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The purpose of this paper is to examine the flow, heat transfer and entropy generation characteristics for an inclined channel of two immiscible micropolar fluids.

The flow region consists of two zones, the flow of the heavier fluid taking place in the lower zone. The flow is assumed to be governed by Eringen’s micropolar fluid flow equation. The resulting governing equations are then solved using the homotopy analysis method.

The following findings are concluded: first, the entropy generation rate is more near the plates in both the zones as compared to that of the interface. This indicates that the friction due to surface on the fluids increases entropy generation rate. Second, the entropy generation rate is more near the plate in Zone I than that of Zone II. This may be due to the fact that the fluid in Zone I is more viscous. This indicates the more the viscosity of the fluid is, the more the entropy generation. Third, Bejan number is the maximum at the interface of the fluids. This indicates that the amount of exergy (available energy) is maximum and irreversibility is minimized at the interface between the fluids. Fourth, as micropolarity increases, entropy generation rate near the plates decreases and irreversibility decreases. This indicates an important industrial application for micropolar fluids to use them as a good lubricant.

The problem is original as no work has been reported on entropy generation in an inclined channel with two immiscible micropolar fluids.

Miniaturization with high thermal performance and lower cost is one of the advanced developments in industrial science chemical and engineering fields including microheat exchangers, micro mixers, micropumps, cooling microelectro mechanical devices, etc. In addition to this, the minimization of the entropy is the utilization of the energy of thermal devices. Based on this, in the present investigation, micropolar nanofluid flow through an inclined channel under the impacts of viscous dissipation and mixed convection with velocity slip and temperature jump has been numerically studied. Also the influence of magnetism and radiative heat flux is used.

The nonlinear system of ordinary differential equations are obtained by applying suitable dimensionless variables to the governing equations, and then the Runge–Kutta–Felhberg integration scheme is used to find the solution of velocity and temperature. Entropy generation and Bejan number are calculated via using these solutions.

It is established to notice that the entropy generation can be improved with the aspects of viscous dissipation, magnetism and radiative heat flux. The roles of angle of inclination (α), Eckert number (Ec), Reynolds number (Re), thermal radiation (Rd), material parameter (K),  slip parameter (δ), microinertial parameter (aj), magnetic parameter (M), Grashof number (Gr) and pressure gradient parameter (A) are demonstrated. It is found that the angle of inclination and Grashof number enhances the entropy production while it is diminished with material parameter and magnetic parameter.

Electrically conducting micropolar nanofluid flow through an inclined channel subjected to the friction irreversibility with temperature jump and velocity slip under the influence of radiative heat flux has been numerically investigated.

This paper aims to study a non-Newtonian micropolar fluid flow over a bidirectional flexible surface for multiple exact solutions of momentum boundary layer and thermal transport phenomenon subject to wall mass flux, second-order slip and thermal jump conditions.

The coupled equations are transformed into ordinary differential equations using similarity variables. Analytical and numerical techniques are used to solve the coupled equations for single, dual or multiple solutions.

The results show that the stretching flow, shrinking flow, the wall drag, thermal profile and temperature gradient manifest large changes when treated for special effects of the standard parameters. The role of critical numbers is definitive in locating the domains for the existence of exact solutions. The nondimensional parameters, such as mass transfer parameter, bidirectional moving parameter, plate deformation strength parameter, velocity slips, material parameter, thermal jump and Prandtl number, are considered, and their physical effects are presented graphically. The presence of governing parameters exhibits special effects on the flow, microrotation and temperature distributions, and various exact solutions are obtained for the special parametric cases.

The originality and value of this work lie in its exploration of non-Newtonian micropolar fluid flow over a bidirectional flexible surface, highlighting the multiple exact solutions for momentum boundary layers and thermal transport under various physical conditions. The study provides insights into the effects of key parameters on flow and thermal behavior, contributing to the understanding of complex fluid dynamics.

The purpose of this paper is to study a two‐dimensional steady convective flow of a micropolar fluid over a stretching sheet in the presence of radiation with constant temperature.

The corresponding momentum, microrotation and energy equations are analytically solved using homotopy analysis method (HAM).

To validate the method, investigate the accuracy and convergence of the results, a comparison with existing numerical and experimental results is done for several cases. Finally, by using the obtained analytical solution, for the skin‐friction coefficient and the local Nusselt number as well as the temperature, velocity and angular velocity, profiles are obtained for different values of the constant parameters, such as Prandtl number, material, boundary and radiation parameter.

In this paper, a series solution is presented for the first time.

The purpose of this paper is to consider the problem of fully developed laminar mixed convection flow of a couple stress fluid in a vertical channel with the third-kind boundary conditions in the presence or absence of heat source/sink effect.

Through proper choice of dimensionless variables, the governing equations are developed. These governing equations are solved analytically by the differential transform method and numerically by the Runge–Kutta shooting method. Analytical solutions for the velocity and temperature profiles for heat generation and absorption of the problem are reported.

The mass flow rate and Nusselt numbers at both the left and right channel walls on mixed convection parameter, Brinkman number, couple stress parameter and heat generation/absorption parameter for equal and unequal Biot numbers are presented. Favorable comparisons of special cases with previously published work are obtained. It is found that velocity, temperature, mass flow rate and Nusselt number decrease with couple stress parameter and increase with mixed convection parameter and Brinkman number.

The work done in this paper is not done earlier to the authors’ knowledge. This is the first paper in which the sixth-order differential equation is solved using the semi-numerical method, which is a differential method.

The purpose of this paper is to investigate the effect of exponential viscosity-temperature relation, exponential thermal conductivity-temperature relation and the combined effects of variable viscosity and variable thermal conductivity on steady free convection flow of viscous incompressible fluid in a vertical channel.

The governing equations are solved analytically using regular perturbation method. The analytical solutions are valid for small variations of buoyancy parameter and the solutions are found up to first order for variable viscosity. Since the analytical solutions have a restriction on the values of perturbation parameter and also on the higher order solutions, the authors resort to numerical method which is Runge-Kutta fourth order method.

The skin friction coefficient and the Nusselt number at both the plates are derived, discussed and their numerical values for various values of physical parameters are presented in tables. It is found that an increase in the variable viscosity enhances the flow and heat transfer, whereas an increase in the variable thermal conductivity suppresses the flow and heat transfer for variable viscosity, variable thermal conductivity and their combined effect.

This research is relatively original as, to the best of the authors’ knowledge, not much work is done on the considered problem with variable properties.

This investigation has been carried out for thermal-diffusion (Dufour) and diffusion-thermo (Soret) effects on the boundary layer flow of Jeffrey fluid in the region of stagnation-point towards a stretching sheet. Heat transfer occurring during the melting process due to a stretching sheet is considered. The paper aims to discuss these issues.

The authors convert governing partial differential equations into ordinary differential equations by using suitable transformations. Analytic solutions of velocity and temperature are found by using homotopy analysis method (HAM). Further graphs are displayed to study the salient features of embedding parameters. Expressions of skin friction coefficient, local Nusselt number and local Sherwood number have also been derived and examined.

It is found that velocity and the boundary layer thickness are increasing functions of viscoelastic parameter (Deborah number). An increase in the melting process enhances the fluid velocity. An opposite effect of melting heat process is noticed on velocity and skin friction.

The boundary layer flow in non-Newtonian fluids is very important in many applications including polymer and food processing, transpiration cooling, drag reduction, thermal oil recovery and ice and magma flows. Further, the thermal diffusion effect is employed for isotope separation and in mixtures between gases with very light and medium molecular weight.

Very scarce literature is available on thermal-diffusion (Dufour) and diffusion-thermo (Soret) effects on the boundary layer flow of Jeffrey fluid in the region of stagnation-point towards a stretching sheet with melting heat transfer. Series solution is developed using HAM. Further, the authors compare the present results with the existing in literature and found excellent agreement.

The purpose of this paper is to focus on the stratified phenomenon through vertical stretching cylinder in the region of stagnation point with slip effects.

Homotopy analysis method is used to find the series solutions of the governing equations.

Velocity profile decreases with an increase in stratified parameters due to temperature and concentration. Velocity and thermal slips cause a reduction in the velocity profile. Thermally stratified and thermal slip parameters reduce the temperature field.

The present analysis has not been existed in the literature yet.

Microfluidics is one of the extensive elaborated technologies in thermal and engineering fields due to its wide range of applications, such as micro heat exchangers, micro mixture and microchannel heat sinks, which is used to develop a large number of microscopic devices and systems. Enhancement of thermal energy using verity of nanoliquids is one of the challenges in these applications of microfluidics. Therefore, using single wall carbon nanotubes for enhancement of thermal energy in microchannel is the main purpose of this study. Hall effect of natural convection flow in a vertical channel with slip and temperature jump condition is considered. The impacts of radiative heat flux, uniform heat source/sink, viscous dissipation and joule heating are also taken into account.

Suitable non-dimension variables are applied to the governing equations to reduce the system into ordinary differential equations. The reduced nonlinear system is then solved numerically using Runge–Kutta–Fehlberg fourth–fifth-order method along with shooting technique. The impact of different pertinent parameters on numerical solutions of primary velocity, secondary velocity, temperature, entropy generation and Bejan number is comprehensively discussed in detail. Also, the obtained numerical results are compared with existing one which perfectly found to be in good agreement.

It is established that, with the aspects of Joule heating, viscous dissipation, radiative heat flux and uniform heat source/sink, the production in the entropy can be improved. Further, it is found that the increasing ratio of wall ambient temperature difference and nanoparticle volume fraction leads to enhance the entropy generation. The same effect reverses with increasing values of fluid wall interaction parameter (FWIP) and rare faction. The irreversibility ratio enhances with larger values of nanoparticle volume fraction and decelerates with increment values of FWIP.

The impact of single wall carbon nanoliquid in a vertical channel flow by using radiative heat flux, heat source/sink, joule heating and viscous dissipation is first time investigated. Further, the influence of Hall current is explored in detail.

This study aims to examine the flow characteristics of Ree–Eyring fluid between two rotating disks. The characteristics of heat transfer are discussed in presence of viscous dissipation, heat source/sink and nonlinear radiative heat flux.

Nonlinear flow expressions lead to ordinary ones through adequate similarity transformations. The ordinary differential system has been tackled through optimal homotopic method. The impact of different flow variables on the velocity field, entropy generation rate and temperature fields is graphically discussed. The surface drag force and heat transfer rate are numerically examined via various pertinent parameters.

By minimization of values of stretching parameter and Brinkman number, the entropy generation rate can be controlled. The entropy generation rate enhances for higher values of magnetic parameter, while the Bejan number is decreased via magnetic parameter.

No such work is yet published in the literature.