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[Display omitted] • A computational framework applied to consider the natural convection problem in a cavity with micropolar fluid. • The material parameter decreases with Rayleigh number and particle volume fraction. • The values of Ψ max and N u a v e decrease 17.1% and 10.8%, respectively while N m a x increases 19.8% when K increases from 1 to 2. Micropolar fluids are the media in which their behavior is affected by the microrotation of the substructure particles. In the present work, the natural-convection flow of a micropolar-nanofluid (Al 2 O 3 /water) in the presence of an inclined magnetic field in a semi-annulus enclosure is investigated. The influence of active parameters on magneto-natural convection is investigated. The governing equations (mass, momentum, microrotation, and energy) are numerically solved by CVFEM. Moreover, for some conservative comparisons, the equations are solved by Ansys Fluent CFD code which is conjugated by an innovative nondimensionlization scheme. The effects of important parameters are investigated on the streamlines, isotherms, microrotation contours, the maximum absolute value of stream function ( Ψ max ) , the average Nusselt number (N u a v e ) and the maximum absolute value of microrotation N max ∗ . The results discovered that the values of N u a v e descend with ascending the Hartmann number (H a) and material parameter (K) while it ascends with ascending Rayleigh number (R a) and particle volume fraction (ϕ). The value of N u a v e descends 10.8% while N max ∗ increases 19.8% when K increases from 1 to 2. The value of N u a v e descends 44.83% when Ha increases from 25 to 75 at λ = 45 °. The minimum value of N u a v e occurs at λ = 45 ° for H a = 25 and at λ = 30 ° for H a = 50 and H a = 75. [ABSTRACT FROM AUTHOR]

Nanofluids flow through porous media constitutes an emerging perspective in many thermodynamic processes and thermal processing optimization. The primary goal of contemporary research from the standpoint of such thermal applications is to examine the nanofluid flow across a vertically placed stretching surface embedded in a porous media. The mathematical formulation of the considered flow is modeled with the consequences of inclined magnetic field and thermal radiations. The Darcy-Forchheimer-Brinkman model addresses the fluid transport within the porous medium. Carbon nanotubes (CNTs) and alumina ceramics are considered nanoparticles and porous media, respectively, and water is regarded as a base fluid in this study. Appropriate transformations have been developed to reduce the governing equations into the dimensionless system. The highly nonlinear transformed system is addressed by using a local non-similarity approach via the bvp4c built-in MATLAB function. The physical implications of the emerging dimensionless parameters on the velocity and thermal profiles of considered nanofluids are studied and discussed in detail. It is perceived that the thermal profile of nanofluid is enhanced with increasing estimations of nanoparticles concentrations and radiation parameters. Furthermore, an increment in Hartmann's number and magnetic field inclination angle diminishes fluid velocity. Furthermore, increasing the Darcy number reduces the temperature distributions of the nanofluids under consideration. Comparing the current study with published articles is also performed to corroborate the reported results. In this regard, an excellent agreement has been achieved. This work is expected to provide important information for the future implementation of innovative heat transfer devices, as well as a valuable reference for researchers studying nanofluids flows under varied assumptions. [ABSTRACT FROM AUTHOR]

The current study aims to investigate the effect of partial slip conditions over double diffusion convection. The phenomenon is applied with the inclined magnetic flux of peristaltic flow on Ellis nanofluid model in an asymmetric channel. The fundamental differential equations are constructed and solved through lubrication approximation that gives the coupled system of ordinary differential equations. This resultant system is further solved numerically, and graphic representation are used to physically comprehend the flow quantity data. The whole procedure is carried out under the trapping mechanism by drawing contour streamlines. The knowledge gained from this work will be useful in the creation of intelligent magneto-peristaltic pumps for specific heat and medication delivery phenomena., Competing Interests: The authors declare no conflict of interest., (© 2023 The Authors.)

The main objective of this investigation is to deliberate the novel analysis of buoyancy-driven nanofluid flow across a vertical stretching surface embedded in a porous medium with the consideration of an inclined magnetic field and heating effects caused by viscosity, thermal radiations, and heat source factor. A material made of glass ball is applied as the porous medium. Water is regarded as a base fluid, while carbon nanotubes are termed as the nanoparticles. The governing equations are formulated by employing fundamental laws. With the application of appropriate non-similar transformations, the emerging flow system is translated into dimensionless differential form. The obtained coupled, non-similar system of nonlinear partial differential equations (PDEs) is tackled by employing local non-similarity technique up to second level of iterations in conjunction with the Lobatto III technique in MATLAB. According to the findings, increasing the Hartmann number diminishes fluid velocity while augmentation in radiation parameter and nanoparticle volume fraction raises the temperature profile. Moreover, nanofluids contain MWCNTs as such nanoparticles exhibit larger estimations of Nusselt number than SWCNTs-water nanofluid. Authors introduced appropriate transformations for considered problem and argued the local non-similarity approach for simulating the dimensionless structure. To the best of authors' observations, no such study is yet published in literature. [ABSTRACT FROM AUTHOR]

This investigation looks at the influence of an inclined magnetic field on peristaltic transport of hyperbolic tangent nanofluid in inclined channel having flexible walls. Nanofluid consisting of Brownian motion and thermophoresis effects is employed in the definition of problem. Thermal radiation and Joule heating are present. Formulation is further completed by consideration of slip conditions in terms of velocity, temperature and concentration. Lubrication approach has been followed for the development of problem formulation. The key role of various involved parameters on the flow phenomenon are sketched. Slip effect causes the velocity and temperature to increase while reduces the concentration. Reduction in temperature is noticed with thermal radiation whereas temperature enhances for larger Hartman number in responce to the Joule heating effect. [ABSTRACT FROM AUTHOR]

In this paper, a numerical investigation is presented to study Buongiorno's mathematical model for hydromagnetic free convection flow in an isosceles triangular cavity filled with nanofluid. The inclined walls of the cavity are maintained at constant cold temperature whereas various combinations of the thermal boundary conditions at the bottom heated wall are considered. The cavity is permeated by an inclined uniform magnetic field and the effects of Brownian motion and thermophoresis are incorporated into the nanofluid model. The Galerkin weighted residual finite element method has been employed to solve the governing partial differential equations after converting them into a non-dimensional form using a suitable transformation of variables. In the numerical simulations, alumina-water based nanofluid has been taken into account. Comparisons with previously published work are performed and excellent agreement is obtained. The effects of various parameters such as Hartmann number, Rayleigh number and inclined magnetic field angle on streamlines, isotherms and isoconcentrations have been displayed graphically. The heat transfer augmentation for various combination of model parameters as well as various thermal boundary conditions have been done in light of the average Nusselt number from the bottom heated wall. The results show that the heat transfer rate can be decreased with the increasing values of the Hartmann number and inclination angle of the magnetic field but it can be increased by increasing the Rayleigh number and by reducing the diameter of the nanoparticles. The obtained numerical results also indicate that the variable thermal boundary conditions have significant effects on the flow and thermal fields. [ABSTRACT FROM AUTHOR]

This paper is intended for investigating the effects of heat and mass transfer on the peristaltic transport of magnetohydrodynamic couple stress fluid in an inclined asymmetric channel through porous medium. The governing two-dimensional equations of momentum, heat and mass transfer are simplified under the long wavelength and low Reynolds number approximations. The exact solutions are calculated for the stream function, pressure gradient, temperature and concentration. The pressure difference is calculated using numerical integration. The effects of different parameters on the velocity, pressure gradient, pressure difference, temperature and concentration fields, heat transfer coefficient, Nusselt number and trapping phenomena are highlighted through various graphs. It is observed that, pressure gradient and pressure difference increase with increase of Reynolds number and inclination angle of the channel. Temperature and heat transfer coefficient are increasing functions of Darcy number and inclination of the magnetic field. The size of the trapped bolus decreases with increase in couple stress fluid parameter, the trend is reversed with increase in Darcy number. [ABSTRACT FROM AUTHOR]

The inclined magnetic field effect on the boundary layer flow of a Casson model non-Newtonian fluid over a stretching sheet in the existence of thermal radiation and velocity slip boundary condition is investigated for both prescribed surface temperature and power law of surface heat flux cases. It is assumed that the magnetic field is applied with an aligned angle which varied from 0° to 90°. Both analytical and numerical solutions are obtained for the transformed non-dimensional ODE's using confluent hypergeometric function and fourth order Runge–Kutta method with shooting technique respectively. The combined effects of inclined magnetic field with other pertinent parameters such as Casson parameter, velocity slip parameter, radiation parameter and Prandtl number on velocity profile, temperature profile, local skin friction coefficient, local Nusselt number and non-dimensional wall temperature are discussed through graphs. It is found that the aligned angle plays a vital role in controlling the magnetic field strength on the Casson fluid flow region and the increasing values of aligned angle of the magnetic field lead to decrease the skin friction coefficient and the Nusselt number and increase the non-dimensional wall temperature. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the effects of variable viscosity and thermal conductivity on peristaltic flow of Jeffrey fluid in an asymmetric channel. The inclined magnetic field, viscous dissipation and Joule heating are also considered. Wave frame and long wavelength approximations are made to formulate the problem. Pressure gradient, pressure drop per wavelength, velocity and temperature profiles are calculated analytically and discussed graphically. Comparison is made with the previous work for reliability. [ABSTRACT FROM AUTHOR]

In this paper a numerical study which treats the effect of the magnetic field inclination on 3D double diffusive convection in a cubic cavity filled with a binary mixture is presented. The two vertical walls are maintained at different temperatures and concentrations. A particular interest is reserved to determine the effect of the magnetic field inclination on the flow structure and heat and mass transfer. The problem is formalized based on the vector potential vorticity procedure in its three-dimensional configuration and discretized based on the finite volume method. The results are given for Ra = 105, Pr = 1 and Le = 2. This paper presents respectively the inclination effects of the magnetic field direction on the three-dimensional flow structure and on heat and mass transfer. The main results show that the increase of the inclination of the magnetic field direction damped the flow. A critical angle, which depending on Hartmann number, caused big change on the flow structure and accented the three dimensional aspect in the cavity. [ABSTRACT FROM AUTHOR]

This article addresses the peristaltic transport of Eyring-Prandtl fluid in an inclined asymmetric channel. Heat and mass transfer phenomena along with Soret and Dufour effects is analyzed. Effects of inclined magnetic field and Joule heating are also discussed. Long wavelength approximation is adopted. Numerical computations for flow quantities of interest are analyzed. It is found that the parabolic velocity profile tends to shift from center of the channel towards the channel walls in the case of opposing flow. Velocity and temperature decrease whereas concentration increases by increasing the non-Newtonian parameter. Further the dependence of magnetic field on the angle is quite significant. [ABSTRACT FROM AUTHOR]

The present article investigates the inclined magnetic field effects on slip flow of Casson fluid over a stretching sheet. The governing boundary layer non-linear PDEs are converted into non-linear ODEs using similarity transformation. The analytical solutions for the present problem are obtained in terms of confluent hypergeometric function. The effects of various non-dimensional parameters onvelocity, temperature, skin friction and Nusselt number are discussed in detail through plots. [ABSTRACT FROM AUTHOR]

Scientists and researchers have recently been very interested in copper nanoparticles due to their potential modern uses, such as high temperature superconductors, gas sensors, catalytic processes, and solar cells, as well as their usage in wound dressings and biocidal properties. Therefore, in this analysis, the authors have investigated the applications of an inclined magnetic field, radius of nanoparticles, nonlinear thermal radiation, and inter-particle spacing on the two-dimensional flow of an electrically conducting water-based copper nanofluid over a stretching surface using a porous medium. Furthermore, the effects of chemical reaction, exponential heating, thermophoresis and Brownian motion are also taken into account. The nanofluid flow is considered under strong suction, convective, and mass flux conditions. The present model is solved by means of HAM. Convergence of HAM is shown with the help of Figure. The current findings are contrasted with previously reported findings to confirm that the current model is accurate. The outcomes of this study showed that the surface drag gets higher with the increasing angle of inclination. A maximum impact of angle of inclination on the surface drag is found, when α = π /2. Also, it is found that the impact of angle of inclination is greater when the inter-particle spacing is small. While on the other hand, exploring the role of radius of nanoparticle, a higher impact is found when radius of nanoparticle is higher. The velocity profiles are highly affected by the embedded parameters when the inter-particle spacing is small as compared to large inter-particle spacing. The temperature profiles are highly affected by the embedded parameters in the case of nonlinear thermal radiation as compared to linear thermal radiation. [ABSTRACT FROM AUTHOR]

The prime motive of this disquisition is to deal with mathematical analysis of natural convection energy transport driven by combined buoyancy effects of thermal and solutal diffusion in a trapezoidal enclosure. Casson fluid rheological constitutive model depicting attributes of viscoelastic liquids is envisioned. The influence of the inclined magnetic field governed by Lorentz field law is also considered. To raise the essence of the presently used computational and physical domain, an innovative structural design called fillet is capitalized at the edges of the cavity. A numerical solution of the leading formulation is sought through Galerkin finite element discretization. Momentum, temperature, and concentration equations are interpolated by quadratic polynomials, whereas pressure distribution is approximated by a linear interpolating function. Domain discretized version is evaluated in view of triangular and rectangular elements. Newton's scheme is employed to resolve the non-linearly discretized system and a matrix factorization-based non-linear solver renowned as PARADISO is used. Validation of results is ascertained by forming an agreement with existing studies. Streamlines, isothermal and iso concentration contours patterns are portrayed to evaluate variation inflow distributions. Kinetic energy, local heat, and mass fluxes are also divulged in graphical and tabular formats. [ABSTRACT FROM AUTHOR]

In this paper, the electrostatic and electromagnetic instabilities of a magnetized proton–DT plasma relevant to the fast ignition scheme of inertial fusion were examined. The magnetic field and proton beam define a plane and the magnetic field vector has the orientation angle of θ. The dispersion relation of two-stream and filamentation modes was first derived using the conservation, Euler, and Maxwell equations. Then, the more general case describing the wave propagation in an arbitrary direction in the two-dimensional case was derived symbolically. It is demonstrated that in a magnetized beam–plasma system, the two-stream instability depicts two separated growth curves, one larger than the other and there exists a stable frequency band between them. This zone will grow as the magnetic field inclination angle increases such that the smaller two-stream peak vanishes at the limiting angle of θ → π / 2. The splitting in the growth rate curve becomes obvious at magnetic field parameter Ω e >0.5. The pure filamentation instability of the beam–plasma is about two orders of magnitude smaller than the two-stream instability and it just contributes to magnetic field orientation θ = 0. In a two-dimensional case, the mixed electrostatic/electromagnetic instabilities contribute to the final growth rate curve producing an X-like shape. The interface point of two growth curves is characterized by coordinate (∼ 1.0, tan(θ)) in the zx-plane. [ABSTRACT FROM AUTHOR]

In the present contribution, a numerical investigation is presented to study Buongiorno’s nanofluid model for MHD mixed convection of a lid-driven cavity filled with nanofluid. A sinusoidal temperature and nanoparticle volume fraction distributions on both vertical sides is considered where the horizontal walls are kept adiabatic. The cavity is permeated by an inclined uniform magnetic field and the effects of Brownian motion and thermophoresis are incorporated into the nanofluids model. An accurate collocated finite volume method is employed to discretize the governing partial differential equations after converting them to a non-dimensional form using a suitable transformation variables. Comparisons with previously published work are performed and excellent agreement is obtained. The computation is carried out for wide ranges of the Hartmann number Ha ( 0 ⩽ Ha ⩽ 100 ) , buoyancy ratio Nr ( 0.1 ⩽ Nr ⩽ 1 ) , thermophoresis number Nt ( 0.1 ⩽ Nt ⩽ 1 ) , Brownian motion parameter Nb ( 0.1 ⩽ Nb ⩽ 1 ) , Lewis number Le ( 1 ⩽ Le ⩽ 10 ) , Prandtl number Pr ( 0.054 ⩽ Pr ⩽ 10 ) , inclined magnetic field angle γ ( 0 o ⩽ γ ⩽ 3 π / 2 ) , Amplitude ε ( 0 ⩽ ε ⩽ 1.5 ) , phase angle ξ ( 0 o ⩽ ξ ⩽ 3 π / 4 ) and Richardson number Ri ( 0.001 ⩽ Ri ⩽ 100 ) . The obtained results are presented in terms of the streamlines, isotherms and nanoparticles volume fraction contours as well as local Nusselt number. Results demonstrate that, the presence of an inclined magnetic filed in the flow region leads to lose the fluid movement. Also, the fluid flow is dominated by the movement of the upper wall in the case of the highest values of the buoyancy ratio. [ABSTRACT FROM AUTHOR]

Simple analytical formulas are derived for calculation of the electric field potential distribution in the magnetic pre-layer and the Debye layer near the plasma facing surfaces. It is shown that the calculated potential profiles are in good agreement with the dependences of the potential distribution on the magnetic field inclination obtained by solving the magnetic hydrodynamic (MHD) equations and modeling using the PIC code SPICE2. Dependences of the angular distribution of ions incident on the surface of plasma facing elements on the magnetic field inclination are obtained. Results of calculations demonstrate that the surface areas, on which the magnetic field is incident at sliding angles, are critical from the viewpoint of the increase of sputtering. [ABSTRACT FROM AUTHOR]

The intention of this investigation is to study the effects of heat transfer and inclined magnetic field on the peristaltic flow of Williamson fluid in an asymmetric channel through porous medium. The governing two-dimensional equations are simplified under the assumption of long wavelength approximation. The simplified equations are solved for the stream function, temperature, and axial pressure gradient by using a regular perturbation method. The expression for pressure rise is computed numerically. The profiles of velocity, pressure gradient, temperature, heat transfer coefficient and stream function are sketched and interpreted for various embedded parameters and also the behavior of stream function for various wave forms is discussed through graphs. It is observed that the peristaltic velocity increases from porous medium to non-porous medium, the magnetic effects have increasing effect on the temperature, and the size of the trapped bolus decreases with the increasing of magnetic effects while the trend is reversed with the increasing of Darcy number. Moreover, limiting solutions of our problem are in close agreement with the corresponding results of the Newtonian fluid model. [ABSTRACT FROM AUTHOR]

This article describes the influence of an inclined magnetic field on the mixed convective peristaltic transport of fluid in an inclined channel. Two types of non-Newtonian fluids are considered. The problem formulation is presented for the Eyring-Prandtl and Sutterby fluids. Viscous dissipation and Joule heating in the heat transfer process are retained. The presence of a heat source in the energy equation is ensured. The resulting problems are solved by the perturbation method. The plots for different parameters of interest are given and discussed. Numerical values of a heat transfer rate are given and analyzed. [ABSTRACT FROM AUTHOR]

An attempt has been made to study the influence of inclined magnetic field with hall current of a viscous incompressible electrically conducting free convection fluid flow through the parallel plates in a rotating system. The channel is rotating with uniform angular velocity about an axis normal to the plates. For numerical solution, the problems have been transferred into dimensionless form and then the explicit finite difference technique has been used. The stability conditions and convergence criteria of the explicit finite difference scheme are established for finding the restriction of the values of various parameters to get more accuracy. The effects of Rotation parameter, Hall parameter, Magnetic parameterand Angle of inclination on primary and secondary velocities have been shown in graphical representations. Finally the effects of these parameters have been analyzed by the figures of local shear stress and average current density at the moving plates of channel. [ABSTRACT FROM AUTHOR]

The effect of an inclined magnetic field in the peristaltic flow of a Jeffrey fluid with variable thermal conductivity is discussed. The temperature dependent thermal conductivity of fluid in an asymmetric channel is taken into account. A dimensionless nonlinear system subject to a long wavelength and a low Reynolds number is solved. The explicit expressions of the stream function, the axial velocity, the pressure gradient, and the temperature are obtained. The effects of all physical parameters on peristaltic transport and heat transfer characteristics are observed from graphical illustrations. The behaviors of θ ∈ [0, π/2] and θ ∈ [ π/2, π] on fluid flow and heat transfer are found to be opposite. Further, the size of trapped bolus is greater for the case of the inclined magnetic field ( θ ≠ π/2) than that for the case of the transverse magnetic field ( θ = π/2). The heat transfer coefficient decreases when the constant thermal conductivity (Newtonian) fluid is changed to the variable thermal conductivity (Jeffrey) fluid. [ABSTRACT FROM AUTHOR]

Magnetohydrodynamic free convection flow past a flat plate with ramped wall temperature and radiative heat transfer embedded in a porous medium in the presence of an inclined magnetic field is studied. Fluid flow is induced due to an impulsive movement of the plate. Exact solution of the governing equations for the fluid velocity and fluid temperature is obtained in closed form. To compare the results obtained in the case of a flow past a ramped temperature plate with that of isothermal plate, exact solution of the governing equations is also obtained for isothermal plate. The expressions for the skin friction and Nusselt number are derived for both ramped temperature and isothermal plate. Numerical values of fluid velocity and fluid temperature are displayed graphically, whereas the values of skin friction and Nusselt number are presented in tabular form for various values of pertinent flow parameters. [ABSTRACT FROM AUTHOR]

• The conventional model for thermo-solutal mixed Marangoni flow is modified by incorporating the solutal buoyancy force effects. • The nanoliquid is modeled by considering experimentally estimated properties. • The conventional thermosolutal and thermal Marangoni flow cases can be obtained as a limiting case of the present problem. • The dynamics of the nanoliquid flow are visualized for the buoyancy-assisted and opposed flow cases. • The optimum levels of heat and mass transport is obtained at the high level of thermal radiation and the low levels of the cross-diffusion aspects. The control of heat transfer in the hydromagnetic semiconductor crystal involves Marangoni convection with buoyancy forces. In this study, the conventional thermo-solutal Marangoni mixed flow model is modified by incorporating the solutal buoyancy effects that are significant in the flow phenomenon. The heat and mass transfer (HMT) characteristics of the Marangoni convective flow of a Cu − H 2 O nanofluid subjected to the assisting/resisting buoyancy forces and cross-diffusion are numerically studied. The homogeneous single-phase nanoliquid model is used in conjunction with experimental data of dynamic viscosity and thermal conductivity. The Dufour and Soret effects are considered. Governing equations are solved using the finite difference-based algorithm. The problem is analyzed in a unified way considering the cases of buoyancy-assisted flow and buoyancy-opposed flow. The response surface methodology (RSM) based on the face-centered composite design (CCD) is used to optimize the heat and mass transfer rates. A multivariate regression model is proposed and authenticated prior to optimization. Additionally, sensitivity analysis is performed using the full quadratic regression model. The increase in the temperature profile is more significant due to the radiative heat flux than the inclined magnetic field. Heat transfer has a high sensitivity to the appearance of thermal radiation, while mass transfer has a high sensitivity to the Soret effect. Simultaneous optimization of HMT rates is achieved with the high level of thermal radiation and low levels of the cross-diffusion aspects. [ABSTRACT FROM AUTHOR]

The investigation of the interaction between the wall driven fluid stream and the partially heated barriers is a filed of great interest for the researchers. The present analysis aims to evaluate free and forced convection in a corrugated-wall parallelogram cavity. A Heated source is located at the bottom of enclosure and the upper boundary maintained the mixed convection in the enclosure. Flow dynamics and thermal profiles are established with regard to magnetic field. The non-linear partial differential equation obtained from the mathematical interpretation of such complex physical system are solved numerically using finite element method. The outcomes of the simulation towards flow controlling parameters (Richardson number 0 < Ri ≤ 100 , Hartmann number 0 ≤ Ha ≤ 100 , amplitude 0.02 ≤ A m ≤ 1.00 , magnetic field inclination 0 ≤ φ ≤ π 2) are presented in line graphs and contour maps. It is observed that forced convection dominates at low value of Richardson number and free convection dominates at larger values of Richardson number. Further, the results indicate that increasing wall undulation A m the velocity profile enhances the Nusselt number also possess higher values at maximum A m. It is also reported that heat the transfer rate has maximum behavior at large Ha and φ = π 2. [ABSTRACT FROM AUTHOR]

This study aims to investigate the Hall effect on an unsteady flow in a composite channel of an upper oscillating wall in the presence of an inclined magnetic field. The flow field considered in the channel is composed of porous medium and clear viscous layers. The governing equations for flow and magnetic field are solved numerically by the Crank-Nicolson implicit finite-difference scheme. The results obtained are discussed graphically for various values of the pertinent parameters. doi:10.14456/WJST.2014.42

In this paper, we investigate the pulsating flow of an incompressible and slightly conducting micropolar fluid between two homogeneous permeable beds in the presence of an inclined uniform magnetic field. The flow between the permeable beds is assumed to be governed by Eringen's micropolar fluid flow equations and that in the permeable beds by Darcy's law with the Beavers-Joseph slip conditions at the fluid-permeable bed interfaces. It is assumed that a uniform magnetic field is applied at an angle θ with the y -axis. The equations are solved analytically and the expressions for velocity and microrotation are obtained. The effects of the magnetic parameter and the other material parameters are studied numerically and the results are presented through graphs. [ABSTRACT FROM AUTHOR]

In this article, we have discussed inclined magnetic field on the peristaltic flow of biviscosity with the impact of thermal and velocity slips in an irregular channel. The momentum governing equations are fabricated under long wavelength and low Reynolds number guesstimate. Exact solutions are found in closed-form for flow equations representing stream function and pressure gradient. The flow comportment is examined over the properties of the governing parameters such as, the upper limit apparent viscosity coefficient β, slip parameters Λ, γ , Hartmann number M and amplitudes ϕ , a , b and d on pressure rise, velocity, pressure gradient and subsequently on streamlines. [ABSTRACT FROM AUTHOR]

The problem of natural convection in an inclined L-shaped enclosure filled with Cu/water nanofluid that operates under differentially heated walls in the presence of an inclined magnetic field is presented in this paper. The fully implicit finite difference method is used to solve the governing equations. A comparison with previously published results in special case of the present study is performed and a very good agreement is found. Heat transfer and fluid flow are examined for parameters of the Hartmann number (0 ≤ Ha ≤ 100), the nanoparticles volume fraction (0% ≤ ϕ ≤ 20%), the cavity inclination angle (0 ° ≤ ϑ ≤ 300 ° ), the magnetic field inclination angle (0 ° ≤ γ ≤ 270 ° ), the cavity aspect ratio (0.25 ≤ AR ≤ 0.6) and the Rayleigh number (10 3 ≤ Ra ≤ 10 6 ). It is found that, the presence of the magnetic field in the fluid region causes a significant reduction in the fluid flow and heat transfer characteristics. Also, a good enhancement in the heat transfer rate can be obtained by adding the copper nanoparticles to the base fluid. [ABSTRACT FROM AUTHOR]

This study aims to investigate the Hall effect on an unsteady flow in a composite channel of an upper oscillating wall in the presence of an inclined magnetic field. The flow field considered in the channel is composed of porous medium and clear viscous layers. The governing equations for flow and magnetic field are solved numerically by the Crank-Nicolson implicit finite-difference scheme. The results obtained are discussed graphically for various values of the pertinent parameters. [ABSTRACT FROM AUTHOR]

Effect of Hall current on peristaltic transport of couple stress fluid in an inclined asymmetric channel is investigated. An incompressible fluid is conducting in the presence of inclined magnetic field. Problem formulation is developed through heat and mass transfer aspects. Soret and Dufour effects are present. Long wavelength and low Reynolds number approaches are adopted. Closed form expression for longitudinal velocity, pressure gradient, temperature and concentration are presented. Important results reflecting the influence of embedded parameters in the problems have been pointed out. Pumping and trapping phenomena are especially focused. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we investigate the onset of convection in a horizontal layer of fluid which is heated from the underside. An inclined magnetic field is applied to the layer. The Galerkin truncated approximations were used to obtain a Lorenz-like model. The nonlinear system was solved by the fourth-order Runge–Kutta method. The results show that the Hartmann number and the angle of inclination of the magnetic field could inhibit or enhance the onset of chaotic convection. [Copyright &y& Elsevier]

Peristaltic flow of viscous fluid in an asymmetric inclined channel with heat transfer and inclined magnetic field is examined. The convective boundary conditions have been handled. Complexity of emerging equations is simplified by utilizing long wavelength and low Reynolds number approximation. Variation of emerging parameters embedded in flow system are discussed. It is observed that an increase in Brikman number increases the temperature profile. Further, it is seen that temperature distribution is an increasing function of Biot number at lower wall. [ABSTRACT FROM AUTHOR]

This study investigates the impacts of thermal jump and inclined magnetic field on the peristaltic transport of Jeffrey fluid containing silver nanoparticles in the eccentric annuls under the long wavelength and low Reynolds number assumption. In medical studies, the impact of thermal jumps and slanted magnetic fields on public health is of interest. Peristaltic motion's ability to transmit heat and create a magnetic field has several uses in biomedical and bioengineering. The non-Newtonian Jeffrey fluid with silver nanoparticles is considered in the space between two cylindrical tubes that are eccentrically aligned. The homotopic perturbation method is semi-analytical for modeling and nonlinear partial differential equations (HPM). Analytical solutions for velocity, pressure gradient, and pressure rise were found. To show how physical parameters affect temperature, velocity, concentration, frictional force, and pressure rise of inner and outer tubes were plotted. A comparison of the present method with the exact solution for temperature and nanoparticle concentration profile is shown graphically. The present analysis of analytical solution approaches to the exact solution. The most significant thing in the current investigation is that the Hartmann number and thermophoresis number make the velocity profile decline. Jeffrey fluid parameter and magnetic field angle make the velocity rise. The nanofluid's temperature rises as a result of the thermal jump. In addition, the Jeffrey nanofluid has a higher momentum and temperature than the Jeffrey fluid. This analysis can better evaluate the syringe's injection speed and fluid flow features during cancer treatment, artery blockage removal, and reduced bleeding throughout the surgery., Competing Interests: The authors declare no conflict of interest., (© 2022 Published by Elsevier Ltd.)

This study explored the impact of double diffusive convection and inclined magnetic field in nanofluids on the peristaltic pumping of fourth grade fluid in non-uniform channels. Firstly, a brief mathematical model of fourth grade fluid along inclined magnetic fields and thermal and concentration convection in nanofluids was developed. A lubrication approach was used to simplify the highly non-linear partial differential equations. An analytical technique was then used to solve the highly non-linear differential equations. The exact solutions for the temperature, nanoparticle volume fraction and concentration were calculated. Numerical and graphical outcomes were also examined to see the effects of the different physical parameters of the flow quantities. It was noted that as the impact of Brownian motion increased, the density of the nanoparticles also increased, which led to an increase in the nanoparticle fraction. Additionally, it could be observed that as the effects of thermophoresis increased, the fluid viscosity decreased, which lowered the fraction of nanoparticles that was made up of less dense particles.

An inclined MHD (Magnetohydrodynamics) micropolar fluid flow due to stretching/shrinking sheet in the presence of mass transpiration and thermal radiation is examined in the present analysis. The governing non-linear PDEs (Partial differential equations) are altered into ODEs (Ordinary differential equations) by using similarity variables. These types of flow problems have many industrial applications such as polymer extrusion, glass blowing and so on. The flow and heat problems were examined analytically especially heat transfer analysis is examined under two different cases namely PST (Prescribed surface temperature) and PHF (Prescribed heat flux) cases, then these solutions are expressed in terms of Kummer's function. Thermal radiation is also taken into account in heat equation and the analysis is carried out by using the microrotation parameter throughout the equation. Coefficient of Skin friction and local Nusselt number are also examined, analytically. Furthermore, graphical scenario have been considered by using different physical parameters namely Prandtl number, Chandrasekhar's number, radiation parameter, mass transpiration and so on. By using these results, it is cleared that microrotation parameter helps to increase Nusselt number, but dual nature behavior is observed for shrinking sheet condition. The induces magnetic field slightly increases the surface skin friction and slightly reduces the surface mass transfer. • The laminar micropolar fluid flow with mass transpiration is investigated. • Sheet is moving in both stretching and shrinking conditions. • The liquid flow is under the impact of heat source/sink and radiation. • The PST and PHF cases are illustrated for temperature profiles. • Impacts of inclined MHD on the liquid flow is investigated [ABSTRACT FROM AUTHOR]

A mathematical model is constructed to investigate the mixed convective heat and mass transfer effects on peristaltic flow of magnetohydrodynamic pseudoplastic fluid in a symmetric channel. An analysis has been carried out to examine the impact of an inclined magnetic field and chemical reaction in presence of heat sink/source. Mechanics of flow and heat/mass transfer described in terms of continuity, linear momentum, energy and concentration equations are predicted by using long wavelength and low Reynolds number. Expressions for stream function, temperature, concentration and pressure gradient are derived. Numerical simulation is performed for the rise in pressure per wave length. Effects of several physical parameters on the flow quantities are analyzed. [ABSTRACT FROM AUTHOR]

The current article discusses the outcomes of the double diffusion convection of peristaltic transport in Sisko nanofluids along an asymmetric channel having an inclined magnetic field. Consideration is given to the Sisko fluid model, which can forecast both Newtonian and non-Newtonian fluid properties. Lubricating greases are the best examples of Sisko fluids. Experimental research shows that most realistic fluids, including human blood, paint, dirt, and other substances, correspond to Sisko's proposed definition of viscosity. Mathematical modelling is considered to explain the flow behavior. The simpler non-linear PEDs are deduced by using an elongated wavelength and a minimal Reynolds number. The expression is also numerically calculated. The impacts of the physical variables on the quantities of flow are plotted graphically as well as numerically. The results reveal that there is a remarkable increase in the concentration, temperature, and nanoparticle fraction with the rise in the Dufour and thermophoresis variables.

A mathematical model is developed to study the characteristics of blood flow through flexible inclined arteries under the influence of an inclined magnetic field. The blood is supposed to be couple stress fluid and the geometry of wall surface of inclined arteries is taken as peristaltic wave. The expressions for axial velocity, volume flow rate, pressure gradient and stream function are obtained under the assumptions of long wavelength and low Reynolds number. The effects of different physical parameters reflecting couple stress parameter, Hartmann number, Reynolds number, Froude number, inclination of channel and inclination of magnetic field on velocity profile, pressure and frictional force are discussed. The stream lines are drawn for various values of emerging parameters and the trapping phenomenon is discussed. The significant features of the blood flow characteristics are analyzed by plotting graphs and discussed numerically in detail. [ABSTRACT FROM AUTHOR]

Unsteady hydromagnetic Couette flow of a viscous incompressible electrically conducting fluid ma rotating system in the presence of an inclined magnetic field taking Hall current into account is studied. Fluid flow within the channel is induced due to impulsive movement of the lower plate of the channel. Exact solution of the governing equations is obtained by Laplace transform technique. The expression for the shear stress at the moving plate is also derived. Asymptotic behavior of the solution is analyzed for small and large values of time I to highlight (i) the transient approach to the final steady state flow and (ii) the effects of Hall current, magnetic field, rotation and angle of inclination of magnetic field on the flow-field. It is found that Hall current and rotation tend to accelerate fluid velocity in both the primary and secondary flow directions. Magnetic field has retarding influence on the fluid velocity in both the primary and secondary flow directions. Angle of inclination of magnetic field has accelerating influence on the fluid velocity, in both the primary and secondary flow directions. [ABSTRACT FROM AUTHOR]

Abstract: This paper investigates the peristaltic motion of a magnetohydrodynamic (MHD) non-Newtonian fluid in an inclined asymmetric channel. Constitutive equations obeying the fourth grade fluid model are employed. Mathematical modeling is developed in the presence of a constant inclined magnetic field making an angle with the vertical axis. Assumptions of long wave length and low Reynolds number are used in deriving solution for the flow. Closed form expressions for the stream function and pressure gradient are developed. Pressure rise per wave length and frictional forces on the channel walls have been computed numerically. Effects of Hartman number, Froude number and inclination of magnetic field on the axial velocity, pressure gradient, pumping and trapping are discussed in detail and shown graphically. Several limiting results can be obtained as the special cases of the problem under consideration. [ABSTRACT FROM AUTHOR]

Abstract: In this paper the influence of inclined magnetic field on the peristaltic flow of a Williamson fluid in an inclined symmetric or asymmetric channel has been investigated initially in the wave frame of reference. The highly nonlinear equations are simplified under lubrication approach. The analytical and numerical solutions of the proposed problem have been computed and analyzed. The graphical results are displayed to see the effects of various physical parameters of interest. [Copyright &y& Elsevier]

Closed-form solutions are presented for the transient hydromagnetic flow in a rotating channel with inclined applied magnetic field under the influence of a forced oscillation. Magnetic Reynolds number is large enough to permit the inclusion of magnetic induction effects. The Maxwell displacement current effect is also included and simulated via a dielectric strength parameter. The governing momentum and magnetic induction conservation equations are normalized with appropriate transformations and the resulting quartet of partial differential equations are solved exactly. A parametric study is performed of the influence of oscillation frequency parameter (ω), time (T), inverse Ekman number, i.e. rotation parameter (K²), square of the Hartmann magnetohydrodynamic (MHD) parameter (M²), and magnetic field inclination (θ) on the primary and secondary induced magnetic field components (bx, by) and velocity components (u, v) across the channel. Network solutions are also obtained to validate the exact solutions and shown to be in excellent agreement. Applications of the study arise in planetary plasma physics and rotating MHD induction power generators and also astronautical flows. [ABSTRACT FROM AUTHOR]