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Development of thin Casson liquid (CL) film on a heated nonlinear flat stretching surface is examined under influences of thermal radiation and transverse magnetic field. The velocity and temperature at any point of the stretching surface are assumed as the generalized nonlinear functions of the distance of that point. The analytical expressions for velocity components and temperature are obtained using long-wave approximation technique. The numerical solution for nonlinear film evolution equation is incurred by the Newton–Kantorovich method. It is found that initial non-uniform film thickness becomes flat with due course of time. It is further observed that the film thinning rate enhances for larger values of the Marangoni number and radiation parameter. It is also discovered that the rate of film thinning diminishes for the larger Hartmann number and Casson parameter.

The objective of this study is to determine the irreversible losses and associated entropy generation within a fluid system, considering the combined effects of magnetic field, convective boundaries, and porous media. It accomplishes this objective by a thorough investigation into the second law analysis and entropy generation of a magnetohydrodynamic (MHD) Eyring–Powell fluid flowing through a symmetric porous medium. To achieve this, the governing equations for the Eyring–Powell fluid are formulated using the conservation laws of mass, momentum, and energy, while incorporating the magnetic field’s effects. In order to account for the porous character of the medium, the equations are coupled with the Darcy model. Using appropriate computational techniques, the resulting system of partial differential equations is numerically solved. The local irreversibility ratio calculates the system’s entropy generation number, revealing its distribution. The Hartmann number and Eyring–Powell fluid parameters are also studied. The primary findings indicate that $A^{\ast }$ enhances velocity and diminishes temperature and entropy, while $B^{\ast }$ has the opposite effect. Entropy is also increased by Hartmann and Brinkman numbers, which are a result of the enhanced heat transfer and stronger magnetic fields. The findings emphasize the need and importance of studying irreversible losses and improving fluid system energy efficiency.

This research utilizes the bvp4c method to conduct a detailed numerical analysis of the hydrothermal behavior of magnetized hybrid nanofluids flowing across a permeable curved surface. The study explores the impact of crucial parameters such as curvature, magnetic field strength, viscosity and suction/injection, alongside the heat absorption coefficient, on the transport properties of copper (Cu) and ferric oxide (Fe₃O₄) nanomaterial’s suspended in water. Results reveal that as the curvature parameter increases, velocity profiles exhibit a decrease under suction conditions and an increase under injection conditions for both conventional and hybrid nanofluids. Furthermore, higher magnetic parameters are found to decrease velocities in general. Hybrid nanofluids display enhanced velocity and thermal performance compared to conventional nanofluids, manifesting higher skin friction and heat transfer rates. Temperature profiles exhibit a complex interplay with curvature, magnetic parameters and the injection/suction scenario, where injection conditions intensify thermal effects. The incorporation of the heat absorption coefficient further amplifies the thermal efficiency of hybrid nanofluids. These findings, supported by previous research, offer valuable insights for optimizing industrial processes, especially in sectors like ceramics, plastics and polymers, where efficient heat management is paramount.

This paper investigates the influence of magneto-tangent hyperbolic nanofluid on the flow of a tri-hybrid nanoliquid consisting of ${\mathrm{\text{MoS}}}_2,\mathrm{\text{Si}}{\mathrm{\text{O}}}_2$, and $\mathrm{\text{GO}}$ particles suspended in $\mathrm{\text{EG}}$. The entropy production is encountered in this analysis. The fluid flows over a stretch sheet is considered. In addition, the energy equation also assumes the existence of a uniform heat source or sink and thermal radiation. Furthermore, the concentration equation emphasizes the chemical reaction. The current proposed model yields a set of nonlinear governing equations. The modeled formulation is transformed into a dimensionless system through the application of a suitable alteration. The complex nonlinear equation system was solved using the bvp4c through numerical methods. The main motive of this exploration is to emphasize the rate of heat and mass transfer in a flow of ${\mathrm{\text{MoS}}}_2,\mathrm{\text{Si}}{\mathrm{\text{O}}}_2$, and $\mathrm{\text{GO}}/\mathrm{\text{EG}}$-based hybrid nanofluid across a stretch sheet. The graphical study illustrates that Weissenberg number and magnetic field enhancement result in decreasing the velocity. But thermal layer, entropy production, and Bejan number are enhanced with larger values of Weissenberg number and magnetic field. This study focuses on different profiles with various flow parameters. Furthermore, we have compared the tri-hybrid nanofluid with the hybrid and mono nanofluid in all the figures and tabular format. Additionally, we have compared tri-hybrid, hybrid, and mono nanofluid using graphs for velocity, temperature, concentration, entropy production, and Bejan number.

The aim of this study is to analyze heat transfer over two horizontal concentric cylinders in the influence of MHD, internal heat source containing porous nanofluids and thermal radiation are considered. The novelty of this work is internal heat source and porous media of H₂O–Cu nanofluids with the Lorentz effect are investigated and its applications are cooling systems, and heat exchangers. In addition, transformation for the momentum and energy equation is applied to obtain a set of ODEs for governing equations in the heat transfer flows. Further, the numerical technique BVP4C is used to solve the resulting system of nonlinear, coupled equations with boundary conditions. The influence of Hartmann number, volume fraction, radiation parameter, internal heat source parameter, Darcy number and different nanoparticles are examined in velocity and temperature profiles. The results show good agreement with the existing work of velocity and temperature graphs. Moreover, they reveal that thermal radiation significantly influences temperature distribution within the annulus, leading to a higher heat transfer rate. Furthermore, the presence of a porous medium and internal heat source modulates the flow patterns. This study provides optimizing MHD nanofluid systems for engineering applications such as thermal management systems, hyperthermia treatment in cancer therapy, food processing, rotating machinery and cooling systems.

Energy restoration is the prime issue for the researcher and they have tried to develop advanced techniques and resources for renewable energy. The nanofluid is one of the resources for the restoration of energy which depends on the dynamic thermophysical properties of metal nanoparticles. The recent study is concerned with the thin film flow of carbon nanotubes (CNTs) water-based nanofluid for the improvement of heat transfer applications. The flow of two types of CNTs nanofluid was studied, comprising single-walled carbon nanotube (SWCNT) and multi-walled carbon nanotube (MWCNT) over the surface of a thin stirring needle. The study has been carried out in the presence of a magnetic effect and viscous dissipation. The BVP 2.0 package has been used for the solution of the modeled problem. The effect of the physical constraints like Prandtl number, magnetic field and Eckert number vs the momentum and thermal boundary layers has been analyzed. The sum of the residual errors has been obtained up to the 20th order estimates to settle the strong convergence of the problem. The obtained results show that the thin film has a quick response to the increasing of heat transfer rate over the surface of a thin needle as compared to the thick boundary layers.

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.

During the cancer treatment, one of the successful methods is to inject the blood vessels which are closest to the tumor with magnetic nanoparticles along with placing a magnet nearer to the tumor. The dynamics of these nanoparticles may happen under the action of the peristaltic waves generated on the walls of tapered asymmetric channel. Analyzing this type of nanofluid flow under such action may highly be supportive in treating cancer tissues. In this study, a newly described peristaltic transport of Carreau nanofluids under the effect of a magnetic field in the tapered asymmetric channel are analytically investigated. Exact expressions for temperature field, nanoparticle fraction field, axial velocity, stream function, pressure gradient and shear stress are derived under the assumptions of long wavelength and low Reynolds number. Finally, the effects of various emerging parameters on the physical quantities of interest are discussed. It is found that the pressure rise increases with increase in Hartmann Number and thermophoresis parameter.

The peristaltic flow of a carbon nanotubes (CNTs) water fluid investigate the effects of heat generation and magnetic field in permeable vertical diverging tube is studied. The mathematical formulation is presented, the resulting equations are solved exactly. The obtained expressions for pressure gradient, pressure rise, temperature, velocity profile are described through graphs for various pertinent parameters. The streamlines are drawn for some physical quantities to discuss the trapping phenomenon. It is observed that pressure gradient profile is decreasing by increase of Darcy number $D_a$ because Darcy number is due to porous permeable walls of the tube and when walls are porous fluid cannot easily flow in tube, so that will decrease the pressure gradient.

The migration of Red Blood Cells (RBCs) from the wall towards the center of a narrow vessel is the result of the Fahraeus–Lindqvist effect which contemplates the dependence of viscosity and diameter. The kinetic theory explains the formation of the near-wall cell-depleted layer introducing the granular temperature that is defined as the mean square of RBCs fluctuations. The proposed mathematical model elucidates the effect of an externally applied magnetic field on the velocity and granular temperature of RBCs in a microvasculature. The effect of the volume fraction of RBCs on the velocity and granular temperature profiles is also presented and discussed. Based on the insight of the kinetic theory, the application of a stronger static magnetic field probably leads to a restriction of the migration process of RBCs towards the center of the microvessel.

The objective of this study is to conduct a numerical examination of the influence of nonlinear chemical reaction and heat source or sink on magnetohydrodynamic (MHD) heat and mass transmission nanofluid flow through a shrinking permeable surface. In addition, the investigation considers thermal radiation and the occurrence of viscous dissipation. Ethylene glycol (EG) is used as the primary fluid medium, whilst the nanoparticles consist of nickel–zinc ferrite. The use of nanofluid flow has garnered significant interest as a result of its potential applications across several sectors. Nanofluids possess a notable benefit in comparison to traditional fluids as a consequence of their enhanced heat transfer capabilities. This advantage may be ascribed to the inclusion of nanoparticles, which augment thermal conductivity and therefore lead to enhanced heat dissipation and efficiency. The mathematical flow model, which is formulated using nonlinear partial differential equations (PDEs), may be transformed into a set of ordinary differential equations (ODEs) by the application of suitable similarity conversions. In order to address the complexities of the nonlinear system, the bvp4c and shooting techniques are used inside the MATLAB program, a widely utilized commercial platform, to effectively solve the associated ODEs by numerical means. This study presents a graphical analysis of the effects of flow parameters on several variables of interest.

The effect of axial magnetic field along with axial temperature gradient, in a confined cylindrical cavity packed with incompressible electrical conducting fluid having a top rotating lid, has been investigated. Due to the presence of axial magnetic field, Joule heating effect is considered in this study. The governing parameters ranges are as follows: $1\le J\le 8$, $1\le \mathrm{\text{Ri}}\le 10$ at Re$=$1000, Pr$=$0.015. It is found that the internal heat generation due to Joule heating in mixed convection is governed by interaction parameter and temperature gradient. However, the Joule heating effect has very less effect on primary flow in comparison to the secondary flow along the meridional plane.

This paper presents a computational scheme for compressible magnetohydrodynamics (MHD). The scheme is based on the same elements that make up many modern compressible gas dynamics codes: a high-resolution upwinding based on an approximate Riemann solver for MHD and limited reconstruction; an optimally smoothing multi-stage time-stepping scheme; and solution-adaptive refinement and coarsening. The pieces of the scheme are described, and the scheme is validated and its accuracy assessed by comparison with exact solutions. A domain-decomposition-based parallelization of the code has been carried out; parallel performance on a number of architectures is presented.