Narrow Results

We consider the non-stationary 3-D flow of a compressible viscous and heat-conducting micropolar fluid with the assumption of spherical symmetry. We analyze the flow between two concentric spheres that present solid thermo-insulated walls. The fluid is perfect and polytropic in the thermodynamical sense and the initial density and temperature are strictly positive. The corresponding problem has homogeneous boundary data.

In this work, we present the described model and provide a brief overview of the progress in the mathematical analysis of the associated initial-boundary problem. We consider existence and uniqueness of the generalized solution, asymptotic behavior of the solution and regularity of the solution.

An attempt is made to analyze the effects of micropolar fluid squeezing film implementation between porous elliptical plates under the application of an external magnetic field. The appropriate improved hydromagnetic Reynolds equation governing the pressure distribution is acquired. The Reynolds equation is solved for lubrication features such as pressure distribution, load-carrying capacity and time-height relationships. It is noticed that a micropolar lubricant with a magnetic field may considerably impart a much-appreciated increase in load-carrying capacity, pressure distribution and response time compared to the classical case. Nevertheless, it is found that, as with the magnetic field, the larger values of the fluid gap number and the coupling number increase lubrication characteristics. Also, it is found that such a bearing cannot support a large number of lubrication characteristics because of the pores on the main path of fluid flow.

The primary purpose of this work is to investigate the influence of a magnetic field on a micropolar fluid, which is rotating between two horizontally arranged parallel plates. A uniform magnetic field acts perpendicularly to the porous plate, which consumes fluid with a steady suction velocity. The obtained higher-order nonlinear partial differential equations (PDEs) are converted into nonlinear ordinary differential equations (ODEs) by using similarity transformation. A semi-analytical methodology has been applied to obtain the result to the problem. The influence of various flow parameters of the flow field like coupling parameter, viscosity parameter, Reynolds number, porosity parameter, rotation parameter and magnetic field parameter has been examined and explained by graphs. A resemblance between the results obtained by solving by the differential transform method (DTM) and the outcomes of the former research works has also been displayed which shows the correctness and efficiency of the used analytical method. The numerical values of the coefficient of skin friction at the lower plate are also displayed in tabular form and compared with the literature.

In this paper, we focused on time-dependent flow of micropolar fluid between parallel permeable plates. Fluid is electrically conducting. Magnetic field is applied in the transverse direction to flow. Energy equation is modeled in the presence of viscous dissipation, thermal radiation and Joule heating. Suction is considered at lower plate while injection is considered at upper plate. Appropriate dimensionless variables are employed to reduce the governing PDE’s system into dimensionless one. Nondimensional PDE system is tackled numerically by finite difference technique. Effects of flow parameters on velocity, micro-rotation, temperature, couple and shear stresses at plates and Nusselt number are discussed. The obtained outputs show that for nonzero electric field parameter the velocity increases with Hartmann number. For zero electric field parameter the velocity decreases with Hartmann number. Temperature increases with both electric and magnetic field parameters. Micro-rotation decreases with micro-rotation material parameter and it increases with time.

The main purpose of this work is to study the steady incompressible second-grade micropolar fluid flow over a nonlinear vertical stretching Riga sheet. Velocity slip and zero mass flux are considered at the solid surface of Riga shape such that the friction of nanoparticle maintains itself with strong retardation. The influence of Lorentz forces produced by the Riga plate is an important aspect of the study. The influences of thermophoresis and Brownian motion under the heat generation and e bouncy forces are studied on the nonlinear vertical Riga sheet. The mathematical model is developed under the flow assumptions. The mathematical model in terms of partial differential equations is formed by implementing the boundary layer approximations. The partial differential equations are further reduced to ordinary differential equations by means of suitable transformations. The ordinary differential equations are solved through the numerical procedure. The variations in the horizontal movement of nanofluid, thermal distribution and concentration distribution of the nanoparticle have been noted for different fluid parameters. The values of velocity profile and temperature profile are larger in the case of injection ($S<0)$ as compared to suction ($S>0$). The values of concentration distribution are smaller in the case of injection ($S<0)$ as compared to suction ($S>0)$. The validation of this analysis with decay literature is provided in the form of tables.

Aluminum alloys are used to make wheels that are suitable for aeroplanes and automobiles, as well as all types of ground vehicles and watercraft. Aluminum alloys are made through melting, sintering (assembly of formed parts utilizing metal particles that melt together at intense temperatures), or mechanical braiding. Aluminum alloys have had a major impact on aeroplane manufacturing. Aluminum alloys like AA7075 and AA7072 are especially useful in transportation applications including maritime, aviation, and automotive, and are also utilized in the construction of bicycles, glider rock climbing equipment, and planes. This attempt sheds light on the magnetically influenced methanol-based micropolar nanofluid containing aluminum alloy nanoparticles (AA7075) over a variable thickened stretching sheet. A variable magnetic field is applied normal to the flow direction. The flow is considered at a stagnation point. Also, the Joule heating impact is considered in this analysis. The similarity transformations are used for the transformation of partial differential equations into ordinary differential equation. The authors have chosen to solve the proposed model with the help of NDSolve technique which can handle a wide range of ordinary and partial differential equations (ODEs and PDEs). The results showed that, as the volume fraction of AA7075 nanoparticles grows the velocity profile of the AA7075–methanol nanofluid decreases, while the microrotation and temperature profiles of the AA7075–methanol nanofluid increases. The velocity profile of the AA7075–methanol nanofluid reduces, while the microrotation and temperature profiles of the AA7075–methanol nanofluid increase with the increasing magnetic parameter. The growing micropolar parameter augments the velocity and temperature profiles of the AA7075–methanol nanofluid, whereas a dual impact of the micropolar parameter is found against the microrotation profile of the AA7075–methanol nanofluid. The growing variable wall thickness factor augments the velocity, microrotation and temperature profiles of the AA7075–methanol nanofluid. It is found that the embedded factors highly affected the AA7075–methanol nanofluid as compared to methanol fluid.

This paper aims to analyze the problem with the study of thermal and momentum transport with entropy generation in view of the second law of thermodynamics in Magneto hydrodynamics (MHD) micropolar fluid through porous medium under the consideration of the non-Darcy model, temperature-dependent viscosity and thermal conductivity. In practical situations at higher temperatures and high speed fluid flow, it becomes reasonable to consider variable fluid flow parameters. The governing boundary layer flow equations are first converted into a coupled system of the ordinary differential equations (ODE) under the assumption of differing plate temperatures by applying appropriate similarity transformations. A shooting method has been applied to solve ordinary differential equations numerically. The last effect of microrotation, magnetic field, variable viscosity coefficient, variable thermal conductivity, etc. on momentum and thermal transport has been depicted through various graphs. The table for skin friction coefficient and Nusselt number for ideal cases has been shown to validate the model by previous findings. It is seen that K and m enhance the velocity profile on their increment opposite to this M, $\delta$, F and Da have been found to reduce the velocity profile. Table 3 is constructed for numerical values of skin friction coefficient and Nusselt number for different values of parameters where it can be concluded that magnetic parameter M has a tendency to enhance the skin friction and heat transfer, while variable viscosity parameters have a tendency to decline the skin friction and heat transfer.

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

This research examines the flow of 2D micropolar fluid across an inclined linear shrinking/stretching surface with suction, convective, slip and thermal radiation impact. The governing partial differential equations (PDEs) are transformed into an ordinary differential equations (ODEs) system using a linear similarity transformation, and the bvp4c technique is then used to solve the ODEs system in MATLAB. Comparisons of both solutions are presented. The effects of regulating flow parameters on dimensionless temperature profiles, angular velocity, velocity, skin friction, wall couple stress and heat transfer are shown graphically. Stable velocity profiles are inversely related to velocity slip and material parameter. For a given suction and stretching/shrinking parameter value, graphs show double solutions. The couple stress and skin friction in the first solution, drop then increase as the material parameter K increases. Critical points of the stretching/shrinking parameter, ${\lambda }_{ci}\ge \lambda$ where both solutions occur, are indicated by the symbols ${\lambda }_{ci}$ (i.e., $i=1,2,3)$, and that there is no solution when ${\lambda }_{ci}>\lambda$. A table summarizes the stability study’s results and highlights.

The regulation of energy associated with heat transfer is the most important problem in the food processing, chemical and biomedical engineering industries. Therefore, this investigation explores the heat transfer qualities of micropolar hybrid-nanofluid also considering entropy generation which has recently become central focus of research in the field of heat transfer processes. The purpose of this analysis is to explore the influence of magnetohydrodynamics (MHD), viscous dissipation, and heat radiation on the flow of hybrid-nanofluid with micropolar properties above an exponentially shrinking/stretching sheet. A mathematical model is constructed and the solution is acquired by utilizing numerical technique bvp-4c in MATLAB. The befitting usage of the second law of thermal physics helped in conducting the entropy production analysis. The study obtains numerical results for the governing equations, which reveal dual solutions when analyzing a shrinking sheet, contrary to a stretching sheet. The paper presents graphical depictions of the influence of different attributes upon micro-rotation, velocity, surface-friction, temperature, Nusselt number and also the entropy generation plus the Bejan number. Moreover, a comparison of heat transfer rates between conventional nanomaterial and hybrid-nanofluid is provided. The study concludes that dual solutions appear and the wall shear stress coefficient decreases as the values of micropolar parameter $R_1$ increase with critical values of $\lambda$ being ${\lambda }_c=-1.28$, $-1.34$ and $-1.37$. Also thermal irreversibility, which results from fluid friction near the sheet rather than far from it, is more dominant than total entropy generation.

In the existing investigation, impacts of slip and chemical reactions on mass and heat exchange on an incompressible and electrically conducting micropolar fluid past a porous wedge within the sight of Hall and ion slip are examined. By employing similarity conversion, the relevant highly nonlinear PDEs are reformed into a collection of nonlinear linked ODEs. The equations framed in this manner have been resolved by using the bvp5c, the in-build MATLAB. Examination of magneto-hydrodynamic micropolar fluid on stagnation point flow is significant due to its uses in the production of plastic substances, polymer extrusion, lubricants, etc. The influence of the magnetic field, heat generation, microrotation, along with Hall and ion slip on the liquid flow is analyzed. Examination with prior published research papers is performed and the outcomes are compared with each other. Numerical simulations for shear stress coefficients, Sherwood and Nusselt numbers are provided in tabular form, and in addition, the variations in axial and microrotation velocities, temperature and solutal profiles are evaluated visually for various parameters in detail. The ion slip and slip velocity both slow down the shear rate, whereas the elevated values of the Hall and magnetic parameters show an opposite trend. The profile shows thinning of the bounding surface and offers its greatest magnitude in the case of a Newtonian liquid.

This paper reports the flow features and distributions of concentration and temperature of a micropolar type nanofluid (water-based) past a stretchable and shrinkable wedge, influenced by variable magnetic force, nonlinear sort thermal radiation and chemical reaction. Along with the consideration of multiple convection, the model of Buongiorno is stated. The Brownian motion and thermophoresis have been kept in the analysis. Suitable similarity alteration is approached to renovate the foremost equations to dimensionless ordinary differential equations (ODEs). Associated conditions became nondimensional forms according to this conversion. Then the numerical solutions of the reduced governing equations with boundary conditions are obtained by adopting the RK-4 technique with shooting criteria. The language MAPLE 17 assisted in developing this solution. Significant upshots of prime parameters on the fluid transmission, mass and heat transport properties are represented with suitable tables and graphs. In tabular form, we have reckoned the physical quantities of heat, mass transfer rates and drag friction coefficients to fulfill the engineering interest. This study acquaints that the material parameter negatively influenced nanofluid’s angular velocity. The fluid’s temperature improves with thermal and mass Biot numbers, but this response goes opposite for the parameter of wedge angle. Chemical reaction and wedge angle parameters amplify mass transport. This study can be beneficial in the blowing of chilled air by AC panels, the abstraction of crude oils, the nuclear power hub, the working of warships, making flaps on the wings of aeroplanes for advanced lift, submarines, the extraction of polymers and several other sectors in advanced science and industrial developments.

This paper presents a model of nonisothermal blood flow through a diseased arterial segment due to the presence of stenosis and thrombosis. The rheological properties of the blood in the annulus are captured by utilizing micropolar fluid model. The equation describing the blood flow and heat transfer is developed under the assumption that stenosis growth into the lumen of the artery is small as compared to the average radius of the artery. Biological processes like intimal proliferation of cells or changes in artery caliber may be activated by small growths that cause moderate stenotic blockages. Closed-form solutions for temperature, velocity, resistance impedance and wall shear stress are obtained and then utilized to estimate the impact of various physical parameters on micropolar blood flow. Graphs are plotted to illustrate variations in temperature, velocity, shear stress at the wall and resistance impedance against different controlling parameters. The results are also validated via the bvp4c approach.

An analysis is carried out for the free convection of magneto-micropolar liquid via a stretching surface for the inclusion of thermal radiation and chemical reaction. The transverse magnetic field is employed on the normal direction of flow with the impact of Peclet number relating to thermal and solutal transfer profiles. Referring to the current applications in several engineering problems, industrial applications, and more importantly the peristaltic pumping processes, blood flow phenomena, etc. the role of micropolar fluid is significant. Therefore, the objective of thismodel is to develop by incorporating thermal radiation which has several applications in aforesaid areas. However, the proposed model is solved analytically using the differential transform method (DTM) and prior to that transformation to ordinary system is obtained by using similarity transformations. The characteristic of various physical components associated with the governing equations is deployed graphically. The analysis of these parameters is described briefly in the discussion section. Further, a statistical approach response surface methodology (RSM) is used to optimize the heat transfer rate for the factors such as magnetic parameter, thermal radiation, and Peclet number.

This work is about the investigation of the flow of a micropolar nanoliquid over a stretching surface, taking into account the effects of thermal radiation, thermophoresis, and Brownian motion. The study focuses on the impact of these factors on heat and mass transfer rates, with the assumption that the Newtonian heat impact dominates. The homotropy approach is used to generate non-dimensional transformational parameters, which are then used to create a system of nonlinear differential equations. The study includes charts and tables that define transfer rates based on various parameters, and the results suggest that increased radiance levels and Nb parameters lead to improvements in heat and mass convection. The graphics used in the study are accurate and consistent with previous research in the field. Overall, this research provides insights into the complex dynamics of micropolar nanoliquid flow and the factors that impact heat and mass transfer in this system.

This study investigates the impact of electroosmosis on the peristaltic flow of unsteady micropolar nanofluid with heat transfer. The findings could enhance the design of peristaltic pumps, potentially improving drug delivery systems, simulations of blood flow in medical devices, and cancer treatments. The fluid under investigation adheres to a micropolar model and flows through a microchannel that exhibits peristalsis along its walls. Moreover, the system is subjected to various external effects, including a uniform magnetic field, the electroosmotic phenomenon, heat absorption, and a chemical reaction with activation energy. Consequently, the problem is mathematically modulated by a system of nonlinear partial differential equations governing the velocity, temperature, and nanoparticle concentration. By employing wave transformation, these governing equations are reduced to ordinary differential equations (ODEs). The reduced equations were solved both analytically, using the homotopy perturbation method, and numerically, using the Runge–Kutta–Merson method. A comparison was made between the solutions, which were found to be closely aligned. Furthermore, a series of figures were employed to provide visual representation and discussion of the implications of the physical properties. The calculations reveal that the electroosmotic flow (EOF) enhances the axial flow of the micropolar fluid along the direction of the applied electric field. It is also observed that the increase in the activation energy (which indicates a low reaction rate) increases the concentration profile whereas the increase in the reaction rate parameter reduces the concentration profile. Additionally, the spin velocity of the particles is diminished by either an increase in the magnetic parameter or the coupling parameter.

A thin micropolar fluid with new boundary conditions at the fluid-solid interface, linking the velocity and the microrotation by introducing a so-called "boundary viscosity" is presented. The existence and uniqueness of the solution is proved and, by way of asymptotic analysis, a generalized micropolar Reynolds equation is derived. Numerical results show the influence of the new boundary conditions for the load and the friction coefficient. Comparisons are made with other works retaining a no slip boundary condition.

Nanoparticles have the capability to augment the thermal conductivity of nanofluids. For the transmission of heat, the material’s low thermal conductivity is the key problem. Therefore, to increase the thermal conductivity, researchers mixed different nanoparticles in the base fluids. In this field of study, utilizing three different particles is the most recent strategy to form a ternary hybrid nanofluid that gives us better results in terms of heat transfer. The interaction of three different kinds of nanoparticles, i.e. copper, alumina and silver, is considered with water serving as the base fluid to form a ternary hybrid nanofluid. The paper explores the behavior of ternary hybrid nanofluids on heat and mass transportation phenomena of the two-dimensional magnetohydrodynamic (MHD) micropolar flow across a porous extending surface with zero mass flux and convective conditions. The Brownian motion, thermal radiation, heat source and sink, and joule heating are taken into consideration in the temperature equation. The chemical reaction is incorporated into the concentration equation. Appropriate similarity transformations are used to transform the system of partial differential equations (PDEs) to a coupled system of ordinary differential equations (ODEs). The homotopy analysis method (HAM) is used to solve the system of the flow equations. The effects of the nanoparticle’s volume fractions and other different physical parameters on the surface drag force, Nusselt number, velocities, microrotation, temperature and concentration profiles are scrutinized through figures and tables. The outcomes of the present investigation show that the heat transfer rate is augmented with the increasing value of thermophoresis parameter. The magnetic field has augmented temperature while the opposite result is seen in velocity and microrotation profiles. With the escalating values of thermophoresis parameter, the concentration and temperature of ternary hybrid nanofluids are boosted while the increasing Brownian and chemical reaction parameters have decreased the concentration profile. The surface friction coefficient exhibited by the ternary hybrid nanofluid is higher than hybrid and conventional nanofluids.

The oscillatory flow of micropolar fluid in an annular region with constriction, provided by variation of the outer tube radius, is investigated. It is assumed that the local constriction varies slowly over the cross-section of the annular region. The nonlinear governing equations of the flow are solved using a perturbation method to determine the flow characteristics. The effect of micropolar fluid parameters on mean flow and pressure variables is presented.

With an aim to investigate the effect of externally imposed body acceleration and magnetic field on pulsatile flow of blood through an arterial segment having stenosis is under consideration in this article. The flow of blood is presented by an unsteady micropolar fluid, and the heat-transfer characteristics have been taken into account. The nonlinear equations that govern the flow are solved numerically using finite difference technique by employing a suitable coordinate transformation. The numerical results have been observed for axial and microrotation component of velocity, fluid acceleration, wall shear stress (WSS), flow resistance, temperature, and the volumetric flow rate. It thus turns out that the rate of heat transfer increases with the increase of Hartmann number H, while the WSS has a reducing effect on the Hartmann number H and an enhancing effect on the ratio of viscosity K as well as on the constriction height δ.