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This analysis theoretically investigates the transport phenomena of mixed convection flows in an enclosure of rectangular geometry saturated with a permeable medium filled with an electrically conducting nanofluid. An inclined magnetic field is taken into consideration. Buongiorno's model is utilized to characterize the nanoliquid. The enclosure has adiabatic walls and hot slits. A uniform cold temperature is maintained at the enclosure's lower and upper walls. The enclosure's vertical walls are thermally insulated with hot slits at the center of the walls. This kind of analysis on mixed convective, electrically conducting nanofluid flows in enclosures finds applications in smart nanomaterial processing systems and hybrid electromagnetic nanoliquid fuel cells. The Marker-And-Cell (MAC) method is utilized to solve the transformed nondimension system of governing equations subject to the fitted boundary conditions. The effects of key physical parameters on streamlines, isotherms, iso-concentration contour plots and the heat transmission rate are examined. The simulations demonstrate that the Richardson number has a predominant impact on the thermo-solutal features of nanofluid flow in the rectangular enclosure. Variations in magnetic field and buoyancy ratio parameters exert a notable influence on the iso-concentrations and isotherms. An increase in the Darcy number values exhibits a tendency to magnify the local heat transfer rate. Higher Grashof number values reduce the local Nusselt number profiles. The effect of porous parameter is significant in the streamlines, isotherms and iso-concentrations. Thus, the porous medium can significantly control the transport phenomena in the enclosure. The concentration, temperature and velocity contours are strongly modified by the variations in the Grashof number. [ABSTRACT FROM AUTHOR]

This analysis explains the magneto-hydrodynamic flow on Williamson nanofluids previous stretching surface surrounded by the permeable media. The apt magnetic field was suggested for the angle of the axial direction of the flow. Anyhow, this flow phenomenon was characterized into the added heat source/sink and conjunction of radiating heat. The impacts of convective heating and viscous heating by expanding surface were again the significant feature of the analysis. This originality arises by the combination of the cross-diffusion effects of reverse behavior on the thermophoresis and Brownian motion. This form sketched into the aforesaid phenomenon was modified into the nonlinear ordinary form by the appropriate assumptions on comparison transformations. Therefore, the sets of equations were controlled for the numerical access using Lobatto-IIIa collocation method applicable to this Matlab bvp4c shooting process. This parametric performance of many components about their statistical values was given numerical imitations graphically by the rate coefficients in tabular forms. The validation and the compliance of the current result were acquired by the past study on the specific case. Further, the significant results of this analysis were: This non-Newtonian Williamson parameter combination of that magnetizing property diminishes the fluid velocities. In addition, the important influence of both viscosity parameter and radiation parameter of heating process was noted. [ABSTRACT FROM AUTHOR]

AbstractThis study investigates how thermal radiation, viscous dissipation, double-diffusive convection, and slip boundaries collectively affect the peristaltic movement of a magneto-pseudoplastic nanofluid within a uniform channel. The inclusion of slip boundary conditions at the channel walls helps to accurately represent the flow behavior of the nanofluid near these boundaries. The magneto-pseudoplastic nanofluid exhibits peculiar rheological features to flow dynamics due to pseudoplastic characteristics of nanoparticles in its composition and exposure to magnetic force. The mathematical formulation of motion equations is done through appropriate technique combining the properties of heat radiation, magnetic flux, double diffusion convection, and rheological features. The equation is further simplified by suitable method. The current study aims to evaluate the peristaltic movement under influence of slip boundaries characteristics, sort of concentration, heat radioactivity, flux properties, and temperature profile. Moreover, it will assess the flow dynamics with ratio of mass and heat exchange under the effect of critical parameters which include Prandtl number, Grashof number, slip limitations, and Hartmann number. So, the research will widen the theoretical underpinning of complex fluid transportation of magneto-pseudoplastic nanofluids under peristaltic flux and explicate the practical outcomes in terms of slip boundary settings in such systems. The results and conclusions are imperative for restructuring and devising biomedicine engineering, microfluidic equipment and gadgets, manufacturing techniques for complex fluid with peristaltic flow under the influence of slip limitations and magnetic force. [ABSTRACT FROM AUTHOR]

This article investigates the effect of activation energy on Carreau fluid flow in the presence of variable thermal conductivity, inclined magnetic field, melting heat transfer, and Soret and Dufour phenomena. A set of suitable similarity transformations is applied for transforming the governing partial differential equations (PDEs) considered for the physical phenomena into non-linear ordinary differential equations (ODEs). We obtained the results by solving the non-linear ODEs numerically which describe the behavior of the velocity, temperature, and concentration profiles of the fluid against the governing parameters and illustrated these graphically. The velocity distribution decreases for angle of inclination while it is increasing against higher melting parameter. The temperature distribution enhances with higher modified Dufour parameter and Prandtl number while it declines for thermal conductivity, activation energy, and melting parameters. The concentration distribution increases for melting parameter, Soret number, and activation energy parameter while decreasing for temperature difference parameter, Schmidt number, and reaction rate parameter. Skin friction, Nusselt and Sherwood numbers are evaluated numerically against the various governing parameters. Accuracy of the present work is illustrated and established through comparison carried out for skin friction versus magnetic parameter with existing results in the literature. [ABSTRACT FROM AUTHOR]

Theoretical analysis is performed to investigate the double-diffusive convection in Sisko fluid on peristaltic propulsion under inclined magnetic field and asymmetric channel. The mathematical modeling of Sisko fluids with double-diffusive convection and inclined magnetic field with various wave forms is given. Under the constraints of long wavelength and low Reynolds number, exact and numerical solutions are obtained. With aid of computational data achieved using Mathematica software, the impact of thermophoresis, Brownian motion, Soret and Dufour parameters, Grashof numbers (concentration, nanoparticle and thermal) on peristaltic pumping with double-diffusive convection are examined. [ABSTRACT FROM AUTHOR]

Aerospace research is increasingly focusing on propulsion system analysis. Heat transmission at high temperatures controlled by thermal radiation is used in spaceship propulsion systems. Hence, the current work investigates the magneto-Williamson nanofluid peristalsis flow in relation to thermal effect and slip-boundary circumstances with double-diffusion convection. In the flow's opposite direction, a steady, static magnetic field is applied. A mathematical model with appropriate boundary conditions is built by considering the momentum, continuity and energy equations. By considering the long wavelength and low Reynold estimation, the resulting equations are further made simpler. Then a numerical solution to the resulting reduced partial differential equations is obtained. Finally, there is a visual representation of the non-Newtonian propelling flow parameters, which include the Brinkman number, Prandtl number, Hartmann number, radiation parameter, particle volume fraction, electric field and slip parameters. It is highlighted that enhancing the coefficient of thermophoresis strengthens the temperature contour because increasing the number of particles merged enhances thermophoretic power. Furthermore, because of the substantial migration of nanoparticles from a heated region to a cooled one, the distribution of concentration becomes less cumbersome. It is also revealed that the fraction of nanoparticles rises because of rising thermal radiation and Brownian motion because nanofluids have a significant temperature distribution that may affect the system's distribution. [ABSTRACT FROM AUTHOR]

This work focuses on the heat transfer analysis of the magnetohydrodynamic peristaltic flow of blood through the gap between two coaxial flexible tubes of different wavelengths. In this model, the non-Newtonian biviscosity fluid is assumed to be blood, which is flowing through the annulus region between the inclined tubes. The governing equations for the considered problem are simplified under the assumptions of a zero Reynolds number and long wavelength approximations. An analytical expression for the temperature is obtained in its closed form, while a semi-analytical solution for the axial velocity of the moving fluid is determined using the homotopy perturbation method. Expressions for various flow variables such as shear stress, volumetric flow rate, pressure rise, and frictional force at the surface of inner and outer tubes are also obtained. In this work, we discussed the impact of various flow parameters like the Hartmann number, Grashof number, heat source, upper limit apparent viscosity coefficient, amplitude ratios of inner and outer tubes, radius ratio, and wavelength ratio on the above flow variables. The streamline contour plots are also drawn for the realization of the flow pattern of the blood inside the endoscope. The comparison of shear stresses for the peristaltic and rigid endoscopes and the validation of the present result with the previously established results are also discussed. A noteworthy observation drawn from the present model is that the pressure gradient enhances for increasing values of wavelength ratio when the wavelength of the inner tube is less than the wavelength of the outer tube, whereas the pressure gradient gets suppressed for increasing values of wavelength ratio when the wavelength of the inner tube is greater than the wavelength of the outer tube. From the present analysis, it is also found that the shear stress τrz of blood is the least for a peristaltic endoscope as compared to the rigid one. Therefore, this study may be applicable to medical practitioners for laparoscopic purposes, as a peristaltic endoscope may be a more appropriate device due to its flexibility than a rigid endoscope. [ABSTRACT FROM AUTHOR]

In this analysis, a numerical investigation of hybrid nanofluid flow composed of copper and alumina nanoparticles over an extending sheet is deliberated. The sheet surface is assumed to be heated by considering the convective condition, and there is no mass flow at the sheet surface by assuming the zero flux of mass constraints. The modeled ordinary differential equations, which are obtained by transforming the partial differential equations using suitable similarity variables, are evaluated numerically by adopting the bvp4c scheme. The main theme of this analysis is to investigate the applications of an inclined magnetic field toward the hybrid nanofluid flow over a convectively heated surface. The results obtained from this analysis show that the dragging force at the sheet's surface has been greatly increased by the magnetic factor and angle of inclination. Additionally, the angle of inclination greatly influenced the heat transfer rate, temperature, and concentration distributions when α = 900 as compared to α < 900. [ABSTRACT FROM AUTHOR]

AbstractIn this article, an effort is made to analyze the 3−D flow of hybrid nanofluid over a rotating stretching sheet. The hybrid nanofluid contains engine oil as a base fluid amalgamated with nano-particles MoS2 and ZnO. The flow is assumed to pass through a Darcy–Forchheimer medium subjected to the influence of an inclined magnetic field. In addition, heat radiation, Joule heating, viscous dissipation, nonlinear heat source, and quartic autocatalytic chemical reaction are applied to discourse heat and mass transfer features. The PDEs representing the physical problem are converted to ODEs with the introduction of similarity transformations. The solution of the problem is determined numerically by using MATLAB built-in bvp4c method. The proposed mathematical model’s validation is ascertained by comparing it with an earlier study in limiting case. In this regard, an excellent consensus is accomplished. The current investigation reveals that the flow along axial direction gets retarded by enhancing the values of rotational parameter, inertial parameter, and magnetic parameter, whereas the flow along radial direction gets accelerated. The increasing value of angle of inclination admirably resists the motion of nanofluid and hybrid nanofluid. The concentration profile gets decreased under the increasing influence of inclination angle and Schmidt number while it enhances for homogeneous reaction parameter. The enhancing values of rotational parameter, solid volume fraction and temperature, and exponential dependent heat generation parameters enhance the value of Nusselt number. [ABSTRACT FROM AUTHOR]

In this paper, the entropy generation of natural convection Jeffrey fluid flow through an inclined porous channel is investigated by taking into account the impact of angled magnetic field, Soret parameter, thermal radiation, and Hall current. On the basis of simplified assumptions, the governing equations are transformed into dimensionless equations by using suitable transformations, and the spectral quasi-linearization method (SQLM) is used for the numerical solution. Graphs are utilized to address the effects of new thermophysical parameters. The calculations reveal that increasing the Soret parameter, inclination angle, Hall parameter, magnetic parameter, and Jeffrey fluid parameter induces an increase in entropy generation. Conversely, it decreases as the radiation parameter and channel angle of inclination increase. [ABSTRACT FROM AUTHOR]

The behavior of a Maxwell nanofluid in mixed convection Darcy–Forchheimer inclined MHD flow across a stretched sheet is investigated in this research study. In order to analyze heat and mass transfer, the inquiry takes into account a number of variables, including the magnetic field, variable thermal conductivity, activation energy, suction/injection, and nonlinear thermal radiation. The controlling nonlinear PDEs with BCs are converted via similarity transformation into nonlinear ODEs in order to solve the ensuing nonlinear ODEs. These ODEs are then solved using the shooting method and a fourth‐order Runge‐Kutta methodology. The study explores how fluid flow velocity is affected by magnetic field inclination and suction/injection effects. This is attributed to the strengthening of the magnetic field with an increase in the inclination angle α. Additionally, the imposed magnetic field generates an opposing force, known as the Lorentz force, which contributes to a reduction in the velocity curve. Furthermore, various parameters affect the profiles of concentration, temperature, velocity, and Nusselt number. A number of parameters are looked at, such as the response rate constant, mixed convection, buoyancy ratio, suction/injection, Brownian motion, Lewis number, and thermophoresis. Interestingly, the results show that activation energy and mixed convection parameters, respectively, have an increasing effect on concentration and velocity curves. [ABSTRACT FROM AUTHOR]

Due of high degree polymerization distributions, Sutterby model accurately projects it. In addition, in response to infinite shear stress, polymer aqueous solutions exhibit shear thinning and thickening liquid properties. For representing the characteristics of liquids at large stress magnitudes, the Sutterby fluid is thought to be the most accurate model. Thermal radiation affects Sutterby fluid non-Newtonian two-dimensional mixed convection nanofluid flow approaching stagnation point on a convectively heated stretched surface under aninclined magnetic field and convective boundary conditions. Similarity transformations turn the nonlinear flow equations into an ordinary differential equation system, which can be solved numerically using the boundary value method. Subsequently, we applied the boundary value technique to crack ordinary differential equations in MATLAB. An analysis of varied pertinent parameters on flow field such as mass and heat transport rates, temperature,velocity, and nanoparticle concentration patterns is computed. Inclined angle causes the momentum profiles of Sutterby flow to decelerate. Thermal radiation parameter values rise together with the temperature and the Nusselt number rises as well. Impact of Soret parameter reduces the temperature gradient driving the mass transfer and thereby decreasing the concentration gradients. Brownian motion, the random motion of particles due to thermal fluctuations, efficiently improves the mass transfer process, thus increasing the mass transfer rate. [ABSTRACT FROM AUTHOR]

Solar collectors are devices that transform solar irradiation energy into thermal energy for various purposes. Among different solar thermal collectors, solar dish collectors are remarkable for having the highest solar-to-thermal energy conversion efficiency. These collectors are available with various receiver shapes like external, cavity, spiral and volume receivers. Notably, cavity receivers, with their unique structure, exhibit superior efficiency compared to other receiver types. Recently, researchers have explored different shapes of cavity receivers, such as triangle, circular, square and hexagonal, to enhance thermal efficiency. In light of this, the present study investigates the heat transfer behavior occurring in an inclined permeable triangular enclosure with heated fins, using a (Ag–TiO2/H2O) hybrid nanofluid as the working fluid. The mathematical modeling of hybrid nanofluid flow within the triangular enclosure is accomplished using the Navier–Stokes equations under the Boussinesq approximation, and dimensionless governing equations are solved through an in-house MATLAB code integrated with a finite difference method. The findings indicate that enhancing the Rayleigh number, thermal radiation and magnetic field boosts the heat transfer rate for a nanoparticle volume fraction of 5%. A decrease in the Darcy number leads to a shift in the flow pattern, causing the vortex cell to relocate to the top left. Higher values of Rayleigh number and thermal radiation effects are associated with a superior average heat transfer rate. Comparatively, the average heat transfer rate is slightly greater in an inclined cavity with α = π / 2 compared to an uninclined cavity. This emphasizes the focus of numerous studies on nanofluid flow in inclined square cavities, particularly in the context of solar energy. [ABSTRACT FROM AUTHOR]

AbstractThe applications of the artificial neural network (ANN) have become the focus of interest of researchers due to their convenience for accurate modeling, simulation, and efficiency of evaluation. The primary objective of this study is to investigate the characteristics of heat and mass transfer of the ternary hybrid nanofluid flow (THNF), which is squeezed between two parallel plates, using ANN. The plate which lies on x-axis is stretching while the upper plate (UP) can move in upward and downward direction. An inclined magnetic field (MF) is also applied to the lower plate (LP). A system of partial differential equations of flow, energy, and mass transfer is used to simulate the THNF, which is then condensed using similarity substitution to a collection of ordinary differential equations (ODEs). Using the differential transform method (DTM), the resultant nonlinear ODEs in dimensionless form are further solved. The influence of the different varying physical parameters on velocity, temperature, and concentration is graphically presented and discussed. It becomes apparent that the velocity, heat, and mass transfer in squeezing flows are significantly impacted by the inclination angle of the applied MF. To demonstrate the validity of the study, the numerical findings of the Nusselt and the Sherwood numbers are provided. For the accuracy of the used approach, DTM results are compared with results from the numerical approach. The novelty of the current work is to train the neural network with the Levenberg–Marquardt algorithm in the model. To get the estimated output of the model, different scenarios are set for training, testing, and validation. The analysis is done by mean square error (MSE), histogram, fitness curve, and regression (RG). The created ANN model is shown to be reliable due to its exceptional accuracy throughout the training, validation, and testing stages. [ABSTRACT FROM AUTHOR]

Within the most recent effort, a non-Newtonian inclination magnetized Carreau nanofluid that has such a cubed autocatalysis impact is detailed. When the flow behavior is moved via a magnetic field, the speed of the fluid is thoroughly investigated under these conditions. The findings about the temperature transparency of the Carreau nanofluid are obtained via the use of temperature-dependent heat transfer, and the measurement of the nanofluid's amount is accomplished by the utilization of homogeneous heterogeneous chemical processes. The physical model is used to construct partial differential equations (PDEs), which are then processed via variables that are comparable in order to obtain ordinary differential equations (ODEs). Also offered for operation is bvp4c which generates their analytical data. A combination of charts and statistical diagrams is used to display the findings. The movement of nanoparticles from inside the fluid is represented by the uniform chemical process. Furthermore, due to the fact that these nanoparticles are buried in the fluid, the temperature rises in both shear and shear thickness situations. Additionally, the higher magnetic force decreases the Lorentz force, which in turn decreases the movement of the nanofluid at reduced rates. [ABSTRACT FROM AUTHOR]

This investigation aims to delineate bioconvection in cylindrical-shaped Ag-CuO/H2O Ellis hybrid nanofluid containing gyrotactic microorganisms around a steady stretched cylindrical tube. Considering Brownian and thermophoretic diffusions, along with effects from an inclined magnetic field and slip, we derive a nonlinear system using boundary layer equations. Employing MATLAB's bvp4c function for numerical solutions, validated against established studies, we observe strong agreement. Graphical and tabular analyses demonstrate the impact of various parameters on velocity, temperature, concentration, gyrotactic microorganism profiles, skin friction coefficient, local Nusselt and Sherwood numbers, and gyrotactic microorganism coefficient, offering valuable interpretations. Observations reveal that the Ellis fluid parameter heightens velocity but reduces temperature, concentration, and gyrotactic microorganism profiles. Conversely, thermophoresis and Brownian motion enhance heat and mass transfer rates, while slip exhibits an opposite trend. Peclet number and bioconvective constants exhibit intriguing but contrary trends with gyrotactic microorganism profiles, yielding notable insights. A comparison between Ellis hybrid nanofluid and Ellis nanofluid reveals approximate variations in skin friction coefficients (up by 46.5%) and Nusselt numbers (down by 4%), suggesting improved aerodynamics and enhanced biomedical heat control for industrial optimization. Moreover, the reduction in Sherwood numbers (down by 56%) suggests potential applications in tailored environmental remediation and the optimisation of substance diffusion in pharmaceutical and biomedical therapeutics. This comprehensive analysis delves into intricate fluid dynamics, offering empirical insights applicable across engineering, biomedical sciences, and environmental remediation domains. [ABSTRACT FROM AUTHOR]

This work aims to study heat transfer analysis in a squeezing flow problem of nanofluid. The flow between pistons and nozzles in an automobile engine is one industrial application where the knowledge of the squeezing flow plays a crucial role. The applied magnetic field has a longitudinal inclined angle that ranges from zero to ninety degrees. In addition, viscous dissipation, chemical reaction, and suction injection are taken into consideration. Graphene nanoparticles with transformer oil are considered for Tiwari-Das Model. The transformed system of nonlinear ODEs is solved using the differential transform method. The numerical findings of the skin friction coefficient, the Nusselt and the Sherwood numbers are assessed with previously available works for accuracy. The graphical findings for relevant parameters of all profiles are analyzed. It becomes apparent that the velocity and heat transfer in compressing flows are significantly influenced by the angle of the inclination of the magnetic field. The temperature of the nanofluid and the rate of the heat transfer are both improved in the existence of the viscous-dissipation and thermophoresis. The findings show that the temperature rises with increased Prandtl and Eckert numbers. Furthermore, when Brownian movements of nanoparticles take place, the rate of mass transfer decreases.

In this work, we numerically explore all possible ways to improve heat transmission in a sinusoidal cavity with oxide nanoparticle suspensions in liquid. Engineers aim to improve thermal efficiency in their designs by incorporating an inclined magnetic field into prospective flow configurations. One of the most important advances is the utilization of sinusoidal walls, which significantly improve thermal efficiency. A significant step forward in comprehending thermal management in enclosures filled with nanofluids has been made possible by computational analysis facilitated by finite element analysis. An approximation of the velocity and temperature is provided by the Ladyzhenskaya-Babuska—Brezzi (LBB)-stable element, which is utilized to deliver this information. The accuracy of the computational study has been verified by comparing them to their equivalents in the previous research. It has been demonstrated through the findings that the rate of heat transfer and the kinetic energy are both higher when the volume concentration is lower. Furthermore, in the absence of a magnetic field, the Nusselt number is 7 % higher, and the kinetic energy is 1.89 times bigger for ϕ = 2 % compared to ϕ = 8 % for k = 0.2. Similarly, the KE decreases when there is an increase in the ϕ. Furthermore, a magnetic field has a detrimental effect on their values. As a result, both the fluid flow velocity and the temperature properties decline with increasing Hartmann numbers. These observations play a major role in the development of energy-efficient applications and optimized heat transfer systems, establishing a novel standard for thermal management approaches in real-world engineering scenarios.

Numerical studies of flow in square enclosures attain great interest due to their wide applications in engineering, such as in the meteorology, navigation, mechanology and mining, etc. In this paper, the solutions are obtained to the square lid driven cavity describing classical mixed convection in the presence of an inclined magnetic field, chemical radiation and heat absorption/generation. The problem is mathematically reduced into Navier-Stokes equations. The Coiflet wavelet homotopy approach, a newly suggested computational technique, is then used to solve these nonlinear partial differential equations with their non-homogeneous boundary conditions. The numerical solutions for streamlines, isotherms, iso-concentrations contours, Nusselt number are carefully determined. The solutions so obtained are analyzed through various plots to demonstrate the effects of several physical parameters such as Reynolds numbers (Re), Richardson number (Ri), Grashof number (Gr), Hartman number (Ha), thermal radiation parameter (N R), chemical reaction coefficient (K), heat generation/absorption coefficient (Q h), the angle of inclination of magnetic field (γ), slipping parameter (λ) and Schmidt number (Sc) and their physical insights are also reported. Rigid comparison of with previous studies shows excellent computational effectiveness of newly proposed method. Additionally, according to the results, our recently proposed approach has superior characteristics and strong nonlinear processing capabilities, which render it more appropriate than the Coiflet wavelet analysis method and the traditional homotopy analysis method for tackling complex nonlinear problems. [ABSTRACT FROM AUTHOR]

In this article, we studied the peristaltic motion of Jeffrey fluid with porous medium through an asymmetric channel under the influence of velocity slip parameters. Governing equations for non-Newtonian fluid flow models such as continuity, momentum, energy and mass transfer equations are formulated. Externally applied inclined magnetic field is also considered in the flow pattern. The lengthy governing equation of fluid motion is reduced by taking into the account of approximation of longer wavelengths and smaller Reynolds numbers The resulting governing equations are solved exactly. The graph shows the results of the impact of various related fluid parameters such as Hartmann number, Darcy number, Jeffrey fluid parameter, amplitude ratio, chemical reactions of fluid velocity, temperature, concentration, pressure rise, pressure gradient, streamlines etc. Finally, the various waveforms of the trapping phenomenon are presented. [ABSTRACT FROM AUTHOR]

Studying real-world problems with flow models of Newtonian and non-Newtonian fluids has gained particular attention because of its significance in engineering and other industries. According to trends in the field of research, interest in studying the characteristics of all such fluid flows is expanding. Due to the peculiar nature of the physical foundation of these non-Newtonian flows, no single constituent equation is available in the literature to explain all of their characteristics or rheological behavior. In the current investigation, the continuous 2D Casson fluid heat transfer flow is combined with the effects of radiation and an inclined magnetic field over a linear stretch surface. Newtonian condition is used to heat the sheet. The governing partial differential equations (PDEs) are transformed into nonlinear ordinary differential equations (ODEs) via the similarity transformation. The fourth-fifth-order Runge–Kutta Fehlberg (RKF45) method is then used to numerically solve the problem. The results for temperature distribution, and velocity field are computed and plotted graphically and discussed in detail. It is found that the magnetic parameter reduces fluid velocity and the Casson fluid parameter increases temperature distribution. [ABSTRACT FROM AUTHOR]

This analysis examines the flow of Ree–Eyring nanofluid over a stretching sheet in the presence of an inclined magnetic field. The nanoparticle distribution in the nanofluid is stabilised by the movement of motile microorganisms and it constitutes bioconvection. Meanwhile, the impact of thermophoresis and Brownian motion which plays an important role in the transfer of heat and mass is considered along with the convective boundary conditions. The flow of non-Newtonian nanofluid is widely used in the many manufacturing industries as a major component of cooling. Furthermore, it finds applications in thermal extrusion systems, biomedical engineering, cancer treatment etc. The governing equations are formulated using partial differential equations that are translated into non-linear differential equations employing appropriate relations based on these assumptions. The differential transformation technique (DTM) is used to solve these non-linear differential equations, and the results are shown in graphs and tables for various fluid flow parameters. The skin friction coefficient, local Nusselt, and motile density are all calculated and examined numerically. Fluid velocity is observed to increase as a function of a fluid variable. Furthermore, increasing the value of the thermal and relaxation solutal parameters reduces the temperature and concentration. [ABSTRACT FROM AUTHOR]

The aim of this investigation is to arrange partial differential equations (PDEs) into simplified form for gradients (mass and thermal) in the inclined magneto hydrodynamic flow of hybrid (CuO–TiO2/Water) nanoliquid in a permeable media. The modeled term is extremely nonlinear with the boundary conditions. So, this research focuses on numerical solution by using bvp4c solver in MATLAB software and by applying similarity transformation. Simulations have been done to discover the dynamics of stream and the transport of heat and mass under parametric deviation. To examine the impact of a temperature gradient on the transport of mass and the role of a concentration gradient on the transport of heat energy, outcomes have been documented in tabular form and shown through graphs. Remarkable changes in motion, temperature and concentration are noted when Dufour and Soret numbers vary. [ABSTRACT FROM AUTHOR]

The current study concentrates on the two-dimensional steady flow analysis of a tangent hyperbolic fluid with the significance of an inclined magnetic field over a thin moveable needle. The thermal analysis includes heat generation/absorption and nonlinear thermal radiation effects. Moreover, the two-phase model base analysis of mass and heat transport mechanisms through the Buongiorno model is carried out in this study. The governing equations with dimensionless form are tackled numerically through the ND Solve technique in Mathematica. The analysis of various features of the flow phenomenon corresponding to the two cases of static and moving needle or static and moving fluid is carried out influenced by numerous pertinent parameters. To confirm the validity of the current study, the results obtained are compared with previous findings. A good correlation between the present and previous findings substantiates the validation of the flow problem. This study reveals that in both the cases of moving and stationary needles, the flow rate dwindles corresponding to the escalating magnitude of the power-law index. Moreover, the improved Brownian motion parameter amplifies the rate of heat transport corresponding to both cases of static and movable needles.

The objective of this article is to investigate on the natural convective MHD flow of viscous fluid with assessment of mass and heat transfer effects. The flow is confined by two parallel plates. The walls of plates are assumed to be porous. The thermal radiation effects and inclined magnetic field applications are endorsed. One plate maintains the adiabatic phenomenon. The simplified form of problem is achieved with help of dimensionless variables. The analytical outcomes for given formulated problem are obtained with help of perturbation technique. Effects of various flow parameters involving to the problem are graphically impacted. It is claimed that velocity profile enhances due to modified Grashof number. An enhancement in heat transfer is subject to increasing the radiation parameter. Moreover, concentration profile reduces due to Reynolds number.

The present paper deals with the hybrid nano fluid, for this we have used Single and Multi-wall carbon nano tubes along with CuO and Water. The inclined magneto-hydrodynamics is considered along with Hall effect, soret and dufour for the impact on Williamson fluid flowing through porous medium over stretching/shrinking lamina having suction and injection in consideration. Heat and mass convective boundaries are taken to solve the nonlinear problem using shooting method and bvp4c MATLAB solver. The study shows the comparison between nanofluid (Cuo-Water, SWCNT-Water and MWCNT-Water) and found that the hybrid carbon nanotubes possess excellent result in skin friction and local Nusselt number compared to the SWCNT-water and MWCNT-water.Then the effect of different parameters are analysed through graphical representation and data tables.

The concept of nonlinear thermal convection is taking place for the process of cooling/heating in some thermal industries like solar collectors, combustion, and reactor safety. The significance of linear and nonlinear thermal convection is implemented in the present mathematical modeling to handle nonlinear density-temperature caused by viscous dissipation and flow through a porous medium. Further, the inclined magnetic field is implemented to analyze the flow characteristic at various inclination angles which will be helpful in glass manufacturing, geophysics, crude oil purification, and paper production. Furthermore, entropy generation analysis is made for the stagnation point flow of viscous fluid over a shrinking Riga sheet. Using boundary layer assumptions, the present model made up of fluid motion and energy equations is formed and converted to a system of nonlinear differential equations. Numerical results are collected using the MATLAB bvp4c solver and these results were utilized to study important parameters on the entropy generation and heat transport of fluid flow. The presence of nonlinear thermal convection will intensify the impact of major parameters and the least entropy generated for the inclination angle of the magnetic field. Also, entropy enhanced significantly with the Eckert number and modified Hartmann number. In addition, the surface drag is enhanced by 12%-18 % and the thermal transmission rate is diminished by 4%-7% in the case of nonlinear thermal convection compared to the linear case. The findings of this study are more important to optimize heat transfer and irreversibility in the applications of the automotive industry, ceramics, paints, food packaging, fabrics, pharmaceuticals, and cancer treatment.

This investigation discusses the significance of studying the behavior of non-Newtonian fluids, specifically the Casson fluid, subjected to an electrically conducting and stretching sheet. The study also explores the effects of an aligned magnetic field, Cattaneo–Christov double diffusion, viscous dissipation and chemical reactions on heat and mass transfer, respectively. The partial differential equations governing the flow problem are transformed into ordinary differential equations through the utilization of similarity transformations. Furthermore, the shooting technique is implemented in MATLAB to solve the ODEs. The influence of physical parameters, such as the magnetic field parameter, Eckert number, Prandtl number and chemical reaction parameter, on the velocity profile, temperature distribution, concentration profile, skin friction coefficient, Nusselt number and Sherwood number is studied and presented in graphical and tabular forms. It is found that increasing the Prandtl number causes a drop in the temperature profile. Moreover, the presence of thermal radiation and the Eckert number significantly amplifies the temperature distribution. When the magnetic number undergoes a substantial increase, there is a notable decrease in the velocity profile, and simultaneously, the temperature profile experiences a noticeable rise. Additionally, increase in the chemical reaction parameters leads to a decrease in the concentration profile. The skin friction coefficient, local Nusselt number and Sherwood number exhibit significant reductions as the Casson parameter increases. Additionally, a MATLAB built-in function named bvp4c is incorporated to verify the computed results. The practical implications of the Cattaneo–Christov heat flux model include microelectronics, microfluidic devices, processes involving rapid heating or cooling, such as laser welding or pulsed laser ablation and heat transfer in biological tissues. [ABSTRACT FROM AUTHOR]

Combined buoyancy shifts from temperature and concentricity gradients create double-diffusive convection. Complex Crown form enclosure with heat and mass source brings originality and practicality by enhancing use in a broad variety of technical, industrial, and geophysical operations. Current artifact is to explore thermosolutal diffusion in buoyantly driven flowing of viscid liquid contained in a crown enclosure with the installation of a uniformly heated and soluted circular cylinder. Novel physical characteristics of inclining magnetic field are introduced, and distributions affected by cylinder radius change are compared. Dimensionless PDEs are solved numerically using finite elements. Grid independence test ensures simulation mesh level. Hybrid meshing with triangular and rectangular components discretizes domain. Linear interpolating polynomials approximate pressure, whereas quadratic polynomials approach velocity, temperature, and concentricity. PARDISO solves a non-linear system of equations efficiently. Average Nusselt and Sherwood numbers are estimated by comparing relevant parameters to cylinder radius change. Heat transference rate rises to 40% and mass transport upsurges to 60% when radius of cylinder is increased from 0.1 to 0.2. Hartmann number tends to affect a decline in Nusselt and Sherwood quantities. Reduction in thermal and solutal boundary layers near surface of the cylinder is observed against the improve in radius of cylinder. [ABSTRACT FROM AUTHOR]

The magnetohydrodynamic (MHD) nanofluid flow at non-orthogonal stagnation point, with suspended carbon nanotubes in water on a stretched sheet in a permeable media with non-linear thermal radiation is studied. This work aims to explore the inclined magnetic field impacts on normal velocity, tangential velocity and temperature for both types of carbon nanotubes (CNTs). The governing flow equations which are continuity equation, momentum equation and energy equation are reformed into ordinary differential form with the proper boundary conditions using appropriate transformations. The computational solution of the nonlinear ODEs is obtained using the Bvp4c method. The graphs are presented to show the influence of certain physical factors which ranged as magnetic parameter (0.5 ≤ M ≤ 2.5), inclination angle of the magnetic field (п/2 ≤ ζ ≤ п/4), permeability parameter (0 ≤ Ω ≤ 2), volume fraction of nanoparticle (0.03 ≤ Φ ≤ 0.07), stretching ration parameter (0.3 ≤ γ2 ≤ 0.7), Radiation parameter (0.5 ≤ Nr ≤ 0.9), the heating parameter (0.5 ≤ θw ≤ 1.5) and Prandtl number (5 ≤ Pr ≤ 10). The normal and tangential velocity drops with the augmentation of (M), (ζ) and (Ω), while the temperature rise with enhance of (Nr) and (θw). This study's findings may be used to manage the heat transmission and fluid velocity rate to achieve the required final product quality in numerous manufacturing processes such as electronic cooling, solar heating, biomedical and nuclear system cooling. Validation against previous research available in the literature in specific situations shows excellent agreement. [ABSTRACT FROM AUTHOR]

The primary goal of this research is to look into the rheological aspects of blood flow that contains ternary nanoparticles ($CuO$CuO+ $Ti{O_2}$TiO2+ $A{l_2}{O_3}$Al2O3). For this, the micropolar fluid model is adopted to simulate blood flow transport. Inclined magnetization and porosity characteristics are used to reveal the momentum attributes of flowing fluid, and nonlinearized radiating thermal flux is used to predict the thermal characteristics of the concerned flow. Further, the aspects of suction and injection of fluid over a permeable stretching sheet are also acknowledged. Governing system of partial differential equations are transformed into nonlinear ordinary differential equations by using similarity transformation. An effective built-in routine known as bvp4c, which is based on finite differencing, is used to acquire the solution. The results showed that the trihybrid nanofluid significantly boost fluid motion and temperature profiles more in the mass injection effect in comparison to suction phenomena. The increase in heat transfer rate is also noticed for augmented values of non-linear radiation parameter and micropolar parameter. There is a detailed discussion of the effects of the contributing parameters on the resulting dimensionless profiles. This research has significant implications for the delivery of magnetized blood, hyperthermia therapy, understanding of the bloodstream, transfer of complex bio-waste liquids, and capillary heat exchange. [ABSTRACT FROM AUTHOR]

In this paper, we study the impact of the rotation of an inclined magnetic felid and inclined symmetric channel with slip condition on peristaltic transport using incompressible non-Newtonian fluid. Slip conditions for the concentration and heat transfer are considered. We use the conditions on the fluid, namely infinite wavelength and low - Reynolds number to simplify the governed equations that described - motion flow, energy and concentration. These equations of the problem are solved by the perturbation technique and restricted the number of Bingham to a small value to find the final expression of the stream function. The Bingham number, Brinkman number, Soret number, Dufour number, temperature, Hartman number and other parameters are tested. The effects of different values of these parameters are discussed and illustrated graphically through the set of figures. Numerical results are computed by using MATHEMATICA software. [ABSTRACT FROM AUTHOR]

The outcomes of partial slip on double-diffusive convection of Johnson–Segalman nanofluids in an asymmetric peristaltic path are presented in this research with the effect of inclined magnetic field. The mathematical formulation of Johnson–Segalman nanofluids is also discussed with double-diffusive convection and inclined magnetic field. To simplify extremely nonlinear partial differential equations, a lubricant approach is applied. The numerical calculations are obtained to the equations for the stream function, concentration, pressure gradient, temperature, velocity, nanoparticle volume fraction, and pressure rise. The impact of prominent hydro-mechanical parameters such as Brownian motion, thermophoresis, Soret, Dufour, and slip constraints on the axial velocity, trapping, volumetric fraction, pressure gradient, temperature, pressure rise, and concentration functions is evaluated graphically. It is noted that slip effect in the channel causes the fluid particles to stray, slowing the fluid velocity. Moreover, it has been noted that as thermophoretic effects and Brownian motion increase, nanoparticles rapidly move from the wall into the fluid, significantly raising temperature. [ABSTRACT FROM AUTHOR]

Two-dimensional free convective temperature transportation and fluid flow within the semi-circular cavity occupied by nanofluid with influence of inclined MHD is studied numerically. While bottom wall is warmed by three distinct thermal conditions (uniform, parabolic, and sinusoidal), the upper circular wall is warmed at lower temperatures. A slopping magnetic field acts upon the enclosure whose strength is unchanging. The governing non-linear equations is resolved with the numerical scheme Galerkin type finite element technique. A strong agreement is found with the earlier work. The outcomes for the model parameters likely Rayleigh number, sloping angle of magnetic field, nanoparticles volume, size, shape, and Brownian effects, and Hartmann number are demonstrated through streamlines, isothermal lines, and mean Nusselt number. In addition, investigation is conducted the thermal features of various nanoparticles and the nanofluid produced from them. The outcomes reveal that thermal transfer rate is significantly enhanced by volume fraction nanoparticles and buoyancy-driven parameter Rayleigh number whilst reduces for higher Hartman number. The inclined angles of magnetic field and different thermal conditions have a positive influence on thermal transport. For Cu-H2O nanofluids, thermal transport is enhanced by 10.98 % in a uniform thermal system, where it increases by 14.42 % in the parabolic thermal system and by 15.53 % in a sinusoidal thermal system for the only 5 % volume of nanoparticles. Moreover, nano-sized particles’ shape factor has a noteworthy role in thermal transport. It is found that heat transfer rate rises by 6.79 % for blade-shaped nanoparticles. Additionally, as considering Brownian effects of nanoparticles, the temperature transport rate is improved by 21.45 % for small-sized nanoparticles.

Research has been conducted on the study of the multi-slip impact on the Williamson fluid flow above a stretching sheet in the existence of an inclined magnetic field and Radiation. By applying the proper similarity conversions, the governing equations (PDEs) are reduced to a set of non-linear ODEs, and a numerical solution is produced by using MATLAB in-built solver bvp4c package. The impacts of the dimensionless characteristics on the flow patterns are analyzed visually, and the values of the friction, Nusselt, and mass transfer quantities are tabulated to exemplify how the various physical factors have an influence. As the magnetic parameter strength increases, the fluid velocity decreases, but it increases with mixed convection. As the parameters of Brownian motion and thermophoresis increase, the temperature also increases. The findings provide good agreement when compared to the current literature.

The current study explores the behavior of particle shape on the radiative flow of Casson hybrid nanofluid towards an expanding/contracting convective sheet. The nanofluid under onsideration is a water-based hybrid comprising carbon nanotubes (CNTs) with particle shapes. The particle shape factor is employed to determine its significance on the flow characteristic. The standard equations for the flow and thermal transportation are derived based on the conservation laws, including the simultaneous effects of viscous dissipation, thermal radiation, along with uniform heat source. The Casson based model is employed to pronounce the rheological characteristic of the nanofluid, taking into account the non-Newtonian nature of the fluid. To further explore the system, the influence of multiple slip effects and an inclined magnetic field is considered. Multiple slip effects occur due to the simultaneous presence of velocity, thermal, and concentration slips at the solid-fluid interface. The inclined magnetic field is introduced to investigate the magnetohydrodynamic (MHD) effects on the flow characteristics. Numerical simulations are performed using appropriate numerical techniques to solve the resulting system of equations. The effects of various parameters, such as particle shape, slip parameters, magnetic field inclination, and thermal radiation, are thoroughly analyzed. The main findings of this works are; the interaction of CNTs that enhances the thermal conductivity of the nanofluid boost up the heat transfer rate further, and the particle concentrations enhance the fluid temperature significantly. The observation indicates that the increasing slip enhances both the velocity and temperature distribution.

Abstract The significance of freely oscillating unsteady stagnation flows is attributed to their use in various kinds of engineering processes like cooling systems, heat exchangers and turbomachinery. The restrictive forces produced with the help of magnetic fields are a useful technique in providing optimum flow control in the metallurgical operations and refinement of molten metals. The present study highlights the inclined magnetic field implications on an oscillatory streaming nanofluid which impinges non-orthogonally over a non-smooth surface. The surface roughness of the wall is elaborated by the slip velocity condition. The two-phase Buongiorno nanofluid model is being considered. The energy dissipation due to the active chemical reactions occurring in the flow is adopted with Arrhenius activation energy. Suitable dimension-free variables are chosen to make the mathematical model parameter dependent. The numerical outcomes of the problem are determined through the utilization of the bvp5c solver based on the finite difference method using MATLAB R2023a. The graphical representations depict significant alteration in concentration profiles with thermal ratio ( δ ) and Activation energy ( E * ). The findings indicate that higher activation energy and weaker temperature conditions increased the mass transfer. In conjunction, the velocity profile is enhanced for acute magnetic field angles. [ABSTRACT FROM AUTHOR]

The present work investigates Reiner–Rivlin fluid's movement on a stretching surface with an inclined magnetic field, thermal radiation, and slip impacts. The governing equations are modeled with suitable assumptions. The governing equations are transformed into ordinary differential equations with suitable similarity terms. The numerical results are computed with the help of Runge-Kutta-Fehlberg 4th 5th order (RKF-45) and the shooting technique. The results are discussed in detail with the help of tables and graphs. The analysis mainly focuses on the different inclined angle impact over velocity and thermal profiles. The outcome reveals that the maximum thermal distribution and minimum velocity are seen with an inclined angle ξ = 90 ∘ . The cross-viscosity parameter directly impacts the velocity profile but shows a reverse trend on the thermal profile. The surface drag force is found to be minimum ξ = 90 ∘ followed by ξ = 45 ∘ and ξ = 0 ∘ . The thermal distribution rate is observed maximum at ξ = 90 ∘ than ξ = 45 ∘ and ξ = 0 ∘ . [ABSTRACT FROM AUTHOR]

In this paper, hybrid nanofluid flow with mediated compressions and dilations subject to the temperature-dependent viscosity/ thermal conductivity and inclined magnetic field is considered. In medical science, the flow mediated dilation of the artery exists when the blood flow is enhanced in the artery. The compressed/ dilated type flow can be utilized in food processing, hot plate welding, rheological testing, cardiovascular drugs, measurement of brachial artery dilation, blood vessel damage caused by cigarette smoke. The volume of the dilated flow is maintained by injecting the same fluid into the flow field through the exponentially permeable and stretchable walls of the channel. This phenomenon is modeled mathematically and solved by Chebyshev pseudo-spectral method utilizing quasi-linearization approach. It is interestingly analyzed that squeezing/ dilating forces generate two points of inflection in the flow field where the magnitude of permeable fluid velocity is enhanced by 17.21% in the mid portion of the channel by the increase of dilating forces, however it is reduced by 20.35% due to the strengthening of the compressing forces of the channel. The reported flow mediated dilation/ contraction of the study can be used in targeted drug delivery (especially cardiovascular drugs), assessment of endothelial function, measurement of brachial artery dilation and blood vessel damage. The angled magnetic field can be utilized to successfully control the environmental skin-friction and heat transfer. [ABSTRACT FROM AUTHOR]

The effect of an inclined magnetic field on unsteady magneto hydrodynamic Williamson fluid flow past an exponentially stretching sheet with joule heating, non-uniform heat generation or absorption, and suction or blowing is investigated numerically in this work. The reduced non-linear ordinary differential equations are obtained from governing partial differential equations using appropriate similarity transformations. The reduced equations are then solved with the help of bvp4c in MATLAB. The effects of various physical parameters on velocity, temperature and concentration profile, skin friction coefficient, Nusselt, and Sherwood number are described through graphs and tables. The result indicates that the rising values of the Weissenberg number decrease the velocity profile and increase the temperature and concentration profiles. It is also found that an inclined magnetic field reduces fluid velocity. [ABSTRACT FROM AUTHOR]