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The peristaltic flow with applications of electro-osmotic phenomenon finds novel applications in microfluidic devices, biotechnology, environmental engineering, micro-reactor, and various medical devices. Owing to such motivations in mind, the objective of this analysis is to present the applications of electro-osmotic phenomenon in transport of Prandtl hybrid nanofluid due to non-uniform duct. The characteristics of hybrid nanofluid have been justified by using the single-walled carbon nanotubes (SWCNT) as well as multiple-walled carbon nanotubes (MWCNT) uniformly decomposed to engine oil base liquid. The novel aspects of viscous dissipation and Joule heating effects are attributed. The thermal problem is further influenced by electro-osmotic force. The electric field effects are attributed with the help of Poisson–Boltzmann and Nernst–Planck expressions. The simplification of electric field expressions is done via Debye–Heckle linearization. The problem is modeled under certain constraints of creeping transport and lubrication theory. The novel numerical treatment is performed with the help of Keller Box method. Physical visualization of results is performed for assisting as well as opposing electro-kinetic pumping constraints. It is claimed that the velocity profile increases in the central line of duct with variation of electro-osmotic coefficient. The heat transfer reduces due to potential ratio parameter electro-osmotic constant. Furthermore, the enhancement of Prandtl fluid parameter leads to decrement of axial pressure.

Understanding and optimizing heat transfer processes in complex fluid systems is the driving force behind studying the magnetohydrodynamic (MHD) flow of ${\mathrm{\text{Al}}}_2{\mathrm{\text{O}}}_3$–$\mathrm{\text{Cu}}∕{\mathrm{\text{H}}}_2\mathrm{\text{O}}$ nanofluid across a radiative moving wedge, taking into account the impacts of viscous dissipation and Joule heating. Nanofluids, such as ${\mathrm{\text{Al}}}_2{\mathrm{\text{O}}}_3$–$\mathrm{\text{Cu}}∕{\mathrm{\text{H}}}_2\mathrm{\text{O}}$, increase heat transmission and thermal efficiency. However, the complicated challenges caused by fluid characteristics and radiative heating need a thorough investigation. This study examines MHD hybrid nanofluid heat transfer via a permeable wedge using joule heating, mass suction, viscous dissipation, variable viscosity, thermal radiation, variable thermal conductivity, and variable Prandtl number. We use similarity transformation to solve the ordinary differential equations that follow from the governing partial differential equations. We then check the results for correctness and dependability. To ensure the reliability and validity of the outcomes, source parameters are crucial to the validation process. The consequence of changing these parameters on the heat transmission properties of the MHD hybrid nanofluid is studied for both the scenario without and with thermal radiation by methodically analyzing the percentage increase or reduction. The validation process also includes a comparison of the computed values, such as the heat transfer rate and skin friction factor, with established theoretical predictions. This examination guarantees that the numerical solution, executed using the bvp4c technique in MATLAB, corresponds to the anticipated physical behavior of the system being studied. In addition, the findings exist using both graphical and tabular forms, which allows for a clear and succinct illustration of how different physical limitations affect flow characteristics.

The peristaltic flow of hybrid nanofluid plays an essential role in medical sciences with important applications, advanced therapies, blood flow regulation and urinary obstructions. The design of various medical equipment, like dialysis machines, artificial pumps and drug delivery systems, is based on the peristalsis flow phenomenon. The objective of current continuation is to analyze the buoyancy-driven peristalsis flow of Powell–Eyring hybrid nanofluid due to complex curved conduit in the presence of Hall current. The consideration of hybrid nanofluid is based on the utilization of human blood base fluid with the interaction of aluminum oxide $({\mathrm{\text{Al}}}_2{\mathrm{\text{O}}}_3)$ and copper (Cu) nanoparticles. The Joule heating and mixed convection applications are followed. The propagation of complex sinusoidal waves of conduit channels has been considered. The mathematical simplification of the problem is associated to assumptions of small assumptions of Reynolds approach and high wavelength hypothesis. Such assumptions simplify the mathematical model complexity and accurately capture the insight physics of the flow under practical conditions. A complex mathematical system is obtained under certain assumptions which are solved with ND solver. Comparative simulations are performed for nanofluid (Cu/blood) and hybrid nanofluid (Cu–${\mathrm{\text{Al}}}_2{\mathrm{\text{O}}}_3$/blood). Physical interpretation of the problem is studied. The enhancement of heat transfer due to the Grashof parameter and Weissenberg number has been examined which is more impressive for hybrid nanofluid as compared to $\mathrm{\text{Cu}}$/blood-based nanofluid. A reduction in trapping phenomenon has been noticed due to variation of Weissenberg constant which is more exclusive for hybrid nanofluid.

Entropy measures the disorderness and randomness in the thermal systems. It has significant influence over efficiency and performances of the thermal systems. The motive of the research paper is to present a comparative analysis of entropy generation of a heat dissipative Darcy–Forchheimer flow of copper (Cu/H₂O)-based mono and (CuAl₂O₃/H₂O)-based hybrid nanofluid under the influence of thermal dispersion. The mathematical model of the conceptualized flow problem is formulated using single phase nanofluid model along with Darcy–Forchheimer equation for non-Darcy porous medium flow. The system of dimensional Partial Differential Equation (PDE) depicting the flow problem is converted in the system of dimensionless Ordinary Differential Equation (ODE) using the suitable similarity variables and has been solved by MATLAB’s bvp4c package. The flow variables, engineering parameters like skin friction and Nusselt number along with entropy generation, have been analyzed for the active parameters inherited in the problem. The findings suggest that heat transfer rate on the surface enhances with the increment in thermal dispersion parameter. Further, it is reported that the hybrid nanofluid generates lesser entropy as compared to the mono-nanofluid. This research has potential to serve the real-life applications based on electronics and geothermal systems.

Novel nanomaterial applications claim distinct uses in thermal engineering, cooling processes, heat transfer devices, and automobile industries, among others. Motivated research uses modified heat and mass flux theories to present thermal observations for the unsteady flow of magnetized Maxwell nanofluid, confined by porous bidirectionally stretched surfaces. The heat transfer model’s extension is based on Joule heating and heat source effects. The Cattaneo–Christov theories govern the expansion of mass and heat transfer. We analyze thermal problems under zero-mass diffusion constraints. The use of proper variables simplifies mathematical modeling into a dimensionless form. The Homotopy Analysis Method (HAM) solves the dimensionless system. The paper highlights the convergence criteria for the HAM procedure. Graphics underline the problem’s physical perspective. We observe that the Deborah number enhances heat and mass transfer. The temperature profile decreases when the parameter becomes unstable.

This communication is to analyze the Marangoni convection MHD flow of nanofluid. Marangoni convection is very useful physical phenomena in presence of microgravity conditions which is generated by gradient of surface tension at interface. We have also studied the swimming of migratory gyrotactic microorganisms in nanofluid. Flow is due to rotation of disk. Heat and mass transfer equations are examined in detail in the presence of heat source sink and Joule heating. Nonlinear mixed convection effect is inserted in momentum equation. Appropriate transformations are applied to find system of equation. HAM technique is used for convergence of equations. Radial and axial velocities, concentration, temperature, motile microorganism profile, Nusselt number and Sherwood number are sketched against important parameters. Marangoni ratio parameter and Marangoni number are increasing functions of axial and radial velocities. Temperature rises for Marangoni number and heat source sink parameter. Activation energy and chemical reaction rate parameter have opposite impact on concentration profile. Motile density profile decays via Peclet number and Schmidt number. Magnitude of Nusselt number enhances via Marangoni ratio parameter.

In this paper, He’s homotopy perturbation method (HPM) is used, which is an approximate analytical method for solving numerically the problem of Newtonian fluid flow past a porous exponentially stretching sheet with Joule heating and convective boundary condition. The major feature of HPM is that it does not need the small parameters in the equations and hence the determination of classical perturbation can be discarded. Due to the complete efficiency of the HPM, it becomes practically well suited for use in this field of study. Also, the obtained solutions for both the velocity and temperature field are graphically sketched. The results reveal that the proposed method is very effective, convenient, and quite accurate to systems of nonlinear differential equations. Results of this study shed light on the accuracy and efficiency of the HPM in solving these types of nonlinear boundary layer equations.

In this work, an approximate analytical solution for the problem of non-Newtonian Casson fluid flow past a porous exponentially stretching sheet with Joule heating and convective boundary condition is obtained using a relatively new technique; He’s homotopy perturbation (HPM). The major feature of HPM is that it does not need the small parameters in the equations, and hence the determination of classical perturbation can be discarded. Due to the complete efficiency of the HPM, it becomes practically well suited for use in this field of study. Also, the obtained solutions for both the velocity and temperature field are graphically sketched. The results reveal that the method is very effective, convenient and quite accurate to systems of nonlinear equations.

A 3D model of flip-chip package is established and thermal–electrical coupling is analyzed. The effect of the width of Aluminum (Al) trace on electro-migration mechanism is also studied. Reducing rates of the hot-spot temperature, the max Joule heating, the max temperature gradient and the max current density are defined to research the effects of the Al trace thickness and the UBM thickness on electro-migration.

Main objective of this paper is to investigate comparative analysis of Copper-water and Copper Oxide-Water nanofluids flow due to a stretchable plate. Magnetic field is applied in transverse direction. Energy equation contains impacts of viscous dissipation and Joule heating. Appropriate dimensionless variables are used to transform the nonlinear PDEs system into dimensionless form. The dimensionless PDEs system is solved numerically by FDM (Finite difference method). Impacts of flow variables including Reynolds number, nanoparticles fraction, Hartmann number and Eckert number on velocity, surface drag force, Nusselt number and temperature are analyzed. Obtained outcomes show that velocity increases through Reynolds number and time while it decreases with Hartmann number. Temperature enhances with Eckert number while it decays with time. Skin friction increases for both Hartmann number and Reynolds number. Nusselt number decreases through nanopartical fraction. Comparative analysis of Copper-water and Copper Oxide-Water nanofluids shows that velocity and temperature are higher in Copper-water when compared with Copper Oxide-Water. For higher nanopartical fraction, the velocity and temperature decrease.

The flow of viscous fluid between two parallel plates is investigated. The applications of the magnetic field effect have been considered in the vertical direction to the plates. Velocity has been presented in the presence of suction and injection. The temperature equation is assisted with the Joule heating effect. One of the numerical techniques, that is, finite difference approach has been used to tackle the given partial differential system. This method results in a system of simple algebraic equations. The unknown function is analyzed inside the domain. 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 equation which governs the original problem. The variational method is used to get an approximate solution by reducing the error function. The effects of pertinent variables on temperature and velocity are shown graphically in the discussion section. The obtained results show that the velocity decreases with magnetic and porosity parameters. Temperature increases for larger values of Hartmann and Eckert numbers.

A type I superconductor expels a magnetic field from its interior to a surface layer of thickness ${\lambda }_L$, the London penetration depth. ${\lambda }_L$ is a function of temperature, becoming smaller as the temperature decreases. Here we analyze the process of cooling (or heating) a type I superconductor in a magnetic field, with the system remaining always in the superconducting state. The conventional theory predicts that Joule heat is generated in this process, the amount of which depends on the rate at which the temperature changes. Assuming the final state of the superconductor is independent of history, as the conventional theory assumes, we show that this process violates the first and second laws of thermodynamics. We conclude that the conventional theory of superconductivity is internally inconsistent. Instead, we suggest that the alternative theory of hole superconductivity may be able to resolve this problem.

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.

Hybrid nanofluid is deployed to optimize the heat transfer features of an axisymmetric magnetohydrodynamic (MHD) flow exterior to a rotating cylinder. Hybrid nanofluids contain composite nanoparticles, which improve thermal conductivity. Here, two distinct particles single and multi-walled carbon nanotubes (CNTs) are taken and mixed to form hybrid nanoparticles, and water is taken as the working fluid. The energy transport phenomenon is examined by incorporating the Joule heating effect. The axial pressure gradient is generated as a consequence of the torsional motion of the cylinder, which results in the wall jet phenomenon on the axial axis. The governing equations are transformed into an ordinary differential system in view of the similarity group. The numerical approach bvp4c is employed to solve the problem. The graphical results for flow and thermal energy transport with a comparison of nanofluid and hybrid nanofluid are analyzed. The axial component of velocity escalates by augmenting Reynolds number, while the azimuthal components of velocity and thermal profile decline. Moreover, the numerical outcomes of wall stresses and Nusselt number enhance for higher Reynolds number. The temperature field declines by increasing the Prandtl number because of less thermal diffusivity.

Hybrid nanofluid is a novel nanotechnology fluid created by distributing two distinct nanoparticles into conventional energy transfer fluid. The thermal properties of aluminum alloys, namely AA7072 and AA7075 with engine oil (base fluid) of hybrid nanofluid flow induced over a vertical stretchable rotating cylinder are investigated in this study. The focus here is the analysis of energy transportation in the presence of Joule heating, thermal energy source/sink, thermal radiation and activation energy. Moreover, all energy constraints are analyzed through graphical outcomes, which are computed numerically through bvp4c built-in MATLAB. The significant observation made is that as the Reynolds number and the magnetic field parameter enhance, the flow field declines. Additionally, the convective transport of the thermal energy increases for a higher magnitude of resistive heating and buoyant motion of the fluid. It is also noted that the activation energy in the system decreases for mass diffusion.

The heat conversation medium temperately regulates the heat exploitation effectiveness of solar energy. Nanofluids, a kind of functioning fluids with extraordinary thermal conductivity and strong light concentration, have been scrutinized and functionalized to progress the exploitation of solar energy. In recent times the current progress examines the nanofluids with the consideration of thermal sources as it can raise the heat transportation amount. Here, the purpose is to explore the thermal properties of Joule heating and thermal conductivity in magnetite Maxwell nanofluid. The concept of heat sink/source and chemical reaction are also studied. The achieved ordinary differential equations have been solved via homotopic algorithm. The enactment of functioning variables is examined. For Eckert number and variable conductivity factors, the Maxwell temperature field has analogous tendencies. The fluid concentration inflates for thermophoretic factor; however, slows down for the Brownian motion factor. The Brownian and thermophoretic factors decay for Nusselt number. Additionally, the excellent results have been achieved accompanied with possible existing prose precisely.

Lubrication theory has attained attention lately due to its practical applications, such as the formation of thin films, adhesives, and lubrication of components of machines. Jeffrey’s nanofluid flow over the stagnation region past a power-law lubricated surface is presented in this study. Buongiorno’s model is employed to scrutinize the effects of thermophoresis and Brownian motion phenomena with constant wall and prescribed surface temperature (PST) and effects of heat source/sink, chemical reaction, and Joule heating. Due to the continuity of shear stress of fluid-lubricant and velocity at the interface, interfacial conditions are generated. By similarity conversions, ordinary differential equations are obtained and their solutions are computed numerically. For power-law index equaling $\frac{1}{2}$, local similarity solutions are calculated by adopting a finite difference scheme, viz. bvp4c in MATLAB. The energy profiles for constant and prescribed temperatures are monitored. The effects of pertinent parameters on the flow, thermal, and mass distributions are scrutinized and illustrated in graphs. Flow field decreases significantly by raising slip parameter as the aptitude of power-law lubricant to improve the velocity of the bulk fluid. The numerical comparison of wall stress and Nusselt number is also presented. The slip and Jeffrey’s material parameters raise the numerical outcomes of the wall shear stress. In addition, increment in Prandtl number enhances the numerical value of the Nusselt number; however, it reduces for relaxation-to-retardation times ratio.

The theme of the current effort is to theoretically analyze the entropy generation and heat transfer aspects of Casson nanofluid flow triggered by rotating porous disc with the presence of magnetic dipole, nonlinear thermal radiation, viscous dissipation and Joule heating. The modeling of the nanofluid can be described with the combination of Brownian motion and thermophoresis by incorporating the passive control boundaries, and the governing PDEs are transformed into a set of highly nonlinear ODEs. The resulting equations are then solved analytically using HAM technique. The present results are compared with previously published results, which are in excellent agreement. The effect of pertinent nondimensional parameters on the entropy generation, hydrodynamic, heat and mass transport aspects is discussed via graphical illustrations. Both radial and tangential velocities are affected by accelerating the values of Hartmann number and porosity parameter. The temperature profile is upsurged by improving the radiation and thermal ratio parameter. Increasing the Casson parameter and Brinkman number leads to improved entropy generation rate. Moreover, skin friction, heat and mass transfer rates are examined with the help of the tables. It is believed that this study can be utilized as coolants by numerous automotive and engineering industries, namely the electronic devices, electrical motor, spin coating, fabrication of spacecraft, thermal insulation, nuclear reactors, etc.

Non-Newtonian fluid mechanics is becoming more and more relevant as time marches on due to the increasing number of fluids encountered in everyday life that exhibit non-Newtonian behavior. It is our intention to cover the multitude of aspects of non-Newtonian fluid mechanics: The effects of magnetohydrodynamic (MHD) laminar boundary layer flow with heat and concentration transfers are considered in the case of Darcy–Forchheimer Williamson–Casson fluids installed over an exponentially extending sheet. There has been an examination and comparison of the effects of momentum fields, thermal radiation, Joule heating, suction/ injection, and compound responses. By using a suitable closeness change, the boundary conditions (BCs) and partial differential equations (PDEs) are reduced to dimensionless structures. The following set of ordinary differential equations (ODEs) and associated BCs are to be clarified using the bvp4c technique. The investigation’s findings indicate that boundary layer thicknesses for velocity, temperature, and concentration normally decline as we get farther from the sheet’s edge, and it is discovered that the Williamson–Casson parameter interferes with velocity profiles. Graphs are developed for Darcy–Forchheimer $F_c$, magnetic parameter M, Lewis number Le, radiation parameter $R_c$, porosity parameter $D_a$, and Eckert number $E_c$. The numeric values of $-\sqrt{2{\mathrm{\text{Re}}}_x}{C}_{f_x}$ and $-{\theta }^{\prime }(0)$ are validated with available data and found to be in excellent agreement.

This study presents a mathematical model along with numerical simulation to investigate the viscous dissipation and Joule heating effects on electrically conducting magnetohydrodynamics (MHD) forced convection non-Newtonian power law nanofluid flow through annular sector duct. Hydro-thermal power law nanofluid flow through annular sector duct is not investigated in the presence of Joule heating and viscous dissipation effects. The consideration of Joule heating and viscous dissipation effects makes it very much novel in its own right. The main objective of this work is to explore the Joule heating and viscous dissipation effects on hydro-thermal power law nanofluid. Both Copper, Cu/Titanium oxide, TiO₂ nanoparticles with base fluid water have been taken as a power law model. Numerically simulation is carried out for viscous, incompressible and steady laminar fully developed fluid flow with constant properties, by using the finite volume method (FVM) and strongly implicit procedure (SIP). It has been observed that viscous dissipation effect on temperature profiles is enhanced in the absence of magnetic field/at lower value of Ha, however, when nanoparticles’ concentration is increased, the effect of magnetic field slightly decreases. Furthermore, by adding Cu nanoparticles from 0% to 5%, we observe the increment in average Nusselt number, Nu up to 16.01% and 16.07% in pseudo-plastic and dilatant fluids, respectively, at $\widehat{R}=0.25$.