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This study incorporates the impact of shape factor and slip conditions on a radiative hybrid magnetic nanofluid over slanted sheet being convectively heated within a porous medium, providing valuable insights for enhancing thermal management systems in manufacturing techniques such as the extrusion of plastic films, cooling of metallic plates, and the drawing of polymer fibers. The effect of viscous dissipation, thermal radiation, aligned magnetic field, velocity slip, heat generation, buoyancy force, porosity, and thermal slip on the dynamics of fluid movement are comprehensively discussed. The governing equations were simplified into nonlinear ordinary differential equations through similarity variables and Bvp4c solver in MATLAB was utilized to observe the effects of pertinent parameters on temperature and velocity profiles, alongside the local Nusselt number and skin friction coefficient. It was determined that the hybrid nanofluid’s effective thermal conductivity was most significantly enhanced by blade-shaped nanoparticles. The local Nusselt number enhanced with upsurge of thermal radiation parameter and Biot number whereas opposite trend was observed with incrementation in other parameters. The augmentation in thermal slip and velocity slip resulted in lowering local skin friction coefficient. This research highlights the complex interplay between various physical factors and their influence on the dynamics of hybrid nanofluids, offering potential strategies for optimizing performance of thermal systems comprising hybrid nanofluids.

The purpose of this paper is to study the peristaltic dusty fluid flow where dust particles are distributed uniformly. The passage of flow is asymmetric. Slip conditions have been incorporated into both momentum and thermal profiles. The mathematical model is constructed using the laws of momentum and energy conservation. The resulting coupled equations are solved using small wavenumber approximation. Impacts of important quantities on temperature and velocity profiles of fluid along with solid particles have been debated through graphs. Entropy generation analysis has been carried out for influential parameters. An enhancement is observed in temperature irreversibility as Brinkman and thermal slip are increased. Bejan number is studied for various values of Brinkman number, wavenumber and thermal slip. The analysis of peristaltic flow of particle fluid with slip has a vital role in biomedical sciences and industry.

A theoretical model on MHD hybrid nanofluid flow in accordance with non-uniform heat flux and solar energy radiation has been studied in our work. Also, the impact of multiple slip conditions is presumed at the boundary. Comparative flow analyses for hybrid nanofluid (Al₂O₃/Cu–H₂O) and single nanoparticle-based nanofluid (Cu–H₂O) are addressed here with graphs and charts. The leading partial differential equations with boundary conditions have been converted into ordinary differential equations with the aid of similarity transformation. The final system is tackled via the fifth-order Runge–Kutta–Felberg method with shooting procedure and the computation is done using Maple 17. One of the interesting results shows that with the growth of thermal radiation, the Nusselt number for Cu–H₂O is reduced by 26.16%, whereas for the same, Nusselt number for Al₂O₃/Cu–H₂O is lessened by 27.38%. Fallout shows that with the growing values of velocity slip parameter, the thermal boundary layer thickness enlarges faster for Al₂O₃/Cu–H₂O in comparison to Cu–H₂O.

In this paper, the two-phase flow of non-Newtonian fluid is investigated. The main source of the flow is metachronal waves which are caused by the back and forth motion of cilia attached to the opposite walls of the channel. Magnetohydrodynamics (MHD) of Casson fluid experience the effects of transverse magnetic fields incorporated with the slippery walls of the channel. Thermal effects are examined by taking Roseland’s approximation and application of thermal radiation into account. The heat transfer through the multiphase flow of non-Newtonian fluid is further, compared with Newtonian bi-phase flow. Since the main objective of the current study is to analyze heat transfer through an MHD multiphase flow of Casson fluid. The two-phase heated flow of non-Newtonian fluid is driven by cilia motion results in nonlinear and coupled differential equations which are transformed and subsequently, integrated subject to slip boundary conditions. A closed-form solution is eventually obtained form that effectively describes the flow dynamics of multiphase flow. A comprehensive parametric study is carried out which highlights the significant contribution of pertinent parameters of the heat transfer of Casson multiphase flow. It is inferred that lubricated walls and magnetic fields hamper the movement of multiphase flow. It is noted that a sufficient amount of additional thermal energy moves into the system, due to the Eckert number and Prandtl number. While thermal radiation acts differently by expunging the heat transfer. Moreover, Casson multiphase flow is a more suitable source of heat transfer than Newtonian multiphase flow.

In this paper, the impact of thermal slip and slip velocity on ZrO₂ (Zirconia)–water nanofluid flow through a vertically heated permeable stretching sheet surrounded by a porous medium has been deliberated. The concept of thermal radiation is assimilated into the study. Using similarity transformations, the concerned governing flow model is changed into nonlinear ODEs and gets a solution by the R-K method. The consequence of numerous pertinent parameters in the fluid flow arena is deliberated by employing graphical and tabular approaches. The current investigation will be supportive of understanding the thermal features of heat transfer nanofluids. Outcomes of the present effort are compared with that of previously published works and found a commendable level of settlement. Our analysis sightsees that Zirconia–water achieves high temperatures due to thermal radiation. Also, it is found that Zirconia–water nanofluid lessens the heat transfer rate related to their base fluid.

In this paper, the significance of slip situations in the appearance of a porous medium and frictional heating on unsteady fluid flow through a porous medium has been explored. The numerical solutions of the differential equation representing fluid flow through a porous material, including slip effects, are presented. We have obtained a nonlinear ordinary differential equation using a similarity transformation. Under velocity and thermal slip conditions, the Maple packages were used to numerically solve the resulting set of nonlinear problems. Both the velocity and temperature increase when the Brinkman viscosity ratio parameter $\gamma$ increases. The effects of the nondimensional parameters on the governing flow velocity and temperature are examined with graphical profiles. The implications of relevant parameters on dimensionless temperature, velocity, local Nusselt number and skin friction coefficient are shown and explained. For various flow quantities of interest, the fluctuation of parameters is investigated, and the results are given in the system of graphs and tables.

This study looks at the Darcy–Brinkman flow across a stretched sheet of porous dissipation and frictional heating. The geometry of a steady flow of dust particles fluid through a porous material in the existence of slip effect and porous dissipation is the subject of this study. The equations that govern the system are shown and summarized as boundary layer assumptions, and then modified into framework of first-order DEs using the similarity approach. By using similarity transformation, a two-dimensional nonlinear partial differential equation is decreased to a sequence of nonlinear ordinary differential equations (ODEs). Then, by employing numerical techniques such as Maple packages, the solution of system of nonlinear equations is represented using the RK4 method. The numerical findings are derived under specific unique situations. The Nusselt number and coefficient of skin-friction are also given numerically. The increase in Brinkman number $\gamma$ raises the temperature profile for both the dusty and the fluid phases. The results also demonstrate that rise in the suction number S falls the temperature distribution within the boundary layer for the dusty phase and fluid phase. For a variety of flow quantities of attention, the variation of parameters is studied, and the outcomes are reported in the shape of graphs and tables. Several industrial processes make advantage of boundary layer flow and heat transfer over such a stretched surface in porous materials.

This paper presents an investigation of magnetohydrodynamics (MHD) Casson nanofluid flow along a stretchable surface through a permeable medium. The modeling of the physical phenomena is considered with impact of thermal radiation, heat generation, slip conditions and suction. Transformations of the governing set of mathematical equations for the physical model are carried out into nonlinear ordinary differential equations (ODEs) with appropriate similarity variables. The nonlinear ODE solutions are carried out using the optimal homotopy analysis technique (OHAM), and the findings are presented for determining the influences of the emerging important parameters. The results indicate that velocity field increases in respect of porosity parameter, Casson fluid parameter and magnetic parameter while it declines for enhancing velocity slip and suction parameters. The temperature profile shows rising behavior for heat source, Prandtl number, thermophoresis, radiation and Brownian motion parameters while it declines for enhancing thermal slip parameter. Moreover, the concentration profile enhances for rise in Brownian motion parameter while it reduces for Schmidt number and nanoparticle parameter. We also showed the accuracy of the present results by indicating that skin friction values for varied magnetic parameters agree with earlier findings in the literature.

The objective of this paper is to analyze the unsteady incompressible flow of the viscous nanofluid on a contracting surface with viscous dissipation effects. Presented and contrasted are analyses of both multi-wall carbon nanotubes (MWNTs) and single-wall carbon nanotubes (SWNTs). As the common (or base) fluids, kerosene oil and water are utilized. In the existence of first-order thermal and velocity slip conditions, mathematical modeling and analysis are performed. Using the MATLAB software’s bvp4c solver tool, numerical solutions to the governing nonlinear modeled problems were obtained. This technique is particularly effective for developing many solutions to highly nonlinear differential equations. In addition, a comparison is done between this study and previously published works. The temperature, velocity, skin friction coefficient and heat-transfer rate have been explored for various significant factors included in the problem statements. In the unsteadiness parameter regime, dual solutions can be found. As the velocity slip parameter is increased, the flow slows down. In comparison to SWCNTs kerosene, MWCNTs kerosene oil has a greater velocity curve for the nanoparticles volume fraction. Increases in volume fraction decrease skin friction, whereas increases in the unsteadiness parameter speed up the drag force. Furthermore, as the Eckert number intensity increases, so do the temperature profiles in both solutions. Finally, the stability study revealed that the initial solution is robust, whereas the breakage in the second solution in the Nusselt number shows singularity, and thus the second solution is considered unstable.

The primary purpose of this study is to provide more information on the stable and incompressible stream of a hybrid nanofluid over a poignant tiny needle in two dimensions under slip boundary conditions. In the hybrid nanofluid flow, Al₂O₃ and Fe₃O₄ are nanoparticles, water and ethylene glycol (50:50) are considered as the base fluids. Furthermore, the impacts of Joule heating and inclined magnetic fields are considered. The PDE’s governing equations are converted into ODEs by using similarity transformations and solved by a numerical technique based on Runge–Kutta fourth-order method. The results illustrate that the crucial parameters such as the magnetic parameter, Eckert number, nanoparticles of solid volume fractions, inclined angle parameter, and Prandtl numbers significantly affect the momentum and thermal profiles. The heat transfer rate and skin friction factors are used to calculate the numerical values of various parameters, which are displayed in a table. These analyses manifest that raising the magnetic parameter results in a decrease in the hybrid nanofluid velocity under slip and no-slip circumstances. The Nusselt number has also grown as a result of the volumetric fractions of nanoparticles and the intensification of the angle parameter. This analysis might include areas such as microfluidics, biomedical devices, heat exchangers, and other engineering applications where precise control over fluid behavior and temperature distribution is important.

Industrial applications in domains such as warm rolling, crystal development, thermal extrusion and optical fiber illustration are seeing a significant increase. These applications specifically focus on addressing the challenge of a cylinder in motion inside a fluid environment. Elevated temperatures may affect the viscosity and thermal conductivity of fluids. Understanding the relationship between temperature and the properties of fluids is crucial. In light of these presumptions, the primary goal of this study is to examine, under transverse magnetic field, shape factor, velocity, thermal slip conditions and viscous dissipation, how temperature-dependent fluid properties could enhance the heat transfer efficiency and performance evolution of ternary hybrid nanofluid. In order to study flow fluctuations, the impact of nanoparticle addition and improvements in heat transfer, a variable Prandtl number is also included. The use of similarity variables converts the controlling flow model from partial differential equations (PDEs) to ordinary differential equations (ODEs). Mathematica’s shooting strategy solves ODEs using the fourth-order Runge–Kutta (RK-IV) method. Numerical calculations were done after setting parameters to acquire the desired results. Analytical data are provided in tables and graphs for convenient usage. The results showed that the velocity profile increases as the values of ${\varphi }_3$, Pr, M, Re and S grow, and decreases when the values of ${\theta }_r$ decrease. Re, Pr and S lower the temperature profile, whereas ${\varphi }_3$, ${\theta }_r$ and Ec raise it. The skin friction profile steepens as ${\varphi }_3$, S, Re and M increase relative to the stretched cylinder, and flattens as ${\theta }_r$ and $\omega$ decrease. The Nusselt number profile rises as ${\theta }_r$, Pr, S and Re decrease with ${\varphi }_3$, Ec and $\delta$. When the Prandtl number goes from 3.0 to 6.2 in a ternary hybrid nanofluid with brick-shaped nanoparticles, the Nusselt number goes up by around 55.7%.

Analysis has been carried out to examine the heat and mass transfer effects on the magnetohydrodynamics (MHD) peristaltic flow in a channel with compliant walls. An incompressible Maxwell fluid occupies the porous space. Modified Darcy's law and slip conditions are used in the problem formulation. Solutions for small wave number are derived. The effects of emerging parameters in the obtained solutions are displayed and discussed.

The influence of different shapes of nanoparticles on peristaltic flow of Casson fluid in an asymmetric channel is studied in this paper. The suspension of Copper oxide nanoparticles of needle, platelet and lamina shapes is taken into account. The problem is modeled in partial differential equations with suitable slip boundary conditions. The standard nonlinear equations are solved by the Homotopy Analysis Method in Mathematica Software. The influences of different shapes of nanoparticles on concentration, velocity profile and temperature profile are analyzed through the graphs. It is observed that the different shape of nanoparticles has different thermal conductivity, but the lamina shaped nanoparticles have high thermal conductivity as compared to needle and platelet shaped nanoparticles.