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The motivation of this recent article is to study dusty Walter's B fluid flow due to its wide range of applications in biology and polymer industry. The fluid is traveling peristaltically through an asymmetric channel with wall slip. A discussion is also presented to examine heat transfer effects with thermal radiation and slip. The regular perturbation technique is employed to evaluate the mathematical model of the problem, which is first simplified by using stream functions. Mathematical results are simulated to illustrate flow characteristics of fluid and solid particles in salient quantities. Also, graphs of temperature distribution of fluid and dust particles have been discussed to study the impacts of various parameters. Walter's B fluid parameter reduces speed of both fluid and dust particles. By increasing thermal slip parameter, temperature transference becomes slower through the fluid, while Brinkman number significantly raises the temperature profile of both fluid and particles. This article presents a theoretical analysis of the problem. Moreover, the characteristics of liquids involved in the plastic industry and medical science can also be understood using the current analysis. Walter's B fluid with dust particle suspension has not been investigated for slip and thermal radiation effects. [ABSTRACT FROM AUTHOR]

Motivation: The motivation of this recent article is to study dusty Walter’s B fluid flow due to its wide range of applications in biology and polymer industry. The fluid is traveling peristaltically through an asymmetric channel with wall slip. A discussion is also presented to examine heat transfer effects with thermal radiation and slip. Methodology: The regular perturbation technique is employed to evaluate the mathematical model of the problem, which is first simplified by using stream functions. Mathematical results are simulated to illustrate flow characteristics of fluid and solid particles in salient quantities. Also, graphs of temperature distribution of fluid and dust particles have been discussed to study the impacts of various parameters. Outcomes: Walter’s B fluid parameter reduces speed of both fluid and dust particles. By increasing thermal slip parameter, temperature transference becomes slower through the fluid, while Brinkman number significantly raises the temperature profile of both fluid and particles. This article presents a theoretical analysis of the problem. Moreover, the characteristics of liquids involved in the plastic industry and medical science can also be understood using the current analysis. Originality/Value: Walter’s B fluid with dust particle suspension has not been investigated for slip and thermal radiation effects.

The motivation of the current work is the flow over a slender surface, which includes the manufacture of optical fibers, polymer sheets, photoelectric devices, wire coatings, solar cells, and fiber sheets. In order to enhance the results of the wire coating process, it is necessary to carefully examine the mass and thermal heat transmission rates. The novelty of this study is the ability to forecast complex thermal issues in the tri-hybrid Sutterby nanofluid flow, considering the effects of electro-hydromagnetic and multi-slip circumstances. The study examines the impact of nonlinear thermal radiation, electric field, and slips in velocity, temperature, and solutal properties on the steady flow confined to two-dimensions Au-TiO2-GO/SA in the field of electro-magneto-hydrodynamics. Employing similarity transformations, the regulatory boundary layer equations are converted to nonlinear ODEs. Following that, the resulting equations are solved using the homotopy perturbation method. Numerical simulations are performed for several physical parameter values, and the influences of numerous distributions are examined. It is observed that the thermal distribution exhibits a decreasing trend as the values of the mixed convection flow, electric field, temperature jump, and velocity slip parameters are boosted. Moreover, the Sherwood number is declining by m, De, δ1, δ2, and δ3 and rising due to the enhancement of E1, γ1, and γ3.

Nanofluid is one of the modern heat transfer fluids that offer the potential to substantially enhance the heat transfer efficiency of conventional fluids. Extensive research has been undertaken to explore its fundamental thermophysical properties specifically viscosity and as well as thermal conductivity. This research emphasizes the significance of hybrid nanofluids and investigates the effect of Brownian motion and thermophoretic phenomena on the characteristics of the Agrawal flow that tends to a stagnation point adjacent to a moving porous disk. The model also accounts for the effects of Smoluchowski temperature and Maxwell velocity slip conditions. Through the utilization of similarity ansatz, the governing partial differential equations are simplified into a class of ordinary differential (similarity) equations. Subsequently, these simplified equations achieved numerical solutions by employing the bvp4c solver, which is specifically designed for fourth-ordered boundary value problems. The study delves into the remarkable impacts of the pertinent embedded parameters on key parameters such as mass transfer rate, heat transfer rate, and shear stress. These effects are brilliantly depicted through a combination of graphs and tables. Graphical analyses disclose the presence of dual solutions within a particular range of the stretching/shrinking parameter. Also, enhancing the solid volume fraction of nanoparticles leads to a notable rise in the shear stress and heat transfer for both solution branches, whereas the mass transfer rate experiences a reduction.

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

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

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

Industrial applications in domains such as warm rolling, crystal development, thermal extrusion and optical fiber illustration are seeing a significant increase. These applications specifically focus on addressing the challenge of a cylinder in motion inside a fluid environment. Elevated temperatures may affect the viscosity and thermal conductivity of fluids. Understanding the relationship between temperature and the properties of fluids is crucial. In light of these presumptions, the primary goal of this study is to examine, under transverse magnetic field, shape factor, velocity, thermal slip conditions and viscous dissipation, how temperature-dependent fluid properties could enhance the heat transfer efficiency and performance evolution of ternary hybrid nanofluid. In order to study flow fluctuations, the impact of nanoparticle addition and improvements in heat transfer, a variable Prandtl number is also included. The use of similarity variables converts the controlling flow model from partial differential equations (PDEs) to ordinary differential equations (ODEs). Mathematica’s shooting strategy solves ODEs using the fourth-order Runge–Kutta (RK-IV) method. Numerical calculations were done after setting parameters to acquire the desired results. Analytical data are provided in tables and graphs for convenient usage. The results showed that the velocity profile increases as the values of ϕ3, Pr, M, Re and S grow, and decreases when the values of θr decrease. Re, Pr and S lower the temperature profile, whereas ϕ3, θr and Ec raise it. The skin friction profile steepens as ϕ3, S, Re and M increase relative to the stretched cylinder, and flattens as θr and ω decrease. The Nusselt number profile rises as θr, Pr, S and Re decrease with ϕ3, Ec and δ. When the Prandtl number goes from 3.0 to 6.2 in a ternary hybrid nanofluid with brick-shaped nanoparticles, the Nusselt number goes up by around 55.7%. [ABSTRACT FROM AUTHOR]

In this research, we look at the rate of heat and mass transfer in an MHD viscoelastic (Walter's liquid-B model) nanofluid over a stretching sheet when that sheet is subject to heat generation/absorption and thermal radiation. According to the mathematical configuration, the current flow problem follows the fundamental laws of motion and heat transfer. The governing equations have been converted to nonlinear ordinary differential (ODEs) equations using similarity transformations. Using the homotopy analysis method (HAM), we have obtained the numerical solution to the resulting nonlinear ODEs and their associated boundary conditions. The behavior of the problem's resultant equations under the impact of various flow factors is examined graphically, which ensures that the rate of heat transfer reduces with an elevation in the Brownian motion parameter and improves with an increase in the thermophoresis parameter. Greater viscoelastic and stretching parameter values accelerate velocity slip. The nanofluid's viscoelasticity minimizes local skin friction, Nusselt, and Sherwood numbers. It is noticed that the slip parameter substantially influences flow velocity. The momentum boundary layer thickness diminished and the thermal boundary layer thickness flourished as the velocity slip factor enhanced. The general conclusions obtained in this article provide an opportunity to understand the importance of this fluid flow. [ABSTRACT FROM AUTHOR]

Thermal performance of peristaltic pump are significant to enhance the efficiency of the system. Heat transfer analysis for peristalsis of hybrid nanofluid through a curved duct is investigated here. Effect of radially varying magnetic field, Joule heating and heat generation/absorption are taken into consideration. Viscous dissipation and thermal radiation effects are considered to improve the heat transfer rate. Thermal and viscous characteristics are varying according to temperature. Velocity slip and temperature jump constraints are employed to solve the problem. The solution of resulting system are obtained under the lubrication technique. Curvature effect are also discussed to observe variation in the flow rate. NDSolve is built in shooting technique that are used in Mathematica software to find the solution. Numerical results for pertinent non-dimensional parameters are presented graphically. Heat transfer characteristics are represented through table. Results revealed that the inclusion of nanomaterials in liquid improves the cooling process and perturbs the flow rate. Comparative analysis indicates that heat transfer rate are 4 % higher in the case of copper nanomaterial as compare to iron oxide nanomaterial. The results of present study has relevance with cancer therapy, heart surgery and drug delivery processes.

The significance of heat transfer during a reversible esterification process in a magnetohydrodynamic boundary layer Casson fluid flow along a vertical stretching plate is examined. The multi-slip conditions are considered in a porous medium. The presence of chemical process requiring an activation energy is considered in the analysis. The study also investigates the hydromagnetic boundary layer Casson fluid flow alongwith partial slip conditions across a vertical stretching plate. The incorporation of multi-slip constraints in a porous medium, alongside magnetic fields and other parameters, highlights its relevance in diverse engineering fields such as thermal engineering, polymerization, and biodiesel industries. Understanding the characteristics of such fluids under complex conditions is vital for optimizing heat and mass transfer in industrial applications, making this investigation timely and valuable. The nonlinear differential set of equations are solved numerically involving Runge-Kutta based shooting approach of fourth order and the results are verified with the bvp4c tool and the findings are explored using graphical plots. The predominance of significant factors on flow configurations are analyzed and presented in graphs and tables. A comprehensive analysis is provided on the effects on velocity, concentration, and temperature of diverse parameters such as reaction rate constant, magnetic parameter, suction parameter, mass Grashof number, Prandtl number, Casson parameter, thermal radiation parameter and slip parameters. The tabular representation of the adverse effects of drag coefficient, rate of mass transfer and Nusselt number on flow configurations for various significant parameters is presented. It is inferred that for the case of reversible and irreversible flows, the shear stress rate escalates by 29% when the magnetic parameter elevates from 0.5 to 1.5 and about 35% when the Casson parameter elevates from 0.5 to 1.5. For the suction parameter, the coefficient of drag increased by 27% and 26% for irreversible and reversible flows respectively. When the reaction rate increases from 0.5 to 1.5, the rate of shear stress elevates by 0.5% and 0.02% for irreversible and reversible flows in order. The Nusselt number decreased about 7% and 8% when the magnetic parameter and Casson parameter rises from 0.5 to 1.5 respectively, for irreversible and reversible flows. It is noteworthy that the previous studies are in precise agreement with the present investigation.

This study investigates the flow of a two-dimensional magnetohydrodynamic(MHD) tangential hyperbolic hybrid nano fluid flow towards a porous stretched sheet with an inclined magnetic field under velocity and thermal slip conditions. Two distinct base fluids, (i) water and (ii) a mixture of [Formula: see text] ethylene glycol([Formula: see text]) and [Formula: see text] water are employed as base liquids with Copper([Formula: see text]) and aluminium oxide([Formula: see text]) nanoparticles, to generate two different hybrid nanofluids as [Formula: see text] and [Formula: see text]. Scaling group transformations with a homotopy algorithm is used to study the effects of distinct physical parameters like the Weissenberg number, an inclined magnetic field, thermal radiation, velocity, and thermal slip conditions with a heat generation/absorption parameter and a permeable parameter on the velocity and temperature distributions. The outcomes of [Formula: see text] hybrid nano fluid are compared with [Formula: see text] hybrid nano fluid in significant critical physical circumstances using graphs and tables. It is observed that the parameters [Formula: see text] and [Formula: see text], [Formula: see text], and λ increase the fluid temperature and decelerate the motion of fluid. The obtained results are validated by comparing them with the existing literature and found that the present results are consistent with the given data. Additionally, it is also noticed that the [Formula: see text] hybrid nanofluid has a higher heat transmission rate as compared to [Formula: see text] hybrid nanofluid. Finally, the impact of nano particle volume fractions of copper and aluminium oxide on the velocity and temperature profiles is discussed to study their efficiency.

Hybrid nanofluid problems are used for augmentation of thermal transportation in various industrial applications. Therefore, the present problem is studied for the heat and mass transportation features of hybrid nanofluid caused by extending surface along with porous media. In this investigation, the authors have emphasized to analyze hybrid nanofluid flow containing diamond and copper nanoparticles on an extending surface. Furthermore, the velocity, temperature, and concentration slip constraints are adopted to examine the flow of fluid. Heat source, chemical reactivity, thermal radiation, Brownian motion and effects are taken into consideration. Nonlinear modeled equations are converted into dimensionless through similarity variables. By adopting the homotopy analysis method, the resulting equations are simulated analytically. The impacts of various emerging factors on the flow profiles (i.e., velocities, temperature, concentration, skin frictions, local Nusselt number, and Sherwood number) are shown using Figures and Tables. The major key findings reveal that the hybrid nanofluid temperature is higher but the concentration is lower for a Brownian diffusivity parameter. Moreover, increment role of heat transport is achieved due to the increment in radiation factor, thermophoresis, Brownian motion factors, and Eckert number. It has also been observed that velocity in x-direction converges in the region −0.8≤ℏf≤0.5-0.8\le {\hslash }_{\text{f}}\le 0.5, in y-direction velocity is convergent in the zone −0.6≤ℏg≤0.35-0.6\le {\hslash }_{\text{g}}\le 0.35, while temperature converges in the region −0.6≤ℏθ≤0.4-0.6\le {\hslash }_{\text{θ}}\le 0.4 and concentration converges in the region −0.5≤ℏφ≤0.4-0.5\le {\hslash }_{\text{φ}}\le 0.4.

In this research work, the authors have presented a water-ethylene glycol-based hybrid nanofluid flow which contains MoS2 and GO nanoparticles on a stretching surface. The fluid flow has been examined under the consequences of velocity and thermal slip conditions, magnetic field, and exponential heat source/sink. The hybrid-based fluid flow is composed of 50% water and 50% ethylene glycol. The purpose of this investigation is to propose a comparative analysis among the pure fluid, GO nanofluid, and hybrid nanofluid. A suitable set of variables has been used to convert the leading equation to dimensionless notation. The bvp4c Matlab built-in package is utilized to compute a numerical solution of the suggested model. A comparison of the resultant data with published results exhibits a significant agreement. The outcomes of the present work show that GO nanofluid flow has a greater velocity profile than the hybrid nanofluid and base fluid. Temperature panels, skin friction, and thermal flow rate are much greater in the case of hybrid nanoparticles in contrast to single GO nanofluid and base fluid. Further, it has been noticed that the impact of the porosity factor and magnetic and rotation factors drops the velocity distribution, while the opposite impacts of the porosity and magnetic factors have been found on the radial velocity. [ABSTRACT FROM AUTHOR]

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

Understanding the intricate interplay between variable fluid properties such as slip and thermal conductivity when flowing over porous surfaces is of utmost importance for a wide range of engineering applications. This investigation delves into this uncharted territory, connecting the analytical capabilities of HAM (Homotopy Analysis Method) to reveal captivating insights into the impact of these variables on the dynamics of Casson nanofluid flow. Besides, we documented the flow aspects which include thermal radiation, heat source, variable wall thickness and chemical reaction. We alter the partial differential flow-related conditions into nonlinear ordinary ones employing the similarity transformation approach. Then, using a popular semi-analytical technique known as the Homotopy Analysis Method (HAM), we were able to untangle them. This method yields to power series solutions to nonlinear differential equations. To illustrate the impact of the velocity, temperature and concentration profiles, parametric research has been done using tables and diagrams. In the limiting sense, the numerical results of our methodology are in great association with the outcomes of previous research. Finally, it is noted that higher values of the velocity slip parameter cause an enhancement in fluid velocity, while escalating values of the thermal slip parameter cause a decline in temperature distribution. [ABSTRACT FROM AUTHOR]

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

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

The sodium alginate (SA)-based nanofluid flow comprising alumina nanoparticles on a bi-directional extending sheet has many applications, which include thermal management, automotive radiators, industrial heat exchangers, conductive coatings, flexible electronics, electromagnetic shielding, solar panels, etc. A numerical study based on the SA-based nanofluid flow containing alumina nanoparticles over a bi-directional extending sheet in the presence of variable Darcy porous media has not yet been examined. Therefore, this study focuses on numerically investigating the flow behavior of a nanofluid of SA containing nanoparticles of alumina (Al2O3) over a bi-directional extending sheet. The variable Darcy porous media, magnetic field, thermal radiation, and thermal-dependent and space-dependent heat sources are applied to examine heat transfer flow. The velocity and thermal slip conditions have been used in the present model. The model is first shown as partial differential equations and is then converted to ordinary differential equations (ODEs). A numerical technique called bvp4c MATLAB function is applied to solve the modeled ODEs. The model is validated with previously published results. From the obtained results, it is found that high magnetic factor increases the thermal distribution, skin frictions, and heat transfer rate and reduces the velocity profiles along both directions. The Casson factor reduces the skin friction, heat transfer rate, and velocity profiles along both directions while increasing the thermal distribution. High velocities and temperature distributions of a SA-based nanofluid flow containing alumina nanoparticles are found for the scenario of no-slip condition when matched to the slip condition. It is concluded from the observed results that the percentage increase is higher for the no-slip conditions compared to the slip conditions.

The main objective of this work is to investigate viscous dissipation with thermal radiation impact on hybrid nanofluid flow past an exponentially stretching/shrinking surface along with magnetic field, and heat source/sink, slip boundary conditions. Water ( H 2 O ) is taken into account as a host fluid with copper (Cu) and alumina ( Al 2 O 3 ) as nanoparticles to form a hybrid nano liquid (Cu- H 2 O - Al 2 O 3 ). The coupled nonlinear partial differential equations are transmuted into ordinary differential equations using similarity transformations with boundary conditions and these ODEs are simplified using numerical solver, bvp4c in MATLAB. The behavior of momentum profiles, thermal profiles, coefficient of heat transfer ( Nux 1 ) and skin friction ( C f ) are explored using the pertinent parameters such as Eckert Number ( Ec 1 ), Suction Parameter ( S 1 ), Magnetic Parameter ( M 1 ), Radiation Parameter ( Nr 1 ), Stretching/Shrinking Parameter (λ ), Velocity and thermal slip Parameters ( A 1 and B 1 ), Heat source/sink Parameter ( β 1 ), variable thermal Parameter (ϵ ), thermal conductivity (K) are depicted through tables and graphs. The present simulation is more stable and convergence when compared with the existing literature, which is portrayed in the tables. The presence of dual solution is noticed for Ec 1 = 0.1, 0.11,0.12 when the critical value of λ (= λ c ) are λ c 1 = - 1.60355799, λ c 2 = - 1.60322884 and λ c 3 = - 1.6031348, respectively. The existence of the dual solution is reported due to the presence of shrinking surface and suction, further, the first solution is found to be more stable. The novelty of the current simulation includes MHD hybrid nano liquid flow stability with the impact of viscous dissipation and thermal radiation past stretching/shrinking permeable plane to fill the research gap in the existing literature. The applications of transmission of heat by stretching/shrinking surface in boundary layers is used in various fields such as polymer and material processing, biomedical engineering, heat exchangers, etc. [ABSTRACT FROM AUTHOR]

The current problem is significant because it concerns the modeling of electroosmosis regulated peristaltic flow of hybrid Newtonian liquid as seen within a symmetric tube. This model provides an exciting mathematical formulation with unexpected features, especially when impacted by electroosmotic forces, which aids in understanding how these complex fluids behave under different conditions. It is essential for maintaining product integrity, which can help us avoid problems in the future. The manuscript focuses on the perception of copper and SIO2 hybrid nanoparticles using blood as a means of transport fluid. The theoretical formulation is based on nanoparticles having blades, platelets, and cylindrical forms. At the microscale, physiological transport phenomena generated by pressure to form a pressure gradient, velocity, and thermal slip may be used to articulately construct a theoretical treatment for rheumatoid arthritis and biomimetic thermal pumping systems. The boundary conditions for computation are generated using the proper transformations, and Euler's technique is used to produce an accurate solution of the resulting system of nonlinear ODEs raised by governing PDEs. "Mathematica" computer software applications are associated to the various physical aspects that impact flow and pumping. A comprehensive parametric study found that employing blood-infused nanoparticle blades to treat autoimmune disorders produced positive results. Trapping, a basic peristaltic pumping phenomenon, is also depicted and quickly discussed. This research could have uses in microfluidic devices, medication delivery systems, and other industries where precise fluid flow control is required. Researchers may be able to improve the efficiency and accuracy of such systems by regulating fluid flow using an electric field. [ABSTRACT FROM AUTHOR]

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

This study investigates the flow of a two-dimensional magnetohydrodynamic(MHD) tangential hyperbolic hybrid nano fluid flow towards a porous stretched sheet with an inclined magnetic field under velocity and thermal slip conditions. Two distinct base fluids, (i) water and (ii) a mixture of 50% ethylene glycol(EG or (CH2OH)2) and 50% water are employed as base liquids with Copper(Cu) and aluminium oxide(Al2O3) nanoparticles, to generate two different hybrid nanofluids as Cu − Al2O3/H2O and Cu − Al2O3/EG + H2O. Scaling group transformations with a homotopy algorithm is used to study the effects of distinct physical parameters like the Weissenberg number, an inclined magnetic field, thermal radiation, velocity, and thermal slip conditions with a heat generation/absorption parameter and a permeable parameter on the velocity and temperature distributions. The outcomes of Cu − Al2O3/H2O hybrid nano fluid are compared with Cu − Al2O3/EG + H2O hybrid nano fluid in significant critical physical circumstances using graphs and tables. It is observed that the parameters We and Ha, θM, and λ increase the fluid temperature and decelerate the motion of fluid. The obtained results are validated by comparing them with the existing literature and found that the present results are consistent with the given data. Additionally, it is also noticed that the Cu − Al2O3/EG + H2O hybrid nanofluid has a higher heat transmission rate as compared to Cu − Al2O3/H2O hybrid nanofluid. Finally, the impact of nano particle volume fractions of copper and aluminium oxide on the velocity and temperature profiles is discussed to study their efficiency [ABSTRACT FROM AUTHOR]

Thermal radiations are extensively utilized in the medical sciences, and the investigation of thermal radiation combined with double diffusive phenomena is the burning research area because of its enormous applications in treatment of various diseases. Cilia play significant part in many physiological processes of animal and humans. A novel mathematical prodigy for Prandtl nanofluid with thermal radiations and double diffusion convection by implementing slip at boundaries is presented for cilia induce flow in an asymmetric microchannel. Mathematical scheme for the physiological flow is developed and then pertinent equations are designed exploiting low Reynolds number and long wavelength simplifications. Solution for the physiological nanofluid is gathered by emphasizing on the novel BVP4C technique in MATLAB and resulting outcomes are elaborated with aid of graphical illustrations. Pros and cons of various physical flow parameters like thermal slip parameters, Prandtl fluid parameters, Grashof parameter, Prandtl parameter , Brownian motion parameter, thermal radiation parameter, Brinkmann number, Soret parameter are examined on the velocity, magnetic force function, temperature profile, concentration and nanoparticles volume fraction. It is reported that slip parameter really effects the nanofluid transport within the ciliated microchannel, it reduces the fluid flow, diffusion phenomena of the nanoparticles in the ciliated microchannel surges when radiation parameter is strengthened. The reported investigation will be instrumental in heat radiation effect for regulation of blood circulation to cure the cancer tissues in multiple drug delivery systems and will pave the way for the designs of certain diagnostic and pharmacological devices.

In the present analysis, we have analyzed the three-dimensional flow of an electromagnetohydrodynamic copper–aluminum/water hybrid nanofluid flow on a Riga plate. The heat and mass flux model proposed by Cattaneo-Christov is deliberated here. Thermal radiation, thermophoretic diffusion, Brownian motion, and chemical reaction phenomena are considered in analyzing the flow problem. Thermal convective, mass convective, and velocity slip conditions are adapted in this analysis. Suitable resemblance variables are implemented for the conversion of the model equations to dimension-free form. The homotopy analysis method is adopted to solve the modeled equations. The obtained results show that the velocity profiles are reduced with an increasing estimation of the slip factors. Additionally, the nanoparticles’ concentration and the temperature of the hybrid nanofluid increase with higher values of thermal and solutal Biot numbers. The Nusselt number is increased with an increase in the radiation factor and thermal Biot number.

Objective here is to address impacts of MHD hybrid nanofluids (Fe2O3+Cu/H2O) on peristaltic transport in asymmetric channel. Porous space is taken. Analysis is constructed in the presence of radiation, dissipation, convection and Hall current. Further velocity and thermal slip boundary constraints are considered. Lubrication approach is employed to simplify the dimensionless forms of equations. Quantities of interest are described numerically. The shooting method is used to solve the governing differential systems employing Mathematica. Outcomes of Hartman number, Hall effect, permeability parameter, Grashof number and radiation parameter are analyzed graphically. Result indicates that temperature decreases by increasing the strength of nanomaterials. Axial velocity decays in the presence of Hartman number. Analysis of heat transport process is evaluated using tabulated values. Results show that heat process improved for Hartman number while the opposite behavior observed for Hall current.

In light of the exciting potential of nanofluids, this work presents a new mathematical model for enhancing heat transfer using tri-hybrid nanofluids. In this study, the influence of heat production/abstraction and mass suction on MHD stagnation point flow in a nonlinearly stretching/shrinking sheet of a tri-hybrid nanofluid based on water is investigated. Boundary conditions based on the Maxwell velocity slip and the Smoluchowski temperature are also considered. We shall model the flow-control equations based on our assumptions. An ordinary differential equation system may be constructed from nonlinear partial differential equations for which a similarity transformation does not provide an exact solution. In MATHEMATICA 10, the shooting with Runge-Kutta (RK-IV) technique will be used to solve the reduced equations analytically. There were charts and figures showing how different variables affected the speeds of motion, temperature, skin friction coefficient, and local heat transmission. The characteristics of volume fraction, mass suction, magnetic field, and stretching all contribute to the acceleration of nanoparticles. When the nanoparticle volume fraction and heat production parameters increase, the temperature profile improves, but the mass suction, magnetic, and stretching parameters decrease. Compared to ordinary fluid, the Nusselt number reveals an improvement of around 9.8% for nanofluid, 19.85% for hybrid nanofluid, and 44.04% for tri-hybrid nanofluid when the strength of S is raised from 2.0 to 2.4. The heat transfer rate of the tri-hybrid nanofluid is also superior to that of the hybrid nanofluid and the traditional nanofluid. Results from this study were compared to those already in the literature, and they were determined to be quite consistent. Many other fields might benefit from this study, including those dealing with extreme heat or cold, aerospace technology, medicine, metal coatings, and biosensors.

AbstractThe unsteady nanofluid flow that rotates in both directions over a stretched surface could assist many technological and industrial processes. When the effects of slip conditions, aggregation, and changing viscosity are considered, the flow of nanofluid over a stretched surface can be used in surface coatings and deposition, energy harvesting devices, drug delivery systems, and cooling systems with better heat transfer. The major purpose of this study is to evaluate the influence that variable viscosity, slip conditions, and aggregation have on the flow behavior of nanofluids in three dimensions. This research looks specifically at non-axisymmetric stagnation point flows on stretched sheet. The governing equations are going to be modeled based on the assumptions that have been stated. Through a technique known as a similarity transformation, a complex system of nonlinear partial differential equations can be reduced to ordinary differential equations. This makes the system significantly easier to work with. The algorithm will be employed afterward to numerically solve the simplified set of equations. The results are obtained using the Runge–Kutta (RK-IV) and the shooting method. Graphical displays provide an easy way to examine how different parameters interact with one another and their impacts. With an increase in nanoparticle concentration, heat transfer rate shows an increasing trend. Due to the decrease in the instability parameter, rate of heat transfer decreases. Velocity profiles increases in both directions with increasing strain rate. A comparison of influences of nanoparticle aggregation with and without radiation is shown in the tables, highlighting the differences in Nusselt numbers. The results of the present study closely correspond to those reported in a prior publication for the same scenario, offering robust additional support for the findings. [ABSTRACT FROM AUTHOR]

In this work, a two-fluid phase flow problem involving an axisymmetrical quasi-steady motion of a spherical micropolar droplet translating at a concentric point in a second non-mixable micropolar fluid within a spherical impermeable cavity with a slip surface is analysed under low Reynolds numbers. The two fluid phases that have a microstructure (micropolar fluid) are the case that is being focused on. The Stokes equations are solved inside and outside the droplet for the velocity fields. In addition, based on the concentric position, general solutions in terms of spherical coordinates are obtained. In this case, tangential couple stress and continuity of microrotation are used. For different cases, the normalised drag forces acting on the droplet are represented via graphs for different values of relative viscosity, droplet-to-cavity radii ratio, and the parameter that connects the tangential couple stress with microrotation. The normalised drag force is found to be a monotonically increasing function of the drop-to-cavity radii ratio. It is found that when the droplet-to-cavity radii ratio approaches zero, there is a very strong interaction between the droplet and the cavity. When comparing a solid sphere to a gas bubble, the normalised drag force is larger. Additionally, the results showed that permitting spin and slip at the cavity's interior surface improved the wall correction factor influencing the droplet. The present study is important in the fields of natural, industrial, and biomedical processes such as raindrop formation, liquid–liquid extraction, suspension rheology, sedimentation, coagulation, and the motion of blood cells in an artery or vein. [ABSTRACT FROM AUTHOR]

In science and engineering, analytical and numerical methods have been utilized to compute the solutions of partial differential equations. Mathematicians are now employing artificial neural network (ANN) to investigate complex problem involving highly nonlinear partial differential equations. The aim of current study is to implement the Bayesian regularization methodology (BRM) to investigate the heat generation/absorption in thermally radiative nanofluid flow over stretched surface embedded in a porous medium with slip conditions. The flow governing equations have been obtained through boundary layer approximation theory. Reference data has been accumulated using the simplified form of equations with the help of "ND Solver" in Mathematica. Different scenarios have been created, and for each scenario, three different cases have been developed. Additionally, the reference data has been trained, tested, and validated using Bayesian regularization methodology in MATLAB. The reference data has been distributed in the following portions, training 71% and testing and validation 15% each, during simulation of each scenario. The proposed methodology's effectiveness and accuracy have been validated through generated mean square error (MSE), error histograms (EH), proposed solutions, absolute errors (AE) comparative comparison plots, and regression plots. It has been observed that maximum absolute error 10−08 found for mass suction effect. Convergence of proposed methodology has been validated with mean square error. It has been observed that with high applied magnetization force and permeability motion of fluid declines whereas opposite behavior has been observed for non uniform inertial force. It has been noted that when slip mechanism is significant, contraction has been observed in thermal boundary layer of fluid. Present outcomes of drag coefficient and heat transfer coefficient show good agreement with already published results. [ABSTRACT FROM AUTHOR]

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This study explores the unsteady hybrid nanofluid (NF) flow consisting of cobalt ferrite (CoFe2O4) and copper (Cu) nano particulates with natural convection flow due to an expanding surface implanted in a porous medium. The Cu and CoFe2O4 nanoparticles (NPs) are added to the base fluid water to synthesize the hybrid NF. The effects of second-order velocity slip condition, chemical reaction, heat absorption/generation, temperature-dependent viscosity, and Darcy Forchheimer are also assessed in the present analysis. An ordinary differential equation system is substituted for the modeled equations of the problem. Further computational processing of the differential equations is performed using the parametric continuation method. A validation and accuracy comparison are performed with the Matlab package BVP4C. Physical constraints are used for presenting and reviewing the outcomes. With the increase in second-order velocity slip condition and unsteady viscosity, the rates of heat and mass transition increase significantly with the variation in Cu and Fe2O4 NPs. The findings suggest that the uses of Cu and Fe2O4 in ordinary fluids might be useful in the aerodynamic extrusion of plastic sheets and extrusion of a polymer sheet from a dye.

The problem of treating cancer is considered one of the most important daily challenges that affect the lives of people with cancer. This research deals with solving this problem theoretically. Through previous studies, it has been proven that gold nanoparticles are able to remove these cancer cells. The idea of this research is theoretically based on injecting a cancer patient with gold nanoparticles that are exposed to a magnetic field. When these particles penetrate cancerous cells and are exposed to a magnetic field, this causes their temperature to rise. The high temperature of the nanometer gold particles that penetrate the cells of the affected body leads to the explosion of the cancer cells. In this research, the various external forces that affect the flow movement of the nanofluid are studied and how its physical and thermal properties are affected by those external forces. The MHD peristaltic flow of a nanofluid in an annulus pipe as a result of the effect of the wall properties has been investigated. This has been achieved through slip and thermal conditions. Wave velocity u0 leads to flow development. The inner annulus wall is rigid, while the outer wall of the artery moves under the influence of wave peristaltic movement. The nonlinear equations that describe the flow are solved under long-wavelength assumptions. The results were compared with other numerical methods, such as finite volume and finite element and the long wavelength method and proved to be accurate and effective. The expressions of pressure difference, velocity, stream function, wall shear stress, and temperature are analyzed. It is noted that the flow velocity increases with the Knudsen number, and the increased source heat suggests an increased temperature. The increasing amplitude ratio at most of the interface points between the artery wall and the catheter results in increased velocity. The streamlines are affected by the magnetic field, as increasing the influencing magnetic field leads to a decrease in flow lines. It is observed that this stress decreases when nanoparticles increase, in contrast to the effect of the magnetic field and also the occurrence of slipping. It was found that the mass of the wall cells relative to their area works to decrease the pressure difference, in contrast to the tension between those cells, which works to increase the pressure difference. Without slipping Kn=0 and with slipping Kn=0.1, the temperature decreases with increasing in nanoparticle concentration φ. The temperature also increases with the amplitude ratio δ. This strongly affects the generated drag on the catheter wall, which is mainly responsible for the enhanced temperature on this wall.

The mathematical model to inspect the effects of changeable thermo-physical properties such as thermal conduction, slip effects and viscosity on Maxwellian nanofluid is proposed. The thermal conductivity increases rapidly due to presence of nanoparticles such as metals, carbides, oxides etc. in base fluid. The flow occurs from the stagnated point pass a stretched sheet with slipped conditions. The characteristics of the Brownian motion as well as the thermophoresis processes are also taken into consideration. By means of similarity transformations, the ODEs are reduced from the equations influencing the fluid flow. A built-in solver of MATLAB namely bvp4c which is a collocation formula implementing the Lobatto IIIa finite differences numerical method is applied to solve these transformed equations numerically. The graphs of the numerical outcomes representing impacts of variations in different parameters on the fluid movement, transfer of heat along with mass are analyzed. This investigation leads to an important aspect that as the thermal conductivity in the flow is intensified, the temperature of the fluid reduces with high aggregation of the nanoparticles near the sheet’s surface. Also, the rates of heat and mass transferral depletes due to the relaxation of Maxwellian fluid. Furthermore, the effectiveness of the present numerical computations is determined by carrying out comparisons of heat and mass transferred rates against the previous analytical results for several values of thermophoresis and Prandtl parameters. The effectiveness of its outcomes can be applied in nanoscience technology and polymeric industries for their developments.

The heat transfer phenomenon associated with the lubricated surfaces offers applications in the manufacturing processes, thermal systems, industrial systems, and engineering phenomenon. It is a well-established fact that improvement in heat transfer is recently successfully claimed with the interaction of nanoparticles. Following such motivation in mind, the prime objective of current continuation is to perform the prediction of heat transfer in second-grade material subject to the lubricated surface. The lubricants are filled with non-Newtonian power law material. The varying thickness of the thin lubricating layer permits an imperfect slip surface. The second-grade fluid interfaces with the boundary condition. The modified semi-analytical tool termed as hybrid homotopy scheme is used to perform the simulations. Shooting and homotopy methods are combined in this new approach. Relevant effects of parameters on physical phenomenon are explained. The importance of influencing parameters in relation to the velocity field, temperature, and concentration profiles is investigated graphically. It is claimed that analytical computations existed for shear thinning case. It is observed that there is a noticeable drop in concentration and thermal profiles due to the variation of viscoelastic parameter. The control of free stream velocity is claimed due to the interaction of slip parameters.

The objective of this paper is to examine the flow of a non-Newtonian Maxwell fluid induced by a permeable stretching sheet in motion within a porous medium. The research incorporates the Cattaneo-Christov heat flux model to study the heat transfer process. The utilization of the Cattaneo-Christov heat flux approach becomes relevant in scenarios involving materials with high thermal conductivity or during short time intervals. Consequently, the current investigation holds significant importance. It is assumed that the viscosity of the Maxwell fluid changes exponentially as the temperature changes. The modeling of the physical phenomena being investigated takes into account the effects of a magnetic field, thermal radiation, velocity, and thermal slip conditions. In this study, the viscous dissipation phenomenon is taken into account because it can have notable impacts on the temperature and viscosity of the fluid, and is known to play a crucial role in fluid flow phenomena. The equations developed to model fluid flow are transformed into nonlinear ordinary differential equations through the use of appropriate similarity transformations. The focus of the research revolves around investigating the numerical solution of ordinary differential equations accompanied by boundary conditions using the shooting technique. The findings are then showcased via tables and graphs and scrutinized in order to arrive at conclusions. Furthermore, the precision of the present findings was evaluated by contrasting the heat transfer rate with outcomes that were previously published. Based on the obtained outcomes, it can be concluded that both the Eckert number and thermal radiation have a comparable enhancing influence, whereas the thermal relaxation parameter and thermal slip parameter exhibit opposing effects.

Objective here is to address impacts of MHD hybrid nanofluids (Fe 2 O 3 + Cu / H 2 O) on peristaltic transport in asymmetric channel. Porous space is taken. Analysis is constructed in the presence of radiation, dissipation, convection and Hall current. Further velocity and thermal slip boundary constraints are considered. Lubrication approach is employed to simplify the dimensionless forms of equations. Quantities of interest are described numerically. The shooting method is used to solve the governing differential systems employing Mathematica. Outcomes of Hartman number, Hall effect, permeability parameter, Grashof number and radiation parameter are analyzed graphically. Result indicates that temperature decreases by increasing the strength of nanomaterials. Axial velocity decays in the presence of Hartman number. Analysis of heat transport process is evaluated using tabulated values. Results show that heat process improved for Hartman number while the opposite behavior observed for Hall current. [ABSTRACT FROM AUTHOR]

Abstract The importance of mathematical simulation in studying biological fluids extends to various medical disciplines. The peristaltic process is crucial for comprehending different biological flows. Additionally, nanoparticles serve essential functions in a range of engineering and industrial applications, such as heat exchangers, boilers, cooling systems, and chemical engineering. This current study addresses the numerical investigation of entropy optimization for (magnetohydrodynamic) MHD peristaltic activity of Eyring-Powel nanoliquid. Here channel boundaries are flexible in nature. Effects of mixed convection and hall current were also considered. Slip conditions are imposed on channel walls. Viscous dissipation and nonlinear thermal radiation are also present in thermal transport. Brownian movement and thermophoresis aspects are considered in the nanoliquid model. Chemical reaction of order first is also present the mass transport. Simplification of transport expressions is done by operating lubrication approach. The resulting system of nonlinear equations is numerically tackled. Both numerical techniques for heat transfer rate are validated by comparing them to numerical results computed by MATLAB using bvp4c and NDSolve. Graphical analysis is carried out for different flow parameters by plotting velocity, temperature, concentration, and entropy. [ABSTRACT FROM AUTHOR]

In light of the exciting potential of nanofluids, this work presents a new mathematical model for enhancing heat transfer using tri-hybrid nanofluids. In this study, the influence of heat production/abstraction and mass suction on MHD stagnation point flow in a nonlinearly stretching/shrinking sheet of a tri-hybrid nanofluid based on water is investigated. Boundary conditions based on the Maxwell velocity slip and the Smoluchowski temperature are also considered. We shall model the flow-control equations based on our assumptions. An ordinary differential equation system may be constructed from nonlinear partial differential equations for which a similarity transformation does not provide an exact solution. In MATHEMATICA 10, the shooting with Runge-Kutta (RK-IV) technique will be used to solve the reduced equations analytically. There were charts and figures showing how different variables affected the speeds of motion, temperature, skin friction coefficient, and local heat transmission. The characteristics of volume fraction, mass suction, magnetic field, and stretching all contribute to the acceleration of nanoparticles. When the nanoparticle volume fraction and heat production parameters increase, the temperature profile improves, but the mass suction, magnetic, and stretching parameters decrease. Compared to ordinary fluid, the Nusselt number reveals an improvement of around 9.8% for nanofluid, 19.85% for hybrid nanofluid, and 44.04% for tri-hybrid nanofluid when the strength of S is raised from 2.0 to 2.4. The heat transfer rate of the tri-hybrid nanofluid is also superior to that of the hybrid nanofluid and the traditional nanofluid. Results from this study were compared to those already in the literature, and they were determined to be quite consistent. Many other fields might benefit from this study, including those dealing with extreme heat or cold, aerospace technology, medicine, metal coatings, and biosensors. [ABSTRACT FROM AUTHOR]

Nanofluid consideration has been magnified due to their exceptional heat transfer characteristics and prospective applications in engineering and medical sciences after the pioneering work of Choi. Since, majority fluids are non-Newtonian in nature. Therefore, considering Jeffrey fluid as a base fluid in current study enhance its role in applications. Moreover, geometric configuration of the channel is taken as asymmetric with tapering effects. Since, majority of human physiological systems and industrial machinery have complex geometry and. Therefore, tapering channel consideration cannot be ignored. High molecular weight of non-Newtonian liquids make no-slip condition inapplicable. Thus, slip effects are incorporated in the current analysis. The consider analysis is performed for peristaltic flow of Jeffrey Nano fluid through a tapered asymmetric channel in the presence of magnetic field. Main motivation for performing this study is to analyze the heat transfer properties of nanofluid for the treatment of multiple diseases like cancer. The resulting nonlinear equations are coupled and simplified through lubrication approach. Poisson-Boltzmann equations are linearized through Debye-Huckle linearization. Built-in command of NDSolve in MATHEMATICS is applied to compute the results. The results for velocity, pressure gradient, streamlines, temperature and concentration are discussed for involved parameters. The results indicate that velocity shows parabolic behavior near the center while mixed behavior is observed near the boundaries. It can also be noticed that tapering parameter (m) influence the velocity greatly. As increasing the tapering effect causes the geometry to expand resulting in decreased velocity near the center of the channel. During digestion of food, multiple chemical reactions are performed by enzymes, therefore, studying the impact of (γ) on temperature and concentration cannot be ignored. The outcome of the study shows decrease in temperature and concentration as energy is utilized in performing the digestion. The size of trapped bolus is found to be increasing as the values of Hartman number (M) and fluid parameter (λ1) are increased. Therefore, we can say that this study can provide basics to study physiological system with electroosmotic phenomenon. It also finds promising applications in drug delivery and food diagnostic etc.

The interaction of nanoparticles with a peristaltic flow is analyzed considering a Prandtl-Eyring fluid under various conditions, such as the presence of a heat source/sink and slip effects in channels with a curvature. This problem has extensive background links with various fields in medical science such as chemotherapy and more in general nanotechnology. A similarity transformation is used to turn the original balance equations into a set of ordinary differential equations, which are then integrated numerically. The investigation reveals that nanofluids have valuable thermal capabilitises. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study the effect of heat transfer and flow of non-Newtonian power-law fluids towards a stretching sheet in the appearance of transverse magnetic field with slip boundary conditions. Suitable similarity transformations are used to change the non-linear partial differential equations to ordinary differential equations. For the numerical solution Maple software by applying built-in command dsolve with numeric is utilized. It is noticed from the obtained results that an increase in the magnetic parameter results in a decrease in the dimensionless velocity profile and in the stream function while the temperature profile increases for the Newtonian, dilatant, and pseudo-plastic fluids. Increasing the velocity slip parameter, a reducing behavior can be seen in the stream function and in the velocity profile while temperature profile is enhancing. Moreover, with increasing thermal slip, a decrease occurs in the dimensionless temperature. The variations in the velocity and temperature profiles under dimensionless parameters are significant for n = 0.8 (pseudo-plastic fluid) rather than for n = 1 (Newtonian fluid) and n = 1.02 (dilatant fluid). [ABSTRACT FROM AUTHOR]

The research aims to investigate the motion of a two-dimensional magnetohydrodynamic fluid with hyperbolic tangent properties, combined with nanoparticles, as it approaches a stretching sheet. The flow of nanofluid is hypothesized to be a consequence of the stretching of an elastic sheet within a porous medium. The stretching sheet has a rough surface, and this allows for the consideration of the slip velocity phenomenon. Mathematically modeling the analysis of current flow results in a set of nonlinear partial differential equations, which can be simplified into ordinary differential equations using appropriate dimensionless transformations. Subsequently, the resulting equations are solved utilizing the shooting technique. A comprehensive analysis is conducted to interpret in detail how the various physical parameters influence concentration, velocity, and temperature. Moreover, local Sherwood number, local skin friction, and local Nusselt number are calculated and presented in a tabular form for further analysis. The precision of the computed results is further confirmed by comparing the obtained findings with the body of available literature. It is noted that there is a clear similarity between the current results and the provided data. This demonstrate that the suggested numerical procedure is accurate. Quantitative findings reveal that augmenting the porous parameter, slip velocity parameter, power law index, and magnetic parameter leads to a reduction in the nanofluid velocity. However, a contrasting pattern emerges in the case of the temperature profile. Further, through a comprehensive examination, it has been revealed that the slip velocity phenomenon significantly influences the dynamics of nanofluid flow.

Owing to its bounteous applications in engineering and advanced industrial processes magnetized hybrid Nano fluid influenced by suspended Nano-size particles got unusual consideration. The prime focus of current study rely on the meaningful investigation of the proposed phenomena with the utilization of buoyancy and viscous dissipation influence in the hybrid fluid. Numerical approach appertaining to three-dimensional hybrid Nano fluid flow configured by horizontal stretched surface is developed in the contemporary study. Magneto hydrodynamic viscous flow demeanor of hybrid traditionally water-based Nano fluid is contemplated in current report. Heat transmission phenomenon is taken into consideration on account of suspended Nano-scale size particles namely Magnesium-oxide (MgO) and Titanium-oxide (TiO2). Furthermore, Viscous dissipation along with thermal radiation impacts are also opted for the optimization of energy. Velocity profile along x-component and y-component is observed under buoyancy effects. Cartesian coordinates system have been accounted to mathematically model the proffered nonlinear system of PDEs by invoking appropriate similarity approach. An esteemed and prominent Runge-Kutta (4th - order) established on shooting technique is employed for the determination of velocity as well as temperature distributions. Multifarious parameters influence is sketched graphically. Velocity profile along horizontal components demonstrates the strengthening behavior for the growing values of magnetic parameter M and also buoyancy parameter λb while demonstrates depreciating behavior for the enhanced values of slip parameter K and also rotation parameter λ. Moreover, velocity profile along the vertical components is observed under the consequences of varying values of magnetic parameter M, rotation parameter λ, and slip parameter K and for buoyancy parameter λb.We noticed that horizontal component depicts enhanced demeanor for magnetic parameter M, slip parameter K whilst decaying demeanor for the upshot vales of rotation parameter λ. Local Skin-friction and also Nusselt number influence is reported via tables and found in excellent accuracy. The final outcomes will be validated numerically by aiding suitable techniques (R–K 4th order based Shooting Method). Our findings will be validated through graphs. This research provides significant field of study and will play an extensive role in field of fluid mechanics.

Recently, there has been considerable attention given to a sophisticated fluid system known as the Maxwell nanofluid, which incorporates chemical reactions and the Cattaneo-Christov heat flux. This system has garnered significant interest due to its potential significance in various fields, including heat transfer, chemical engineering, and nanotechnology. Therefore, this numerical investigation proposes a new model for the steady two-dimensional flow of a homogeneous Maxwell nanofluid towards a vertical stretching sheet that incorporated within a porous medium, aimed at revealing the fluid's dynamic and thermal characteristics. The model is specifically tailored for nanofluids and includes thermal radiation, chemical reactions and slip conditions. It is presumed that the viscosity of the Maxwell nanofluid changes with variations in temperature. The governing partial differential equations and corresponding boundary conditions for the nanofluid flow problem are derived in a suitable manner, based on physically valid assumptions and validated experimental correlations. MATHEMATICA software is used to perform arithmetic simulations of the energy, mass concentration, and momentum equations. The simulations are carried out using the fourth-order Runge-Kutta technique in conjunction with the shooting method. Numerical and visual techniques are utilized to examine how the physical parameters that control the model influence it. Subsequent to evaluating our data against prior findings, the reliability and precision of the proposed method are verified. The findings show that the nanofluid's velocity detracts when the slip velocity, Maxwell parameter, magnetic forces, viscosity parameter, and porous parameter rise. The temperature field, which is affected by these parameters, shows the opposite tendency, on the other hand. In addition, the suction parameter application results in a drop in the concentration, temperature, and velocity of the nanofluid.

Introduction: This investigation explores the heat and mass transfer properties of a non-Newtonian nanofluid containing graphene nano-powder and ethylene glycol during peristalsis. The rheological characteristics of the nanofluid are determined using the Carreau-Yasuda model, and various factors such as viscous dissipation, Lorentz force, Ohmic heating, and Hall effects are taken into account. Mixed convection and thermal radiation effects are also considered in the analysis, and the problem is mathematically described using the long wavelength and low Reynolds number approximations.Methods: The resulting nonlinear system is solved using numerical methods to obtain the solutions. The dominant effects of mixed convection and thermal radiation are given particular attention, while the influences of other parameters are discussed in relation to these dominant effects.Results and Discussion: The results demonstrate that increasing the Brinkman number, heat source, and thermal slip parameter leads to higher nanofluid temperatures. However, the heat transfer rate decreases with a higher Hall parameter. The velocity near the center of the channel increases for higher values of the concentration Grashof and Hall parameters. Furthermore, an increase in the Hall and Brownian motion parameters results in a higher concentration of nanoparticles. These findings have practical implications in various fields, including materials science, chemical engineering, and biomedical engineering.