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The effect of source/sink heat location and size on Magneto-hydrodynamic mixed convection in hybrid nanofluid of Al2O3-Cu/Water within the L-shaped cavity is studied in this paper. Two uniform heat sources are put at the corners of the bottom walls of enclosure and the beginning and the end of L-shape enclosure set to be at the cold temperature. The other parts of enclosure’s walls are supposed to be insulated. The finite difference method and Boussinesq approximation is utilized to discrete the governing equations. The fundamental flow physics and thermal behavior are explored in terms of pertinent parameters such as the effects of sink/source heat generation, magnetic field and angle, Hartmann number, cavity length ratio, and hybrid volume fraction on average and surface Nusselt number, streamlines, isotherms, and entropy generation are studied. The results demonstrate that maximum amount of the sink power causes the best heat transfer performance.

Theoretical investigation on the interaction between conducting and non-conducting walls on hydromagnetic natural convection flow of viscous incompressible and electrically conducting fluid through a vertical micro-channel taking into account the effects of induced magnetic field in presence of Hall current is presented. Governing coupled equations responsible for the flow are obtained when either the micro-channel walls are electrically conducting or are electrically non-conducting. Using the method of undetermined coefficients, exact solution are obtained and presented in dimensionless form subject to relevant boundary conditions. Expressions for fluid velocity, induced magnetic field, skin friction, volume flow rate and induced current density in both primary and secondary flow directions are also obtained. Effects of some governing parameters like Hall current parameter, rarefaction parameter and Hartmann number on the different flow situations are given using the aid of line graphs and Tables. The main conclusion of the present analysis is that, in the existence of rarefaction parameter, primary fluid velocity could be enhanced with the increase in Hall parameter when the micro-channel walls are either insulated or when the left micro-channel wall is electrically conducting. Results obtained in this work are relevant in many magnetically controlled devices and could also be used as a benchmark in checking the accuracies of result obtained in some empirical experiments.

The current work pertains to the peristaltic motion of a Casson fluid through a non-uniform channel with exposure to a radial magnetic field. The wall properties of the channel are taken into consideration. Moreover, the fluid is considered to possess variable viscosity which shows exponential variation across the width of the channel. The investigations also consider the mass and heat transfer properties of the Casson fluid, where convective boundary conditions are used and the thermal conductivity is taken be varying with fluid temperature. The model is built to give insight into blood flow through small vessels. Solution to the problem is obtained by the method of perturbation. The graphical analysis reveals an increase in the effect of variable viscosity on the fluid velocity close to the walls of the channel and also on the size of the bolus formed during trapping. Furthermore, an increase in fluid temperature was observed due to variable thermal conductivity.

The investigation of radiation-absorption, chemical reaction, Hall and ion-slip impacts on unsteady MHD free convective laminar flow of an incompressible viscous, electrically conducting and heat generation/absorbing fluid enclosed with a semi-infinite porous plate within a rotating frame has been premeditated. The plate is assumed to be moving with a constant velocity in the direction of fluid movement. A uniform transverse magnetic field is applied at right angles to the porous surface, which is absorbing the fluid with a suction velocity changing with time. The non-dimensional governing equations for present investigation are solved analytically making use of two term harmonic and non-harmonic functions. The graphical results of velocity, temperature and concentration distributions on the analytical solutions are displayed and discussed with reference to pertinent parameters. It is found that the velocity profiles decreased with an increasing in Hartmann number, rotation parameter, the Schmidt number, heat source parameter, while it increased due to an increase in permeability parameter, radiation-absorption parameter, Hall and ion slip parameters. However, the temperature profile is an increasing function of radiation- absorption parameter, whereas an increase in chemical reaction parameter, the Schmidt number Sc or frequency of oscillations decrease the temperature profile on cooling. Also, it is found that the concentration profile is decreased with an escalating in the Schmidt number or the chemical reaction parameter.

Magnetohydrodynamic (MHD) flow through a corrugated curved channel is modelled. The flow is perpendicular to the corrugations and applied magnetic field. A boundary perturbation analysis for small corrugation amplitude is used to find the expressions for the stream function and the flow rate. It is found that the flow is inevitably decreased by the corrugations. For a given Hartmann number, the flow reduction varies with the channel radius of curvature. The effect of the phase difference between the corrugated walls is distinct, with minimum and maximum effects when the corrugated curved walls are in-phase and out-of-phase, respectively, for small corrugation wavenumber. However, when the corrugation wavenumber is large enough, the flow is independent of the phase difference. Generally, the study shows that the Hartmann number decreases the effect of the corrugations on the flow rate.

The present study explores magnetic hybrid-nanoliquid (Al2O3–Cu/H2O) natural convection in a heated incinerator shaped cavity by using the lattice Boltzmann method (LBM). Numerical results are presented in the form temperature contours, stream function and local entropy generation. Complex interaction between various physical phenomena characterizing this problem including the natural convection and the magnetic field has been observed. Influences of Rayleigh number (Ra = 103–106), volumetric fraction of nanoparticles (ϕ = 0–0.04), and Hartmann number (Ha = 0–90) are clarified in details through graphical portraits. Results depict that the average Nusselt number (Num) and average entropy generation (Sgen,A) increases with an increase of the Rayleigh number while are decreased by applying a magnetic field. In addition, it is found that the average Nusselt number (Num) increases with the rise of volumetric fraction of nanoparticles for all Rayleigh and Hartmann numbers. Conversely, an opposite effect is obtained by an increase in volumetric fraction of nanoparticles on the average entropy generation (Sgen,A). Finally, the numerical results demonstrate that the effect of Lorentz force is reduced when the heat transfer regime conduction is considered.

Purpose This paper aims to study the thermal and thermo-hydraulic performances of ferro-nanofluid flow in a three-dimensional trapezoidal microchannel heat sink (TMCHS) under uniform heat flux and magnetic fields. Design/methodology/approach To investigate the effect of direction of Lorentz force the magnetic field has been applied: transversely in the x direction (Case I);transversely in the y direction (Case II); and parallel in the z direction (Case III). The three-dimensional governing equations with the associated boundary conditions for ferro-nanofluid flow and heat transfer have been solved by using an element-based finite volume method. The coupled algorithm has been used to solve the velocity and pressure fields. The convergence is reached when the accuracy of solutions attains 10–6 for the continuity and momentum equations and 10–9 for the energy equation. Findings According to thermal indicators the Case III has the best performance, but according to performance evaluation criterion (PEC) the Case II is the best. The simulation results show by increasing the Hartmann number from 0 to 12, there is an increase for PEC between 845.01% and 2997.39%, for thermal resistance between 155.91% and 262.35% and ratio of the maximum electronic chip temperature difference to heat flux between 155.16% and 289.59%. Also, the best thermo-hydraulic performance occurs at Hartmann number of 12, pressure drop of 10 kPa and volume fraction of 2%. Research limitations/implications The embedded electronic chip on the base plate generates heat flux of 60 kW/m2. Simulations have been performed for ferro-nanofluid with volume fractions of 1%, 2% and 3%, pressure drops of 10, 20 and 30 kPa and Hartmann numbers of 0, 3, 6, 9 and 12. Practical implications The authors obtained interesting results, which can be used as a design tool for magnetohydrodynamics micro pumps, microelectronic devices, micro heat exchanger and micro scale cooling systems. Originality/value Review of the literature indicated that there has been no study on the effects of magnetic field on thermal and thermo-hydraulic performances of ferro-nanofluid flow in a TMCHS, so far. In this three dimensional study, flow of ferro-nanofluid through a trapezoidal heat sink with five trapezoidal microchannels has been considered. In all of previous studies, in which the effect of magnetic field has been investigated, the magnetic field has been applied only in one direction. So as another innovation of the present research, the effect of applying magnetic field direction (transverse and parallel) on thermo-hydraulic behavior of TMCHS is investigated.

The effects of pulsatile pressure gradient in the presence of a transverse magnetic field on unsteady blood flow through an inclined tapered cylindrical tube of porous medium are discussed in this article. The fractional calculus technique is used to provide a mathematical model of blood flow with fractional derivatives. The solution of the governing equations is found using integral transformations (Laplace and finite Hankel transforms). For the semianalytical solution, the inverse Laplace transform is found by means of Stehfest’s and Tzou’s algorithms. The numerical calculations were performed by using Mathcad software. The flow is significantly affected by Hartmann number, inclination angle, fractional parameter, permeability parameter, and pulsatile pressure gradient frequency, according to the findings. It is deduced that there exists a significant difference in the velocity of the flow at higher time when the magnitude of Reynolds number is small and large.

In the present study, the effects of a magnetic field on melting and solidification processes in an isosceles triangular cavity are numerically investigated, using a finite volume method along with an enthalpy-porosity technique. The magnetic field effects (magnitude and direction) on streamlines, isotherms, liquid fraction, and heat transfer are analyzed for Ra = 106 and a wide range of Hartmann number (0 ≤ Ha ≤ 100). As main outcomes, it is observed that contrary to the general trend, the strongest fluid flow stabilization is obtained when the magnetic field is directed parallel to the heated wall. When the magnetic field is horizontally and vertically oriented, the complete melting time is increased by 32.5% and 5.5%, respectively. It is found that the influence of the magnetic field is prominent and reaches a maximum value only during an intermediate stage of melting. Moreover, it is observed that the solidification process is not dependent on the magnetic field direction and magnitude. The complete time of melting at Ha = 100 is almost equal to the time of complete solidification.

Purpose The purpose of this paper is to analyze the unsteady conjugate mixed convective heat transfer characteristics in a vented porous cavity under the combined effects of moving conductive elliptic object and magnetic field. Design/methodology/approach The finite element method and arbitrary Lagrangian-Eulerian (ALE), impacts of Reynolds number, Hartmann number, aspect ratio of the conductive ellipse and moving speed of the object on the hydro-thermal performance are analyzed. Findings It was observed that the dynamic characteristics of the local and average Nu number of each hot wall are different. Magnetic field strength increment resulted in the enhancement of average Nu number for bot steady and transient case while the optimum case for best hydro-thermal performance is achieved for highest Ha number and non-dimensional time of 10. Higher value of average Nu and lower pressure coefficient are achieved for aspect ratio of 4 and non-dimensional time of 10. When the moving velocity of the conductive ellipse is considered, 42% enhancement in the average Nu is obtained at non-dimensional time of 20 and object velocity equals to 0.012 times entering fluid velocity in the negative y direction while the pressure coefficient is higher. The moving object is used as a useful tool to control the dynamic features of heat transfer in a vented cavity. Originality/value The present method of convective heat transfer control inside a vented cavity with a moving elliptic object is novel and can be used as an effective tool with magnetic field effects owing to diverse use of convection in cavities with vented ports in many practical thermal engineering systems.

A theoretical study on the pulsatile flow of Sutterby nanofluid in an inclined porous tapered arterial stenosis under the simultaneous impact of electro-osmotic , magnetohydrodynamic and periodic body forces with slip effect at the arterial wall is presented. Gold (Au) nanoparticles with various shapes (spheres, bricks, cylinders, platelets and blades) are utilized in the analysis. Poisson–Boltzmann equation is used to encounter the phenomena of the applied electric field. By assuming the low zeta potential on the walls, Debye–Huckel approximation is adapted to linearize the Poisson–Boltzmann equation, and then closed-form solution for the electric potential function is obtained. Under the assumption of small Reynolds number and mild stenoses case, the equations that govern the flow are made non-dimensional, and a suitable radial coordinate transformation is used to convert the irregular boundary to a regular boundary. The analytical expression for temperature profile is obtained via Laplace and finite Hankel transforms, from which Nusselt number is derived while the velocity profile is computed numerically employing a Crank–Nicolson scheme with the appropriate boundary and initial conditions. The physical aspect of various emerging parameters is analyzed through various graphs and tables for profiles of dimensionless velocity, temperature, volumetric flow flux, flow impedance, skin-friction coefficient and Nusselt number. It is found that an upsurge in the electro-osmotic parameter serves to reduce the hemodynamic factors (skin-friction and impedance) substantially, whereas an adverse trend is noticed for the Hartmann number. It is also deduced that the utilization of the spherical shape nanoparticles shows the higher heat flux at the stenosed arterial wall compared to the other nanoparticle shapes, and hence, nanoparticles and their shapes play a prominent role in biomedical applications. In order to validate the current results, different comparisons have been made with earlier published studies in a limiting case and an excellent agreement was found.

This article refers to an investigation of peristaltic transport of hybrid nanoparticle suspended blood through an endoscopic annulus with elastic walls in the existence of blood clotting under electromagnetic forces (EMF). The dual effects of Hall and ion-slip currents are accounted for. The energy equation is formulated invoking internal heat source and viscous-Ohmic dissipation terms. Blood is used as a base fluid, and silver and aluminum oxide nanoparticles are dispersed in order to have a hybrid blood suspension. The impacts of the geometrical shape of nanoparticles are examined. The governing partial differential equations (PDEs) for the proposed flow model are simplified under the assumption of long wavelength and low Reynolds number. The transformed non-linear coupled PDEs are solved analytically by employing the homotopy perturbation method (HPM) with Mathematica computational software. The graphical illustrations are presented to interpret various flow constraints of interest. Outcomes reflect that the Hall and ion slip parameters have diminishing behavior on the blood flow while the opposite fashion prevails on it for increasing Hartmann number. Augmenting Hall and ion slip parameters result in an upsurge in the blood temperature. Expanding the volume fraction of nanoparticles enhances the blood temperature. Hall and ion slip effects are to reduce the wall shear stress (WSS) at the peristaltic wall. The maximum amplitude of the heat transfer coefficient is computed for the brick shape of nanoparticles when compared to the other shapes of nanoparticles. The streamlines are configured with trapping ed bolus phenomena to outline the blood flow pattern in the endoscope. Our model may be pertinent to physiological systems, medical simulation devices, transport phenomena in pharmacology, nano-pharmacological delivery systems, surgical procedures, etc. In endoscopy, a magnetic force field is used in order to detect or treat diseases.

In this article, the flow of thin Casson-nanoliquid (CNL) film is examined over a porous stretching sheet with suction/injection and transverse magnetic. Appropriate similarity transformations are used to transmute the governing set of equations to a set of partial differential equations. Analytical expressions for the velocity and temperature fields are obtained by the singular perturbation technique. The non-linear film evolution equations for long time are solved by fourth-order Runge–Kutta method. It is observed that the thickness of the liquid film enhances with the nanoparticle volume fraction, Casson parameter, Hartmann number, and porosity parameter. The rate of film thinning increases for suction, whereas reverse phenomenon is found for injection. A curve $$x=X_c$$ is drawn within the CNL which divides total flow region in two parts, such that in one region, heat is transferred from sheet to the CNL film and on other zone from film to sheet.

Temperature transfer by virtue of natural convection for visualizing heat transport characteristics through heatline method within a prismatic cavity filled with Cu-H2O nanofluid considering two different temperature boundary conditions is performed numerically. Two top inclined walls are warmed-up at low temperature whilst the bottom wall is heated two different heated conditions such as uniform temperature condition and linear temperature condition. Two vertical walls are insulated. Finite element technique of Galerkin weighted residual form is employed for solving nonlinear partial differential equations for numerical calculation. Heatlines, isotherm contours, streamline contours, and Nusselt number are employed for displaying numerical simulated results for the model parameters entitled nanoparticles volume fraction, Hartmann number and Rayleigh number. The outcomes indicate that heat transfer rate has a significant impact on thermal boundary condition and shape of the nanoparticles. The temperature transfer value enhances significantly for higher Rayleigh number as well as nanoparticles volume fraction. Hartmann number has a positive impact on fluid flow and temperature transport. The characteristics of heat transport using heatlines method are also performed for predicting the better energy transform compared to isotherm contours. In addition, different types of nanofluids are also employed to examine the best heat transport performance.

In the present numerical analysis, the forced convection of nanofluid flow is investigated in a microtube with twisted porous blocks while existing a uniform magnetic field based on the first and second laws of thermodynamics with various geometries. Using the finite volume technique and SIMPLE algorithm, the governing equations are discretized and solved. The governing equations are solved using a two-phase mixture model and second-order upwind technique. With the heat flux of 5000 W.m−2, the effects of Hartmann number, Reynolds number, the volume fraction of nanoparticles, as well as porosity percentage of twisted porous blocks are investigated on pressure drop, heat transfer rate, and flow fields. The values of the Hartmann and Reynolds numbers are different within the range of Ha = 0 to Ha = 20 and Re = 250 to Re = 1000, respectively, and the volume fraction of nanoparticles is different within φ = 0 to 2%. The findings indicate that placing the porous blocks in the microtube leads to protrusions in the local diagrams, moreover, by increasing the number of twisted porous block layers, the vertices value of these protrusions increments. By incrementing the Reynolds number, the pressure drop and convective heat transfer coefficient are increased, and the friction factor is decreased. Incrementing φ and the thermal conductivity of the fluid increase the heat transfer rate. Moreover, by increasing the Hartmann number, the local friction factor and the Nusselt number are increased. According to the results, by increasing the number of twisted porous block layers in the highest φ, the average pressure drop becomes 38.171 Pa. The performance evaluation criterion in Ha = 20 and microchannel with three twisted block layers possess the highest value of 1.717.

This paper investigates the magnetic blood flow in an inclined multi-stenosed artery under the influence of a uniformly distributed magnetic field and an oscillating pressure gradient. The blood is modelled using the non-Newtonian Casson fluid model. The governing fractional differential equations are expressed by using the fractional Caputo-Fabrizio derivative without singular kernel. Exact analytical solutions are obtained by using the Laplace and finite Hankel transforms for both velocities. The velocities of blood flow and magnetic particles are graphically presented. It shows that the velocity increases with respect to the Reynolds number and the Casson parameter. Meanwhile, the velocity decreases as the Hartmann number increases. These results are useful for the diagnosis and treatment of certain medical problems.

In this study, the pulsating flow of hydromagnetic nanofluid in a vertical porous channel has been investigated. Blood is considered as a base fluid that is non-Newtonian, and alumina $$(\mathrm{Al}_{2}\mathrm{O}_{3})$$ , copper (Cu), silver (Ag) and gold (Au) are considered as nanoparticles. The effects of Joule’s heating and velocity slip at the walls are taken into consideration. Numerical results are obtained by solving the transformed differential equations using the Runge–Kutta fourth-order in addition to the shooting method. Influences of several flow controlling parameters including Grashof number, cross-flow Reynolds number, Hartmann number and frequency parameter on velocity and temperature profiles are examined graphically. The results elucidates that the velocity-slip plays an important role in increasing the heat transfer and velocity of the nanofluid. Further, the heat transfer rate by means of Nusselt number against different parameters is studied and the numerical results obtained are presented. It shows that heat transfer rate at the injection wall increased with increasing Grashof number, frequency parameter and radiation parameter.

The characteristics of heat transport in nanoliquids under the influence of bio-convection (motile microorganism) have significant applications, since nanoliquids have greater capacity to improve heat transport properties than conventional liquids. With these incredible nanoliquid characteristics, the main objective of current research is to examine the impact of the exponential heat source linked to space and the inclined magnetic force on the nano-bioconvective flow between two turntables. The effect of nonlinear thermal radiation, variable thermal conductivity and viscosity aspects are also considered. The complicated nonlinear problem is treated numerically by using Finite difference method. Optimization procedure implemented via Response surface Methodology for the effective parameters thermophoresis parameter, Hartmann number and radiation parameter on the heat transfer rate. The axial velocity is a dwelling function of the inclined angle of the magnetic field, and the variable viscosity parameter. The temperature profile hikes with an exponential space-related heat source and thermal radiation aspects. Also, the heat transport rate is highly sensitive towards nonlinear thermal radiation parameter compared to the thermophoresis effect and Hartmann number.

This study explores the effects of electro-magneto-hydrodynamics, Hall currents, and convective and slip boundary conditions on the peristaltic propulsion of nanofluids (considered as couple stress nanofluids) through porous symmetric microchannels. The phenomena of energy and mass transfer are considered under thermal radiation and heat source/sink. The governing equations are modeled and non-dimensionalized under appropriate dimensionless quantities. The resulting system is solved numerically with MATHEMATICA (with an in-built function, namely the Runge-Kutta scheme). Graphical results are presented for various fluid flow quantities, such as the velocity, the nanoparticle temperature, the nanoparticle concentration, the skin friction, the nanoparticle heat transfer coefficient, the nanoparticle concentration coefficient, and the trapping phenomena. The results indicate that the nanoparticle heat transfer coefficient is enhanced for the larger values of thermophoresis parameters. Furthermore, an intriguing phenomenon is observed in trapping: the trapped bolus is expanded with an increase in the Hartmann number. However, the bolus size decreases with the increasing values of both the Darcy number and the electroosmotic parameter.

This study proposes Chebyshev wavelet collocation method for partial differential equation and applies to solve magnetohydrodynamic (MHD) flow equations in a rectangular duct in the presence of transverse external oblique magnetic field. Approximate solutions of velocity and induced magnetic field are obtained for steady-state, fully developed, incompressible flow for a conducting fluid inside the duct. Numerical results of the MHD flow problem show that the accuracy of proposed method is quite good even in the case of a small number of grid points. The results for velocity and induced magnetic field are visualized in terms of graphics for values of Hartmann number H-a

The present article aims to probe the impacts of electro-magneto-hydrodynamics (EMHD) peristaltic flow of in-compressible, dusty, non-Newtonian fluid in a hose of predetermined dimension together with homogeneously scattered analogous rigid particles. In the presence of transversal static magnetic field, Navier-Stokes’s equations are employed to design a flow problem for the particulate phase. Governing flow problem is simplified by approximation of long wavelength and zero Reynolds number. The analytical solution for both velocities (solid-liquid) and pressure rise is computed by using well known computational software Mathematica. Perturbation method is employed to extract analytical solution of the resulting ordinary differential equations. Impacts of different physical parameters, expansion in trapped bolus for fluid and particulate velocity profile by increasing Hartmann number are displayed and explained through graphs. Furthermore, a rise in skin friction is noticed with the rise in particle effect and electro-osmotic parameter. This study may have greater significance and viable applications to improve the quality of micro-fluidic devices.

The rotating flow of two fluids having an interface separating the viscous fluid and magnetite-water ferrofluid is studied. The fluids are non-miscible and streaming in an inclined channel. The walls of the channel are smooth enough to examine the slip effects on the flow. The channel is subjected to the transverse magnetic field and thermal radiations. To achieve the flow equations governing the flow phenomena a fully developed flow is taken into consideration. The resultant ordinary differential equations (ODEs) are converted into non-dimensional forms which are coupled and non-linear. Approximate series solutions for flow fields are obtained separately by the aid of the Perturbation technique and then matched at the interface region via relevant matching conditions. The results are drawn graphically to comprehend the effects of various essential parameters on temperature and flow fields. A decreasing response in the primary velocity profile is observed with a rise in rotation parameter, ferroparticles volume fraction and Hartmann number while it increases with a rise in slip parameters. The secondary velocity shows an oscillating behavior for rotation parameter whilst magnetic flux and slip parameters increase the secondary profiles. The primary and secondary velocities will decrease throughout the channel if the fluid in the lower layer is more viscous relative to the upper one. It can also be noticed that the radiation decreases the influence of natural convection by decreasing the temperature difference and temperature profile increases with a rise in thermal conductivity (TC).

Heat sinks are always in the center of electronic cooling researchers' attention. Microchannels are utilized in electronic cooling devices owing to their increased surface and better thermal performance than that of normal heat sinks. In this numerical investigation, the first and second laws of thermodynamics impact of twisted porous ribs on the microchannel are studied. The effects of the Reynolds number, the Hartman number, and the volume fraction of nanoparticles are investigated. The range of the dimensionless number for the Hartmann number and the Reynolds number is 0 to 20 and 250 to 1000, respectively. All types of microchannel in this study consist of clear microchannels in two groups; group one (No. 1, 2 and 3) and group two (No. 4, 5, and 6). The obtained results show that at the end of each porous rib, the reported parameters depict a decrease. Twisted porous ribs cause a significant decrease in the expanding thermal boundary layer. Also, the microchannel with triple-layer porous ribs (No. 3) exhibits considerable performance in the entropy generation. Finally, since group one has a double pitch, it has the better thermal performance and increasing the Hartmann number is one of the reasons for the increasing velocity gradient near the microchannel wall and friction factor.

An analysis is carried out for the steady free convective incompressible electrically conducting Jeffry fluid flow over a stretching surface. In addition, the presence of uniform heat source and first order chemical reaction enhance the heat and mass transfer properties of non-Newtonian fluid. Suitable self-similar transformations are used for the transformation of complex PDEs to nonlinear ODEs. Semi-analytical approach like Adomian Decomposition Method (ADM) is employed for this transformed governing equation to get approximate analytical solution. Further, the behavior of characterizing parameters is presented through graphs. The validation of the present result is obtained with an earlier established result in particular case. However, the major outcomes are; both the interaction parameter and Hartmann number favors in to enhance the velocity profiles whereas the it is interesting to see that, increasing interaction parameter for higher value of Hartmann number retards the fluid temperature but reverse effect is rendered for lower value.

Time-dependent viscous fluid flow due to a stretchable rotating disk is investigated. Magnetic field is applied in vertical direction to the disk. Temperature equation is assisted with Joule heating effect. Governing system of PDE's is transformed to dimensionless form by suitable variables. One of the numerical techniques known as finite difference scheme is adopted to tackle the given dimensionless partial differential system. This method results in a system of simple algebraic equations. The unknown function is analyzed inside domain of interest. In this technique of solution, a system is subdivided into many smaller parts called finite elements. The obtained simpler algebraic equations are then assembled to form a system of equations which governs the original problem. Variational method is used to get approximate solution by reducing the error function. Behaviors of pertinent variables on surface drag force, temperature, velocity and heat transfer rate are shown graphically. The obtained outcomes guarantee that velocity decreases for Hartmann number while it enhances with Reynolds number. Temperature increases for higher Prandtl, Eckert and Hartmann numbers. Skin friction boosts for larger values of Hartmann number. Nusselt number enhances with Hartmann number.

The current study explores the entropy production rate in the flow induced by ciliary pumping systems through cylindrical tubules created under consequences of a magnetic field acting externally in the direction normal to flow. Impacts of Hall currents, viscous dissipation and ohmic heating on heat and mass transferals in bio-magnetic viscous materials are the prominent features of the present model. The governing equations make up a nonlinear coupled system of five partial differential equations in velocity components, pressure gradient, temperature and concentration distributions. However, implication of creeping flow approximation in the wave frame of reference makes the problem linear such that solutions of the aforementioned quantities are obtained analytically. Expressions for entropy production rate and Bejan number are also formulated for the present flow scenario. Effects of heat and mass transfers, Hartmann number, Hall current and cilia length parameters on the flow field, pumping characteristics, temperature, concentration, entropy production rate and Bejan number are discussed in details. Key observations are also summarized in the concluding section. It is found that the inclusion of Hall current not only overcomes the damping effects of magnetic field but also controls the disorderness of thermodynamic systems. Also, cilia with higher lengths stimulate the momentum transfer in the axial flow direction and consequently promote the pumping rate.

Mucus transport mediated by motile cilia in the airway is an important defense mechanism for prevention of respiratory infections. Cilia motility can be affected by temperature difference and magnetic field. In this research, we investigate the combined effects of magnetic field and buoyancy force due to temperature difference. In the present study, mixed convective flow of a Carreau fluid model through a ciliated channel is modeled and analyzed by a symplectic metachoronal wave. The momentum and energy equations for the Carreau fluid are modeled and simplified by the stream function and small Reynold’s number approximation. The influence of magnetic parameter, Carreau fluid parameter, Brinkmann number and Weissenberg number on velocity, temperature and pressure gradient are presented via graphs. It is observed that Hartmann number helps to decelerate the flow, whereas Weissenberg number, Grashof number and Carreau fluid parameter are responsible for the accelerated flow. The heat transfer rate rises by increasing the values of Hartmann number, Weissenberg number, Carreau fluid parameter and Brinkmann number.

In this paper, the groundwork of some thermophysical properties of higher-order chemical processing and dissipation of viscous on nanofluid along with a continuously stretching porous sheet is taken. The porous medium is considered with two space coordinates, laminar, time-invariant, MHD incompressible Newtonian nanofluid. The equations are framed to govern the fluid flow as coupled equations involving nonlinear partial derivatives. The impacts of electric and magnetic fields on nanofluid with viscous dissipation in the presence of higher-order chemical reaction, analyzing conservation of momentum and energy, is the novelty of the problem. The level of raising thermal conductivity and the output of transferring the heat on nanofluid is observed. Finally, the governing equations involving partial derivatives have complied with nonlinear ordinary differential equations. The transformations are subjected to the similarity variable used to solve these equations. Approximate solutions are obtained using a numerical method of the Runge-Kutta-Felburg method with shooting technique. The effects of emerging parameters K r , E r , λ , N t , δ , N b are porous, electric, mixed convection, thermophoresis, chemical process and, Brownian motion, and non-dimensional numbers such as Hartmann, Prandtl, Schmidt, and Eckert are extensively explained. The electrically conducting nanofluid flow for velocity fluid, temperature fluid and, nanoparticles concentration volume fraction fluid with transferring heat, Nusselt, and transferring mass, Sherwood number are examined with graphical representation. The Lorentz resistive force due to the applied strength of electric develops the thickness of boundary layers of momentum and thermal regions. This helps to cool the electronic systems and radiators. The dimensionless Nusselt number diminishes with various values of thermophoresis and Brownian motion parameters as a dependent function of Hartmann, electric number, and homogeneous chemical reaction parameter.

This article mainly emphases on the study of magneto Cu-Al2O3/water hybrid nanofluid flow in a non-Darcy porous square cavity. The square geometry is a lid-driven enclosure with an inside heated square obstacle. Cattaneo-Christov heat flux pattern is used for the formulation of the heat equation. This type of problems may be applicable in the high temperatures in the different scientific processes, extrusion of polymers, aerodynamics extrusion and cooling hot glass. Dimensionless forms of governing flow expressions are computed numerically with Finite Volume Method via SIMPLER algorithm simultaneously. The characteristics of numerous dimensionless parameters such as; Richardson number 0.1 ⩽ R i ⩽ 100 , Hartmann number 0 ⩽ H a ⩽ 100 , height of hot square obstacle 0.1 ⩽ H ⩽ 0.5 , width of hot square obstacle 0.1 ⩽ W ⩽ 0.5 , Reynolds number 0.1 ⩽ R e ⩽ 25 and Darcy number 10 - 2 ⩽ D a ⩽ 10 - 6 are analyzed. The achieved results are projected graphically via streamlines, isotherms, local and average Nusselt numbers. The fluid flow and rate of heat transfer in the direction of the moving heated obstacle isfound to play an important role. The higher values of Ha decreases the local Nusselt number. Hybrid nanofluid provides a higher heat transfer rate than the nanofluids. Increasing the width of the obstacle cause to decline in the thickness of the right wall, this enhances the heat transfer in the clockwise direction.

In this paper, a stability analysis of a hybrid nanofluid flow between two parallel and stationnary plates filled with a porous medium was investigated. The hybrid nanofluid is composed of water as regular fluid, copper ( Cu ) and alumina ( Al 2 O 3 ) as nanoparticles. A mathematical modeling of the problem was developed by taking account other effects such as aspiration (suction/injection) and magnetic field. An eigenvalue differential equation namely the modified Orr-Sommerfeld equation governing the stability of the flow was derived and solved numerically by spectral collocation method with expansions in Chebyshev polynomials. The effect of the density of particles, suction/injection Reynolds number, Hartmann number, Darcy number and volume fraction on the flow stability was examined and presented. It was found the following: the Darcy number affects the stability of the flow, the suction/injection reduces the drag and the transition is delayed/prevented, the magnetic field makes the dissipation very important because the kinetic energy of the electrically conductive fluid is absorbed by the Lorentz force, and the volume fraction and the density of nanoparticles increased the inertia of the fluid which decreased the speed gradient and damped the disturbances.

In the present work, an irreversibility analysis of three- (3D) and two-dimensional (2D) magnetohydrodynamic (MHD) free convection inside cubical enclosure packed with hybrid water nanofluid (alumina, titanium dioxide and copper) is carried out. The discretization of the momentum and energy equations is done by employment of finite volume approach with SIMPLE algorithm. The effect of inclined magnetic on the heat transfer rate and various entropy types is investigated. All numerical tests are obtained for various Rayleigh numbers 103 ≤ Ra ≤ 106, Hartman numbers 0 ≤ Ha ≤ 45, hybrid nanoparticles percentage 0 ≤ φ % ≤ 5%, and the magnetic field angle 0 ≤ α≤90°. The Bejan number is used in this study to show the entropy type dominant. The first part of this study is about showing a three-dimensional shape of the particles trajectory, isotherms, local Bejan number and different local entropy types; then the second part is limited to a two-dimensional study of all physical quantities. As main results, it is demonstrated that the rate of heat transfer and entropy creation are significantly improved by changing the Rayleigh number, Hartmann number and the magnetic field angle. Moreover, it is also found that the effect of increasing the volume fraction of hybrid nanoparticles can be optimized to get good enhancement of heat transfer rate.

This paper investigates the unsteady flow and heat transfer of a viscous, incompressible, and electrically conducting fluid through a porous medium in a horizontal channel. The basic physical properties of the fluid and the porous medium are constant. The fluids considered are those with the Prandtl number less than 1. The channel walls are made of horizontal permeable plates, which are at constant but different temperatures. Fluid suction/injection through the plates occurs at a velocity perpendicular to the plates, whose intensity is a cosine function of time. The applied external magnetic field is homogeneous and inclined in relation to the transverse plane of the channel. The problem is dealt with through an inductionless approximation. Fluid flow is instigated by constant pressure drops along the channel. The equations used to describe the problem are transformed to dimensionless forms and solved analytically using the perturbation method. Approximate analytical expressions for dimensionless fluid flow velocity and dimensionless temperature are determined as functions of the following physical parameters: Prandtl number, Hartmann number, porosity factor, frequency, amplitude, and magnetic field inclination angle. Numerical results are presented as diagrams and tables and are used to analyse the influence of physical parameters on the fluid flow velocity and temperature.

The major goal of this work is to analyze the magnetic effect on the creeping viscous flow past a porous spheroidal particle, a particle of slightly deformed spherical shape. Brinkman’s model is proposed to govern the flow in the porous media. Boundary value problem considers the conditions of continuity of velocity components, continuity of normal stresses, and stress jump boundary condition for tangential stress. A transverse magnetic field of uniform nature is applied to the flow. An expression for the drag force acting on the spheroidal particle is derived analytically. The effects of the physical parameters involved in the flow like permeability, deformation, Hartmann number’s, viscosity ratio, and stress jump coefficient parameters are visualized through graphs and tables. The applied magnetic field seems to suppress the flow of fluid that leads to the increase in the drag experienced on the porous spheroid. It is also observed that the increase in the deformation, stress jump, and permeability decreases the drag coefficient. Our results without magnetic effect match with the results reported earlier in the literature.

In this research, the hydromagnetic natural convection of an incompressible fluid with point heat source by considering the influence of Hall current and induced magnetic field between infinite vertical walls is studied. The Laplace transform procedure is utilized to determine the analytical solutions of the acquired mathematical model with the wavelet function. With the derived solution of velocity, induced magnetic field, temperature field, and induced current density, the flow character is investigated with the influence of the physical parameters (namely Hall current, Hartmann number, and point heat source) for the presented boundary conditions. Also, the skin friction and volumetric flow rate are derived through the velocity expression. Numerical and graphical results are introduced to formalize the solution of the model. The valuable result from the investigation is that an increase in the length of the point heat source leads to enhance both components of induced current density, induced magnetic field, and primary velocity profiles. Moreover, it is noticeable that an enhancement in the Hall current has a reverse connection with both components of the induced current density, induced magnetic field, while the direct connection with the primary velocity component. There are numerous engineering applications such as the metal cutting, grinding, welding, laser hardening of metals, and many others in which the calculation of temperature field is modeled as a problem involving a point heat source.

Binary nanofluids are prepared using a binary liquid (e.g., salt water) instead of a pure liquid as their host fluid. Double-diffusive convection in this type of nanofluids is a kind of triple-diffusive process, which simultaneously includes diffusions of heat, nanoparticles, and solute. This paper is devoted to double-diffusive mixed convection of binary nanofluids flowing through a vertical porous annulus in the presence of an externally applied radial magnetic field. To simulate the problem, a new mathematical model following the Buongiorno’s two-phase model is proposed. The equations are solved numerically by means of the finite-volume method. Thereafter, effects of the involved dimensionless variables on the distributions of stream function, temperature, solute concentration, and nanoparticles fraction as well as the mean values of the Nusselt number and the solute Sherwood number are presented and discussed. Inspection of the results demonstrates the significant contributions of the Peclet number (Pe), the usual Lewis number (Le), and the Soret-solute Lewis number (Ld) on the simulation results. In spite of that, the effects of the Hartmann number (Ha) and the thermophoresis parameter (Nt) on the simulation results are weak, while the consequences of the nanofluid Lewis number (Ln), the double-diffusive ratio (Nc), the buoyancy ratio (Nr), and the Dufour parameter (Nd) on the Nusselt and Sherwood numbers are insignificant.

The problem of an axisymmetric translational motion of an incompressible microstretch fluid past an immiscible stationary microstretch droplet in the presence of a uniform magnetic field is investigated. The inertial terms in the equations of motion are neglected, therefore the microstretch scalar function is uncoupled from the stream function and microrotation component. Analytical solutions are obtained for the stream and microstretch scalar functions. The drag acting on the fluid droplet is evaluated. Numerical results for the drag force coefficient versus the relative viscosity, micropolarity parameter, and Hartmann number are tabulated and presented graphically. The results for the drag coefficient are compared with the available solutions in the literature for the limiting cases.

This paper presents a numerical study of a double diffusive convection in an inclined square porous cavity filled with an electrically conducting binary mixture. The upper and bottom walls are maintained at a constant temperatures and concentrations whereas the left and right walls are assumed to be adiabatic and impermeable. A uniform and tilted magnetic field is applied at an angle, γ, about the horizontal, it is obvious that this is related to the orientation of the magnetic force that can help or oppose the buoyant force. The Dupuit-Darcy flow model, which includes effects of the inertial parameter, with the Boussinesq approximation, energy and species transport equations are solved numerically using the classical finite difference method. Governing parameters of the problem under study are the thermal Rayleigh number, Rt, Hartmann number, Ha, Lewis number, Le, the buoyancy ratio, φ,inclination angle, Φ and tilting angle of the magnetic field, γ,. The numerical results are reported on the contours of streamline, temperature, and concentration and for the average Nusselt and Sherwood numbers for various parametric conditions. It is demonstrated that both the inertial effect parameter and the magnetic field, have a strong influence on the strength of the natural convection heat and mass transfer within the porous layer.