled nuclear reactors. This effort studies the magnetohydrodynamic flow of cross fluid, which is a type of non-Newtonian, along a heated surface. Furthermore, the transportation of heat in the fluid is induced by  thermal radiation. Furthermore, the behavior of opposing/assisting flow and impact of nonuniform heat sink/source is scrutinized. The reserved suitable transformations are carried out to shift the ruling equations into nondimensional class. Through reserved transformations, two nonlinear partial differential equations are altered into corresponding nonlinear ordinary differential equations. Then a scheme of integration referred to as Runge–Kutta–Fehlberg is imposed to get a numerical solution of these. The impact of parameters are mentioned concisely on temperature and velocity profiles in the absence and presence of a magnetic parameter. It is proved that the presence of a magnetic field steps up the velocity and temperature as well.     

Combined effects of variable thermal conductivity and induced magnetic field on convective Jeffrey fluid flow with nth order chemical reaction

This study addresses the impact of variable thermal conductivity and induced magnetic field on an unsteady two‐dimensional channel flow of an incompressible laminar mixed convective and chemically reacted Jeffrey fluid embedded in a non‐Darcy porous medium with an appropriate convective type boundary conditions. The suction/injection velocity distribution has been assumed to be in an exponential form. The set of transport equations is reduced into coupled ordinary differential equations by using appropriate similar variables, which are solved by shooting technique with Runge‐Kutta fourth‐order algorithm. The investigation is carried out for various emerging nondimensional parameters on the axial, radial velocities, temperature distribution, concentration, and induced magnetic fields and also with skin friction coefficient are discussed through graphs. The value of the local Sherwood and Nusselt numbers are analyzed numerically. We noticed that the effect of the induced magnetic field is increased with Strommer's number while it decreases for high magnetic Reynolds number.     

Effect of slip on entropy generation in a single rotating disk in MHD flow

In the present study, the effect of slip on entropy generation in magnetohydrodynamic (MHD) flow over a rotating disk is investigated by semi-numerical analytical solution technique. The nonlinear governing equations of flow and thermal fields are reduced to ordinary differential equations by the Von Karman approach, then solved via differential transform method (DTM), a recently-developed, powerful analytical method. Related entropy generation equations are derived and nondimensionalized using geometrical and physical flow field-dependent parameters. For a rotating surface the form of slip introduced into the governing equations is rarefaction. For comparison, slip and no-slip regimes in the range 0.1 > Kn > 0 and their interaction with magnetic effects are investigated by minimum entropy generation. While minimizing entropy generation, equipartitioning is encountered between fluid friction irreversibility and Joule dissipation.     

Thermal radiation and magnetic field effects on squeezing motion analysis for Cu–kerosene and Cu–water nanofluids

This article examines the squeezing motion of Cu–kerosene and Cu–water nanofluids with thermal radiation and magnetic field between two parallel sheets. By appropriate transformation, the governing nonlinear partial differential equations are converted into ordinary differential equations and then solved numerically by the Runge–Kutta technique. The motion characteristics have been examined with graphs by relevant parameters. It is observed that fluid temperature reduces if squeezing parameter, thermal radiation, and Hartmann number increases, but fluid temperature improves if nanoparticle volume fraction, Eckert number, and Prandtl number increases and it is observed that liquid momentum improves if the squeezing parameter increases, but fluid velocity reduces if nanoparticle volume fraction and Hartmann number increases.     

Steady magnetohydrodynamic Poiseuille flow of two immiscible non-Newtonian and Newtonian fluids in a horizontal channel with Ohmic heating

In this paper, an analytical study has been carried out on a steady magnetohydrodynamics (MHD) Poiseuille flow of two immiscible fluids in a horizontal channel with ohmic heating in the presence of an applied magnetic field. The channel is divided into two sections, Region I and Region II, respectively. Region I contains an electrically conducting, third grade, non-Newtonian fluid while Region II is a Newtonian fluid. The regular Perturbation series method is used to transform the coupled nonlinear differential equations governing the flow into a system of linear ordinary differential equations in both fluid regions. Suitable interface matching conditions were chosen to obtain separate solutions for each fluid in both regions and the results were displayed graphically for various values of physical parameters, such as pressure gradient, suction parameter, Hartmann number, Prandtl number, viscosity, and conductivity ratios to show their effects on the flow. The effect of skin friction and Nusselt number was shown with the aid of tables. The results obtained among other findings clearly shows that as the value of the magnetic parameter increases, the velocity and temperature of the fluid decrease.     

Hybrid nanofluid flow over a stretched cylinder with the impact of homogeneous–heterogeneous reactions and Cattaneo–Christov heat flux: Series solution and numerical simulation

The Catteno–Christov heat flux plays a dynamic role in flow of heat enhancement in various manufacturing, industrial, and engineering applications. This present work focuses on the influence of Catteno–Christov heat flux model on Darcy–Forchheimer flow of a hybrid nanofluid placed in a porous medium. The formulation of the mathematical model is done by considering a fluid with two different nanoparticles Al₂O₃ and Cu dispersed in the water as the base fluid. The set of partial differntial equations is reduced by using similarity variables and boundary conditions to obtain ordinary differntial equations. The coupled nonlinear governing differential equations are solved using Runge–Kutta fourth–fifth order (RKF-45). The impact of numerous dimensionless parameters on the velocity, thermal, and concentration profiles are plotted and studied. Furthermore, the coefficient of skin friction for the relevant parameters are analysed through graphs. Result reveals that, increase in the porosity parameter declines the velocity gradient and shoots up the thermal and concentration gradients. Inclination in magnetic parameter declines velocity and concentration profiles due to the Lorentz force. Enhancement in the thermal relaxation parameter declines the thermal profile. Inclination in homogeneous-heterogeneous reaction parameters declines the mass transfer rate. Also, the well-known differential transform method is used for the validity of RKF-45 method and an impressive agreement is noticed between the results of RKF-45 and DTM.     

Fluid properties of an unsteady MHD free stream flow over a stretching sheet in presence of radiation

Variable fluid properties with thermal radiation in an unsteady magnetohydrodynamics free stream incompressible flow over a stretching sheet has been considered. The thermal diffusivity and viscosity of the fluid varies linearly with temperature. The governing partial differential equations are moulded to ordinary differential equations using time-dependent similarity variables and the stream function. RKF technique with shooting method has been implement to find the solution numerically. In the current analysis the impact of unsteadiness, magnetic field, radiative parameter, variable fluid viscosity and thermal diffusivity parameter on heat and flow behavior with the free stream parameter have been studied. Transition point observed in the velocity profiles with an change in unsteadiness parameter and the effect of magnetic field is reduced in the presence of free stram velocity. The velocity and the temperature gradient are computed on the surface and their outcomes with different parameters have been analyzed in the results shown graphically and in tabular form.     

Lie group analysis of hyperbolic tangent fluid flow in the presence of thermal radiation

The present study is devoted to the flow and heat transfer analysis of the hyperbolic tangent fluid through a stretching sheet by considering the effect of thermal radiation in addition to an applied transverse magnetic field, as well as thermal and velocity slip conditions. The Lie group analysis technique has been utilized for establishing similarity transformations, which effectively transform the governing equations to a system of nonlinear ordinary differential equations (ODEs). These ODEs are numerically solved by utilizing the shooting method. The heat transfer properties and flow features under the influence of various physical parameters are also studied. We noted that by increasing the thermal radiation parameter, the temperature profile increases and also the thermal boundary layer thickens. Furthermore, it is deduced that rising the thermal radiation parameter reduces the local Nusselt number. Moreover, the numerical results obtained are in agreement with the existing results in the literature.     

Effects of heat and mass transfer on MHD nonlinear free convection non-Newtonian fluids flow embedded in a thermally stratified porous medium

This communication examines heat alongside mass transport in a nonlinear free convection magnetohydrodynamics (MHD) non-Newtonian fluid flow with thermal radiation and heat generation deep-rooted in a thermally stratified penetrable medium. The Casson and Williamson fluid considered in this communication flos simultaneously across the boundary layer and are mixed together. The model of heat alongside mass transport is set up with chemical reaction and thermal radiation alongside heat generation to form a system of partial differential equations (PDEs). Appropriate similarity variables are used to simplify the PDEs to obtain systems of coupled ordinary differential equations. An efficiently developed numerical approach called the spectral homotopy analysis method was used in providing solutions to the transformed equations. A large value of Casson term is observed to degenerate the velocity plot while the Williamson parameter enhances the velocity profile. The parameter of thermal stratification is found to enhance the rate of heat transport within the boundary layer. An incremental value of the magnetic parameter declines the velocity of the fluid and the entire boundary layer thickness. The present result was compared with previous studies and was seen to be in good agreement.     

Heat and mass transfer of two immiscible flows of Jeffrey fluid in a vertical channel

In this article, we examined the effect of heat and mass transfer flow of two immiscible Jeffrey fluids in a vertical channel. The highly nonlinear coupled ordinary differential equations are evaluated using regular perturbation parameters, for small values of perturbation parameter. The effect of Jeffrey's parameter on the flow and the effects of various physical parameters entering into the problem on dimensionless velocity, temperature, and concentration distribution is illustrated graphically. We observe that the Jeffrey parameter, thermal, and mass Grashof number enhance the fluid flow, while the chemical reaction parameter suppresses the fluid flow, also it is established that the Nusselt number is boosted by enhancing the thermal and mass Grashof number. We observed that the results are in very good agreement with the results obtained for a viscous fluid.     

Magnetohydrodynamics boundary layer flow and heat transfer in porous medium past an exponentially stretching sheet under the influence of radiation

Buoyancy forces result from the cooling or heating of a continuous stretching sheet, which causes a change in the resulting flow and thermal fields, and hence the heat transfer behavior in the manufacturing process. The study of the thermal buoyancy induced in boundary layer flow is important due to its recent advances in the areas of nuclear energy, electronics, and space technology. In this perspective, the aim of the present study is to investigate the effect of the buoyancy parameter on the magnetohydrodynamics boundary layer flow over an exponentially stretched sheet in the presence of nonlinear thermal radiation and porous media. Using similarity transformation, the flow model of partial differential equations is transformed into a set of coupled nonlinear ordinary differential equations. The efficient fourth‐order Runge‐Kutta scheme with the shooting method is used to solve the reduced equations. The impact of various associated parameters on velocity and temperature profiles were analyzed and computed through graphs. The major outcome of the present study shows the enhancement in the velocity distribution with the increase in the buoyancy parameter. Also, the increase in thermal buoyancy and thermal radiation leads to an increase in fluid temperature. Moreover, it is worth to note that the fluid velocity declines with the augmentation of the magnetic parameter.     

Soret,viscous dissipation,and thermal radiation effects on MHD free convective flow of Williamson liquid with variable viscosity and thermal conductivity

The flow model of heat and mass transport of a Williamson liquid through a porous stretching sheet with radiation, viscous dissipation, Soret effect, and chemical reaction has been explored. The motion starts from the slot to the free stream. The present study is unique, because it examines the flow of a Williamson fluid under the influence of variable viscosity and thermal conductivity. The Williamson fluid term as added to the momentum and energy equation is considered in a nonlinear form as compared with other studies in literature. The flow model is a set of coupled highly nonlinear partial differential equations that are simplified and lead to coupled nonlinear total differential equations by employing sufficient similarity variables. The simplified equations are later solved by utilizing the spectral homotopy analysis method. Our experiment shows that the injected variable viscosity, together with thermal conductivity, has a great impact on the fluid profiles. An increase in the Williamson parameter (β) leads to a decrease in the thickness of the hydrodynamic thermal layer. Our numerical calculations were compared with earlier published work, and they were discovered to be correct.     

Heat and mass transfer flow over a stretching surface with Ohmic heating and chemical reaction

The present study analyzes the effect of chemical reaction on an unsteady magnetohydrodynamic boundary layer viscous fluid over a stretching surface embedded in a porous medium with a uniform transverse magnetic field. A Darcy‐Forchheimer drag force model is employed to simulate the effect of second‐order porous resistance. Dissipative heat energy based on both viscous and Joule dissipation along with a heat source/sink is considered to enhance the energy equation. Similarity analysis is imposed to transform the governing differential equations into a set of nonlinear coupled ordinary differential equations. These sets of equations are solved numerically using the Runge‐Kutta fourth‐order scheme followed by the shooting algorithm. The effects of physical parameters such as magnetic field, Prandtl number, Eckert number, Schmidt number, unsteadiness parameter, and chemical reaction parameters have been discussed on velocity, temperature, and concentration fields. Computation for the coefficient of skin friction, rate of heat and mass transfer is done and presented in a table for validation of the present outcomes.     

Heat transfer analysis for particle–fluid suspension thermomagnetohydrodynamic peristaltic flow with Darcy–Forchheimer medium

This theoretical analysis explores the effect of heat and mass transfer on particle–fluid suspension for the Rabinowitsch fluid model with the stiffness and dynamic damping effects through Darcy–Brinkman–Forchheimer porous medium. In this study, we also incorporate slip and transverse magnetic field effects. Using low Reynolds number, to neglect inertial forces and to keep the pressure constant during the flow, channel height is used largely as compared with the ratio of length of the wave. A numerical technique is used to solve flow governing system of differential equations. Particular attention is paid to viscous damping force parameter, stiffness parameter, and rigidity parameter; also, the numerical data for thermal profile, momentum, and concentration distribution are presented graphically. Outcomes are deliberated in detail for different fluid models (thinning, thickening, and viscous models). It is found that velocity profile increases for greater values of viscous damping effect and stiffness and rigidity parameter for shear thinning, but conflicting comportment is showed for thickening nature model. Viscous dissipation effects increases the thermal profile for all cases of fluid models. The scope of the present article is valuable in explaining the blood transport dynamics in small vessels while considering the important wall features with chemical reaction characteristics. The current analysis has extensive applications in biomedical engineering field, that is, peristaltic pumps.     

Computational study on heat transfer and MHD-electrified flow of fractional Maxwell nanofluids suspended with SWCNT and MWCNT

Recent developments in fluid dynamics have been focusing on nanofluids, which preserve significant thermal conductivity properties and magnify heat transport in fluids. Classical nanofluid studies are generally confined to models described by partial differential equations of an integer order, where the memory effect and hereditary properties of materials are neglected. To overcome these downsides, the present work focuses on studying nanofluids with fractional derivatives formed by differential equations with Caputo time derivatives that provide memory effect on nanofluid characteristics. Further, heat transfer enhancement and boundary layer flow of fractional Maxwell nanofluid with single-wall and multiple walls carbon nanotubes are investigated. The Maxwell nanofluid saturates the porous medium. Also, buoyancy, magnetic, electric, and heating effects are considered. Governing continuity, momentum, and energy equations involving Caputo time-fractional derivatives reduced nondimensional forms using suitable dimensionless quantities. Numerical solutions for arising nonlinear problems are developed using finite difference approximation combined with L1 algorithm. The influence of involved physical parameters on flow and heat transfer characteristics is analyzed and depicted graphically. Our simulations found out that surface drag of Maxwell nanofluid with single-walled carbon nanotubes dominates nanofluids with multiple walls carbon nanotubes, but the reverse trend is noticed for larger Grashof number values.     

Effects of slip on sheet-driven flow and heat transfer of a third grade fluid past a stretching sheet

The entrained flow and heat transfer of an electrically conducting non-Newtonian fluid due to a stretching surface subject to partial slip is considered. The partial slip is controlled by a dimensionless slip factor, which varies between zero (total adhesion) and infinity (full slip). The constitutive equation of the non-Newtonian fluid is modeled by that for a third grade fluid. The heat transfer analysis has been carried out for two heating processes, namely, (i) with prescribed surface temperature (PST case) and (ii) prescribed surface heat flux (PHF case). Suitable similarity transformations are used to reduce the resulting highly nonlinear partial differential equations into ordinary differential equations. The issue of paucity of boundary conditions is addressed and an effective second order numerical scheme has been adopted to solve the obtained differential equations. The important finding in this communication is the combined effects of the partial slip, magnetic field and the third grade fluid parameter on the velocity, skin-friction coefficient and the temperature field. It is interesting to find that slip decreases the momentum boundary layer thickness and increases the thermal boundary layer thickness, whereas the third grade fluid parameter has an opposite effect on the thermal and velocity boundary layers.     

Thermophoresis and Brownian motion effects on Williamson nanofluid flow past a stretching surface with thermal radiation and chemical reaction

The heat transfer mechanism of nanofluids has numerous industrial applications owing to the non-Newtonian behavior and has been exercised as a thermophysical phenomena in presence of thermal radiation. The present paper deals with the thermal transfer characteristics of time-independent magnetohydrodynamics Williamson fluid past a stretching surface in presence of the reaction of chemical equilibrium is dealt. The flow constitutive nonlinear partial differential coupled equations are transmitted into ordinary differential equalities by employing relevant similarity transmutations. These deduced equations are determined by using the Runge–Kutta numerical technique with a shooting approach with the aid of MATLAB software. Influences of distinct pertinent flow parameters like an inclined uniform magnetic field, Soret number, heat generation/absorption, and Schmidt number constrained to convective boundary condition is displayed through graphs with relevant physical interpretations. Computed numerical values for the friction factor coefficient, local Nusselt parameter, and Sherwood number are tabulated.      

Unsteady MHD fluid flow past an inclined vertical porous plate in the presence of chemical reaction with aligned magnetic field,radiation, and Soret effects

The aim of the present paper is to investigate the Soret effect due to mixed convection on unsteady magnetohydrodynamics flow past a semi-infinite vertical permeable moving plate in the presence of thermal radiation, heat absorption, and homogenous chemical reaction subjected to variable suction. The plate is assumed to be embedded in a uniform porous medium and moves with a constant velocity in the flow direction in the presence of a transverse magnetic field. The equations governing the flow are transformed into a system of nonlinear ordinary differential equations by using the perturbation technique. Graphical results for the velocity distribution, temperature distribution, and concentration distribution based on the numerical solutions are presented and discussed. Also, the effects of various parameters on the skin-friction coefficient and the rate of heat transfer in the form of Nusselt number, and rate of mass transfer in the form of Sherwood number at the surface are discussed. Velocity distribution is observed to increase with an increase in Soret number and in the presence of permeability, whereas it shows reverse effects in the case of the aligned magnetic field, inclined parameter, heat absorption coefficient, magnetic parameter, radiation parameter, and chemical reaction parameter.