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Fluid flow across a Riga Plate is a specialized phenomenon studied in boundary layer flow and magnetohydrodynamic (MHD) applications. The Riga Plate is a magnetized surface used to manipulate boundary layer characteristics and control fluid flow properties. Understanding the behavior of fluid flow over a Riga Plate is critical in many applications, including aerodynamics, industrial, and heat transfer operations. The unsteady Micropolar nanofluid (UMNF) flow across a vertically oriented, nonlinearly stretchable Riga sheet is examined in the present study. The effects of variable thermal conductivity, thermophoretic force, and Brownian diffusion on flow and heat transfer are analyzed. The fluid flow has been expressed in the form of a nonlinear system of PDEs (partial differential equations), which are reduced into the non-dimensional form of ordinary differential (ODEs) by employing the similarity transformation approach. The dataset for training the ANNs using the Levenberg–Marquardt backpropagation (LMBP) technique is generated using numerical simulation methods. The influence of physical constraints on the dimensionless temperature, concentration, microrotation, and velocity distributions are graphically displayed and discussed. Numerical results for skin friction, Sherwood, and Nusselt numbers are presented in tabular form. The numerical outcomes are compared to both published numerical and experimental results for validity purposes. It can be noticed that the flow rate is enhanced with the rising influence of the Hartmann number, buoyancy force, and velocity slip parameter. The UMNF flow model is validated, tested, and trained with an average numerical error of 10−9, ensuring high accuracy in energy, velocity, microorganism motility, and concentration predictions. [ABSTRACT FROM AUTHOR]

Synovial fluid is found in synovial joints, which act as a lubricant and shock absorber, that is crucial for the detection and treatment of diseases and injuries associated with the joints. It is significant for enhancing joint health diagnostics and treatment, improving drug delivery systems and advancing the understanding of complex fluid behavior and particle transport mechanisms in biomedical and engineering applications. The biological field utilizes complex analyses of condyloid, hinge, pivot and shoulder joints for current development. This work uses two viscosity models to examine the impact of activation energy and nonlinear heat source on the synovial fluid (SF) with thermophoretic particle deposition. The current model shows how the viscosity of an SF is affected by concentration and deformation. The impact of MHD and variable thermal conductivity on a heated disc is also investigated. The flow has been examined using the Arrhenius equation, which offers a mathematical explanation of how activation energy works in our system. PDEs are transformed into ODEs by employing the similarity transformation. The problem is solved by using the modified shooting method (bvp4c). This study focuses on the velocity, temperature and concentration profiles while presenting the physical significance of all the fluid parameters involved. These profiles are thoroughly described and shown graphically. The results show that when the magnetic parameter rises, the temperature profile rises and the velocity profile declines. The concentration profile decreases with higher values of the reaction rate parameter and the thermophoretic parameter and also increases with a higher value of the activation energy parameter. The flow of SF for model-I is significantly larger than that for model-II. [ABSTRACT FROM AUTHOR]

A mathematical model is analyzed to study the effect of various physical parameters related to non-isothermal flow of third grade fluid in the presence of thermal radiation through a porous medium. Hence, the objective of this paper is to investigate the combined impacts of magnetic field, viscous dissipation, thermal radiation, varying thermal conductivity and viscosity on non-isothermal flow of a third grade fluid with thermal radiation through a porous medium. The Galerkin weighted residual method was used to solve the resulting non-linear ordinary differential equations numerically. The graphic representation and discussion of the effect of various significant parameters on the flow system are presented. The investigation of this problem leads to the conclusion that the thermal radiation parameter, the variable thermal conductivity and viscosity parameters have a significant impact on the mass flow and the energy transfer phenomena in the system. [ABSTRACT FROM AUTHOR]

Mixed convection flows across the revolving bodies have eminent applications in science and technology, such as fibre coating, polymer deposition, centrifugal blood pumps, rotatory machinery, and so forth. In the current work, magnetohydrodynamic (MHD) flow and heat transfer characteristics of Casson hybrid nanofluid (Ag/MgO as nanoparticles) over the rotating sphere at the stagnation zone are being studied. Moreover, an analysis of heat transmission is conducted by considering the influence of thermal radiation, temperature‐dependent thermal conductivity, magnetic field, and viscous dissipation. The relevant partial differential equations are reformed into ordinary differential equations by appropriate transformations, which are solved using the successive linearization method (SLM). The thermal field, velocity components in x and z directions, heat transfer rate, and skin friction coefficient are computed for various physical quantities like rotation parameter mixed convection parameter, radiation parameter, Eckert number, Casson parameter, magnetic parameter, variable thermal conductivity parameter, and so forth. The current findings align well with the literature in a limiting sense. Thermal enhancement in hybrid nanofluid is observed for the viscous dissipation parameter (Ec), thermal conductivity parameter (ε), and radiation parameter (Rd). The degree of heat transfer rises from 12.8% to 20% when the Casson parameter's value (β0) increases. Also, a decrease of approximately 33% is depicted between the peak values of the velocity magnitude with an increase in rotation parameter. [ABSTRACT FROM AUTHOR]

This study presents a novel model for variable fluid properties of a ternary hybrid nanofluid with base fluid polymer suspended on a three-dimensional stretching sheet under the influence of magnetohydrodynamic forces. Viscosity and thermal conductivity are temperature-dependent. This model has potential for use in nanotechnology, particularly in the shaping and design of surfaces for devices that can stretch or contract, wrap, and paint. The nonlinear equations in charge of this physical problem are derived by using similarity transformations. The fluid behavior is examined using the Reynolds viscosity model. The coupled nonlinear governing equations and the necessary boundary conditions are solved using the shooting technique with RK-4. The numerical calculations, including velocity and temperature profiles, are presented graphically to give the results a physical interpretation. The table discusses skin friction and Nusselt numbers at various physical parameters. The study’s findings show that changing the stretching parameter causes a significant change in the flow characteristics. Particularly, the thickness of the boundary layer decreases as the volume fraction of nanoparticles rises. Furthermore, because temperature-dependent viscosity is taken into account, as the viscosity parameter increases, so does the temperature. Key results specify that the Nusselt number Nu{\rm{Nu}} increases with the increase in temperature-dependent viscosity α\alpha , while decreases with the increase in thermal conductivity ϵ\epsilon parameters. Impact of α\alpha shows more convective heat transfer. Greater values of ϵ\epsilon reduce the effectiveness of heat transfer.

Abstract The intricate dynamics of mixed convective thermic and species transport in a power-law flowing fluid through a continuously stretched surface are investigated. The uniqueness of this study lies in the consideration of fluid variable thermic conductivity and viscosity, which introduces a higher degree of realism into the analysis. The transformation of similarity is used to transform the fundamental governing equations, and after that, the set of equations is processed numerically utilizing a non-similarity local approach. Furthermore, the effects of Soret and Dufour represent the cross-diffusion phenomena, accounting for the energy exchange with the surroundings. These factors collectively influence the stretching surface’s gradient velocity, affecting the thermal and species concentration rates. The findings offer a comprehensive understanding of these complex interactions, paving the way for optimizing thermic and species transport processes in various industrial applications. This study, therefore, holds significant potential for enhancing efficiency and performance in relevant industrial sectors. The main terms are the combinations of Dufour and Soret numbers that significantly impact the flow rate profile and mass transfer field. The coupled study of the nonlinear velocity, energy distribution and chemical mixture variance made the study more impactful in practicality. Skin friction variation shows limited impact with variations in the Soret number. The enhanced thermal gradient results in improved non-similarity parameters, yet it demonstrates a decrease with an increase in variable thermal diffusivity. There is a decrease in the temperature gradient as the buoyancy term reduces, while an increase is observed with changes in the Prandtl number. Similarly, the Nusselt number experiences a comparable impact due to changes in the Soret number.

In the fluid transport processes extent of irreversibility causes entropy generation that leads to degrading the life span of any engineering system. The main objective of this investigation is to enhance the span of the system by analyzing the effects of various physical parameters. A nanofluid flow over an inclined stretching cylinder is studied to measure entropy generation due to thermal conductivity, Soret and Dufour effects along with viscous dissipation and internal heat source. Buongiorno model is considered as a base structure. The mathematical equations so formed are solved by shooting technique with Gill's fourth order method. Numerical results are validated with Homotopy analysis method through Bvph2.0. Effects of various parameters have been investigated on transport processes like axial velocity, temperature profile, and nanofluid concentration profiles. It seems that higher intensity of the applied magnetic field (M = 0, 1, 2), variable thermal conductivity (ε = 0.1, 0.3, 0.5), and Brinkman number (Br = 0.35) generates more entropy that degrades the system's life. Magnetic parameter and group parameter (1 ≤ Br/Ω1 ≤ 3), changing thermal conductivity all leads to a rise in entropy. In the study, group parameter reducing Bejan number that makes system more sustainable that full fills the aim of the study. Such physical situations generate more entropy must be reduced or avoided to make the system more efficient and long-lasting. [ABSTRACT FROM AUTHOR]

In engineering and industrial processes, hybrid nanofluids, an advanced form of nanofluid, are used to improve thermal efficiency. Hybrid nanofluids have various uses in refrigeration, tumor treatments, power stations, cooling systems, food processing, biomedical devices, and solar thermal systems. Thus, the major purpose of this article is to examine the heat transport features of a hybrid nanofluid on the dynamics of Zn-Ti6Al4V/H2O. The flow phenomenon of such fluid is produced by a shrinking disk when momentum and the thermal phenomenon are maintained. The classical transformation is employed to alter the flow model of a hybrid nanofluid in the form of non-linear ODEs. The produced model is tackled numerically through the MATLAB solver bvp4c function. The aspects of different emerging physical constraints on the flow field, fluid temperature, drag friction, and Nusselt number are exemplified thoroughly. The study finding reveals that the addition of a hybrid nanofluid in a flow system shows a promising increase in thermal transportation rate. The friction drags coefficient and thermal transportation rate show an upsurge in both solution branches for an increment in the suction parameter. Furthermore, higher values of the thermal conductivity parameter show an enhancement in fluid temperature for both branches.

The current investigation delves into the tangent hyperbolic Williamson hybrid nanofluid flow featuring varying thermal conductivity through the Darcy–Forchheimer medium across an exponentially stretching cylinder. Incorporating the activation energy and chemical reaction effects into consideration also strengthens the mathematical model's vitality. The considered hybrid nanofluid comprises silver and molybdenum disulfide nanoparticles submerged in the water. The highly non-linear system of equations is solved utilizing the MATLAB bvp4c approach. The influences of the leading variables versus involved fields are demonstrated through graphical delineations and tables. The core findings demonstrated that a strong Weissenberg number and Darcy-Forchheimer factor decay the velocity curve and strengthen the thermal curve. Also, the fluid concentration is enhanced for escalating activation energy and tangent hyperbolic factor. Additionally, the hybrid nanofluid betokens substantially enhance the thermal transportation rate of up to 8.8 % in contrast to nanofluid. Also, in contrast to the nanofluid and Williamson hybrid nanofluid, the hybrid nanofluid exhibits notably higher mass and thermal transport rate. This study is a noteworthy advancement in the disciplines of fluid dynamics and nanofluid research, as it provides promising potential for optimizing the transfer of mass and heat in a wide range of engineering and industrial contexts. The findings exhibit good agreement when contrasted with previously published work.

This research focuses on exploring the flow and temperature distribution of forced convection in a channel of horizontally placed parallel plate under the existence of a bidisperse porous medium (BDPM) emphasizing the consequences of viscous dissipation. The temperature-dependent thermal conductivity and viscosity are considered while maintaining the momentum slip and constant wall temperature at the channel walls. Analysis of the dynamics of fluid flow and the temperature distributions in both the fluid and solid phases is conducted by following the two-velocity and two-temperature models in this work. The model governing equations are non-dimensionalized following the relevant dimensionless parameters and the study calculates the temperature and velocity profiles for each phase using the Homotopy Analysis Method (HAM). The obtained temperature and velocity are discussed and explained with the help of graphs. Certain fluids exhibit varying behaviors at different temperatures. Therefore, it is crucial to consider the temperature-dependent physical properties of the fluid for specific applications. This highlights the importance of implementing temperature-dependent physical properties in the analysis. Throughout the investigation, it is discovered that the viscosity parameter has a greater influence on velocity as compared to temperature, the same for thermal conductivity on temperature. The impact of physical parameters including skin friction, volume flow rate, and Nusselt number on both plates are also examined in this study. The findings are discussed, and tables displaying numerical values for various physical characteristics are provided for both the liquid and solid phases. The results obtained were also compared with existing literature, revealing a strong alignment between them.

This paper investigates the characteristics of ternary-hybrid nanoliquid for time-dependent Darcy-Forchheimer flow. Formulation is based for mixture of water subject to ternary nanoparticles with different shapes like (platelet, spherical and cylindrical). Heat transfer consists of convective condition, radiation and heat generation. Appropriate variables are used to generate dimensionless nonlinear system. Analysis is carried out for Cattaneo-Christov heat flux and variable thermal conductivity. Finite difference method (FDM) is utilized to construct solutions. Salient characteristics of sundry variables are discussed. Analysis is carried out for Nusselt number and skin friction. Present results may have relevance in renewable energy process, polymer extrusion and metallurgy.

A mathematical model is analyzed to study the effect of various physical parameters related to non-isothermal flow of third grade fluid in the presence of thermal radiation through a porous medium. Hence, the objective of this paper is to investigate the combined impacts of magnetic field, viscous dissipation, thermal radiation, varying thermal conductivity and viscosity on non-isothermal flow of a third grade fluid with thermal radiation through a porous medium. The Galerkin weighted residual method was used to solve the resulting non-linear ordinary differential equations numerically. The graphic representation and discussion of the effect of various significant parameters on the flow system are presented. The investigation of this problem leads to the conclusion that the thermal radiation parameter, the variable thermal conductivity and viscosity parameters have a significant impact on the mass flow and the energy transfer phenomena in the system.

The study of nanofluids is important due to valuable applications in drug delivery systems, thermal processes, solar management systems, microfluidic devices, extrusion phenomenon, chemical processes etc. The objective of current analysis is to investigates the enhanced thermal performances of magnetized Casson nanofluid with suspension of microorganisms. An unsteady periodically oscillating flow due to bidirectional moving porous surface have been considered. The analysis is subject to assumptions of variable thermal conductivity. The modelled problem is based on implementation of modified Fourier theories. The Buongiorno nanofluid model is used to predicts the significance of Brownian motion and thermophoresis effects. Chemical reaction species are also attributed. For solution methodology, homotopy analysis scheme is implemented. The convergence region is specified. The physical impact of problem is visualized. The significant applications of parameters have been focused. The claimed results offer significance in cooling systems, chemical reactions, air conditioning, solar thermal systems, automotive radiators, heat exchangers in power plants etc.

Cilia flow plays a crucial role in biological systems such as the movement of mucus in the respiratory tract, circulation of cerebrospinal fluid in the brain, and propulsion of sperm cells. Understanding the cilia flow of viscous fluids is essential for elucidating the biomechanics of these processes and their implications for health and disease. Motivated by such numerous biomedical applications, this article aims to exhibit the impact of variable thermal conductivity on the mixed convective cilia beating transport of viscous fluid in a curved channel in the presence of radial magnetic field. The energy equation is also modulated with heat source/sink and viscous dissipation impacts. The constitutive equations are simplified by the hypothesis of lubrication approximation theory and then solved numerically using the implicit finite difference method (FDM). The numerical results concerning the impacts of various physical parameters on the velocity, temperature, pumping phenomena, and streamlines are graphed and explained. The obtained results indicate that as the Hartman number upsurges, fluid velocity reduces, and the Brickman number shows stronger viscous dissipation effects, leading to an increase in the fluid temperature.

In this study, we consider melting heat transfer and inclined magnetic field impacts on the flow of Carreau fluid past a stretched permeable sheet in a along with influences of variable thermal conductivity, diffusion-thermo, and thermal-diffusion. The problem is formulated as a system of nonlinear partial differential equations and using similarity transformations these are converted to non-linear ordinary differential equations. Numerical solutions of the problem are investigated via numerical algorithm by employing Runge–Kutta–Fehlberg fourth–fifth order scheme along with shooting method and the results are reported graphically for velocity, temperature, and concentration profiles. The velocity profile enhanced against the growing power law index, Weissenberg number, and melting parameter while it declines for magnetic parameter, angle of inclination, and porosity parameter. The temperature profile increases with modified Dufour parameter and Soret number while it diminishes for magnetic, thermal conductivity, and melting parameters. The concentration profile enhances for magnetic parameter while diminishes for modified Dufour parameter, Schmidt and Soret numbers. The numerical data is obtained for physical quantities of engineering interests against the various parameters. The skin friction results against the magnetic parameter are compared with previous published studies in the literature which validated the accuracy of our numerical findings.

Cilia flow plays a crucial role in biological systems such as the movement of mucus in the respiratory tract, circulation of cerebrospinal fluid in the brain, and propulsion of sperm cells. Understanding the cilia flow of viscous fluids is essential for elucidating the biomechanics of these processes and their implications for health and disease. Motivated by such numerous biomedical applications, this article aims to exhibit the impact of variable thermal conductivity on the mixed convective cilia beating transport of viscous fluid in a curved channel in the presence of radial magnetic field. The energy equation is also modulated with heat source/sink and viscous dissipation impacts. The constitutive equations are simplified by the hypothesis of lubrication approximation theory and then solved numerically using the implicit finite difference method (FDM). The numerical results concerning the impacts of various physical parameters on the velocity, temperature, pumping phenomena, and streamlines are graphed and explained. The obtained results indicate that as the Hartman number upsurges, fluid velocity reduces, and the Brickman number shows stronger viscous dissipation effects, leading to an increase in the fluid temperature. [ABSTRACT FROM AUTHOR]

The influences of variable viscosity and thermal conductivity on a steady, laminar, viscous, incompressible, hydromagnetic flow passing through a channel filled with a porous medium are investigated. The effects of heat source, thermal radiation, thermophoretic deposition, and Soret and Dufour numbers are considered. The governing equations are solved by the MATLAB bvp4c solver. It is found that increases in the viscosity parameter, thermal conductivity parameter, and the thermophoretic coefficient reduce the fluid velocity, while increasing radiation parameter and Dufour number enhance it. An increase in the thermal conductivity parameter raises the concentration, but reduces the temperature. The influences of the relevant parameters on the skin friction and Sherwood and Nusselt numbers are presented in tabular form and analyzed. [ABSTRACT FROM AUTHOR]

Heat, mass transfer, and non-Newtonian fluid flow processes have gained significant interest in various industrial applications due to their substantial significance in the fields of technology, engineering, and science. The aforementioned processes hold significance in the context of polymer solutions, porous industrial materials, ceramic processing, oil recovery, and fluid beds. This study aims to investigate the impact of temperature-dependent viscosity and thermal conductivity on the cilia-driven flow of tangent hyperbolic fluid with mass and heat transfer. The objectives include analyzing how these variable properties affect the velocity, temperature, and concentration profiles within the fluid flow, thereby providing insights into potential applications in bioenergy systems and enhancing the understanding of non-Newtonian fluid dynamics. Viscous dissipation has been taken into consideration. Firstly, governing nonlinear coupled equations are solved in a fixed frame, and then the results are tracked in the wave frame. MATHEMATICA's NDSolve command is utilized to graphically discuss the findings for several different flow parameters. Analytically stated, solving a problem with such a coupled and nonlinear system is tough. The effect of new parameters is discussed on velocity and temperature profile and graphically shown. It has been observed that the thermal conductivity is improved at moderately low temperatures, whereas the opposite pattern is seen at comparatively high temperatures. On the other hand, the temperature distribution demonstrates a behaviour consistent with lowering as the number of heat Bolus increases. The findings that were provided offer beneficial insight into bioenergy systems and serve as a helpful benchmark for both experimental and extra-progressive computational Multiphysics models.

Magnetized non-Newtonian models nowadays have attracted many researchers because it is an exciting field in the collaboration of material science, fluid dynamics, and applied physics. Their unique properties and adaptability render them invaluable across various technological and industrial applications, promising further innovations as research advances. This research unveils the intricate rheological and thermal behavior of magnetized non-Newtonian nanofluids undergoing peristaltic motion. The study aims to enhance engineering design techniques for optimal biophysiological performance by incorporating second-order slip, convective conditions, and temperature-dependent thermal conductivity. The Buongiorno nanofluid model is adopted to investigate heat and mass transfer phenomena, while the Prandtl non-Newtonian fluid model is employed to comprehend the complex rheological characteristics of the fluid. A long-wavelength approximation with a low Reynolds number was employed to simplify the governing equations. Analytical solutions have been obtained by solving the nonlinear transformed equations using the Homotopy perturbation technique. The findings are validated with previous literature and indicate that magnetic fields play a key role in controlling peristaltic flow behavior and nanofluid pumping rates. Moreover, the interplay between non-Newtonian rheology and nanofluid parameters significantly affects temperature distribution patterns. An increase in the species Biot number and thermophoresis parameter leads to improved concentration behavior. Conversely, a reversible trend is noted with the augmentation of the Prandtl number, Eckart number, variable thermal conductivity, and Brownian motion parameters. This research provides new insights into magnetohydrodynamic transport mechanisms in peristaltic systems. The modeling approach, coupled with analysis, lays the background for improved fluid circulation, oxygen delivery, waste removal, and nutrient transport in biomedical applications. Specifically, the findings are important for advancing the design of peristaltic pumps tailored for targeted drug delivery and optimizing fluid flow within gastrointestinal tracts.

Here flow for radiative hybrid-nanomaterial (MgO+MoS2) satisfying Darcy-Forchheimer relation is addressed. Ethylene glycol C2H6O2 is utilized as a base fluid. Magnesium oxide (MgO) and Molybdenum disulfide (MoS2) are considered as distinct nanoparticles. Thermal expression is examined through heat generation and viscous dissipation. Analysis for Cattaneo-Christov theory is carried out. Condition for melting heat is deliberated. Entropy generation is examined. Variable thermal conductivity of hybrid nanomaterial is taken. Suitable transformations are implemented to obtain nonlinear dimensionless systems. Optimal homotopy analysis method (OHAM) is implemented for computations. Temperature, velocity and entropy generation are scrutinized physically. Nusselt number and skin friction are discussed. Conclusion synthesis salient points. Present work is relevant in metallurgical engineering and polymer processing. The findings conclude that Forchheimer number correspond to decline in velocity. Entropy rate and thermal field have similar trend for heat generation variable. A decrease in velocity against melting variable is noted. Temperature increases for variable thermal conductivity and thermal relaxation parameters. Entropy optimization improved for Brinkman number. Skin friction decays for porosity parameter and Forchheimer number. Skin friction improves for melting variable and Forchheimer number. Entropy augments against higher thermal relaxation time. Higher melting variable lead to an enhancement for Nusselt number. There is an improvement for radiation through Nusselt number and temperature.

The study of hybrid nanofluid flow bounded by double-revolving disks is crucial due to its significant applications in enhancing heat transfer in various industrial processes, including cooling systems, lubrication technologies, and energy storage systems. This manuscript presents an entropy generation analysis of the magnetohydrodynamic Darcy-Forchheimer flow of a non-Newtonian second-grade hybrid nanofluid between double-revolving disks with variable thermal conductivity. The hybrid nanofluid combines titanium dioxide (TiO2) and cobalt ferrite (CoFe2O4) nanoparticles in a base fluid of engine oil. Appropriate similarity transformations convert the dimensional equations governing the flow phenomena into a non-dimensional form. The resulting non-dimensionalized system of equations is then solved using the homotopy analysis method (HAM), a semi-analytical technique. The results are validated by comparing them with previously published work for a specific case of the present analysis, and they are found to be in very good agreement. A comprehensive parametric analysis is conducted to understand the behavior of flow and heat transfer to various physical parameters involved in the study. It was found that there is an enhanced heat transfer rate at both disks when the Reynolds number and titanium dioxide nanoparticle concentration are higher. It was also found that Bejan number declined with increasing Brinkman number.

Abstract Owing to valuable significance of bioconvective transport phenomenon in interaction of nanoparticles, different applications are suggested in field of bio-technology, bio-fuels, fertilizers and soil sciences. It is well emphasized fact that thermal outcomes of nanofluids can be boosted under the consideration of various thermal sources. The aim of current research is to test the induction of induced magnetic force in bioconvective transport of non-Newtonian nanofluid. The rheological impact of non-Newtonian materials is observed by using Casson fluid with suspension of microorganisms. The chemical reaction effected are interpreted. The thermal conductivity of material is assumed to be fluctuated with temperature fluctuation. The flow pattern is endorsed by stretching surface following the stagnation point flow. Under the defined flow assumptions, the problem is formulated. A computational software with shooting technique is used to present the simulations. A comprehensive analysis for problem is presented. It is claimed that the interpretation of induced magnetic force exclusively enhanced the thermal phenomenon.

The thermo-solutal Marangoni boundary layer flow has been studied because it has a number of real-world uses, such as drying silicon wafers, applying thin coats of paint or glue, employing adhesive in heat exchangers, and growing crystals in space. The physical phenomenon of Cross (FeSO4−(CMC−H2O(

In this work, the flow of ternary hybrid nanomaterials filling porous spaces is investigated in the presence of magnetohydrodynamics (MHD) and nonlinear convection. Three dissimilar nanoparticles copper (Cu), alumina (Al2O3), and magnesium oxide (MgO) are employed. Various features including Ohmic heating, heat generation, and variable thermal conductivity are studied, along with nonlinear radiation and entropy analysis. Solutions are developed using the ND Solve (shooting) method in Mathematica software. Analysis of parameters of interest is conducted, with conclusions highlighting key outcomes. Results show an increase in the thermal field for Eckert number and radiation, while a decrease in liquid flow is observed with increasing the magnetic parameter. The heat transport rate exhibits an opposite trend between heat generation and radiation. Temperature ratio parameter and Prandtl number show opposite trends in the thermal field, while the temperature gradient decreases against variable thermal conductivity. The drag force follows a similar trend against nonlinear convective and porosity variables. The entropy rate increases with the Brinkman number, and both porosity and radiation have an increasing impact on entropy rate. An increase in liquid flow is noted with the nonlinear convection variable. A comparative study of heat transport rate through the Prandtl number shows good agreement.

The aim of this study is to investigate the heat and mass transfer characteristics of Burgers nanofluid in the presence of thermo-diffusion effects. The analysis considers higher-order slip effects to study the transport phenomena. Additionally, the study examines the impact of thermal radiation and chemical reactions on the flow. Variable thermal conductivity assumptions are made for heat transfer analysis. The Cattaneo–Christov model, an extension of Fourier heat and mass theories, is employed for the analysis. Heat transfer evaluation is conducted using convective thermal constraints, and numerical computations are carried out using the Runge–Kutta method. The study visually represents the impact of flow parameters through graphical analysis. It is suggested that heat transfer can be significantly improved through the interaction of slip effects, and the concentration phenomenon is enhanced by the Soret number.

Hybrid nanoparticles, which are nanoparticles composed of multiple materials or phases, find applications in various fields due to their unique properties resulting from the combination of different materials. In such fluids, viscosity changes significantly in response to alterations in temperature or pressure. For example, these fluids become less viscous as they are heated and more viscous as they are cooled. Similarly, in certain situations, the application of a temperature variation can cause a change in viscosity. This property is commonly observed in materials like polymers and some oils. The article aims to investigate the heat transfer and flow behavior of fluid from an elastic sheet of hybrid nanoparticles, considering the temperature-dependent variable viscosity and thermal conductivity. The obtained equations for the mathematical model are partial differential equations converted to ODEs by applying a suitable similarity transformation. The findings show that the magnetic field opposes fluid motion. Our main findings are that adding nanoparticles to the base fluid significantly increased its heat conductivity. This improvement has great potential for uses requiring effective heat transmission, especially in engineering systems where heat dissipation plays a crucial role. The study also reveals the complex relationships that influence thermal conductivity, including slip boundary effects, viscosity fluctuations, magnetohydrodynamic effects, and porous media dynamics. Understanding these interactions is critical for optimizing heat transport processes in porous media applications. Comprehending these interplays is essential for refining heat transport mechanisms in applications involving porous media. The graphical representations are used to explain the physical behavior of various model parameters. Previous outcomes are also contrasted with the current ones. The findings show that the magnetic field opposes fluid motion.We range the subsequent list of values for parameters in every graph unless indicated accordingly.ϵ=0.1,Pr=2,M=0.5,R=0.2,K=5,fw=0.1,s=0.1 ,λ=1,φ1=0.02,φ2=0.04.

Power-law fluids have recently received increasing attention because of their applications in different industrial fields. In previous works, the energy and momentum equations for power-law fluids were considered the same as those for Newtonian fluids. However, as the heat transfer of fluids results from thermomolecular motions, the heat-transfer behavior of non-Newtonian power-law fluids should be different from that of Newtonian fluids. The flow of fluids on a smooth plate is a classical problem. In most situations, the plates are rough. In particular, in industrial fields, many plates are deliberately designed to be rough to enhance heat transfer. Herein, according to the Taylor expansion and boundary-layer theory, the boundary-layer equations for the Ostwald–de Waele power-law fluids with a variable thermal conductivity along a horizontal wavy surface are reduced to partial differential equations. An energy equation with a variable thermal conductivity is constructed, where the heat-conduction coefficient is assumed to be a power-law function dependent on the temperature gradient. Through the introduction of a series of transformations, including nondimensional and coordinate transformations, the original wavy-surface problem is transformed into a system of partial differential equations describing the flow problem with boundary conditions on a flat plate, which is solved numerically using the Keller-box method. The effects of some parameters, such as the amplitude–wavelength ratio \begin{document}$ \alpha $\end{document}, power-law index \begin{document}$ n $\end{document}, and generalized Prandtl number \begin{document}$ {N_{{\rm{zh}}}} $\end{document}, on the local friction coefficient and heat-transfer coefficient are discussed. Numerical results show that the velocity of power-law fluids on the surface and pressure gradient varies periodically along the wavy plate. Furthermore, the cycles of the velocity and pressure gradients are the same as the one of the wavy-shape plate. The results show that the local Nusselt number and the friction coefficient vary periodically in a wavelike manner and increase gradually with the amplitude–wavelength ratio, although a sudden change exists near the zero point. With the increasing amplitude, the friction coefficient oscillates more considerably. With the increasing power-law index, the local Nusselt number decreases. For a special case in which the plate is flat, the local Nusselt number and friction coefficient are in a stable state for a short distance along the plate, although initial oscillations appear near the zero point. Owing to the effects of different parameters on the periodicity, the peak and trough of the local Nusselt number and friction coefficient are not consistent, despite occurring in the same cycle.

Abstract The objective of this article is to investigate how the properties of a non-Newtonian Williamson nanofluid flow, which occurs due to an exponential stretching sheet placed in a porous medium, are influenced by heat generation, viscous dissipation, and magnetic field. This study focuses on analyzing the heat transfer process by considering the impact of temperature on the thermal conductivity and viscosity of Williamson nanofluids. Additionally, the research significantly contributes by investigating the flow characteristics of these nanofluids when influenced by slip velocity. Using the spectral collocation method (SCM), the equations that describe the current problem are transformed into a collection of ordinary differential equations and then solved. The SCM proposed here basically depends on the properties of the Appell-type Changhee polynomials (ACPs). First, with the aid of ACPs, we give an approximate formula of the derivatives for the approximated functions. Through this procedure, the provided model is transformed into a nonlinear set of algebraic equations. Physical factors of interest, such as skin friction, the Nusselt number, and the Sherwood number, are explained using tabular expressions. Data are displayed as graphs for the nanofluid’s velocity, temperature, and concentration. The primary findings showed that increasing the Williamson, magnetic, thermal conductivity, and Brownian parameters significantly improves the thermal field. Finally, testing the suggested method with specific cases from some past literature-based publications reveal a good degree of agreement.

Variations in viscosity and thermal conductivity play a vital role in the manufacturing of glass fiber, ceramics, pharmaceuticals, and plastics, as well as in hot rolling, space technology, and high-temperature processes. This article investigates an electrically conducting hybrid nanofluid flowing across an exponentially extended sheet under variable fluid properties, such as thermal conductivity, viscosity, and non-uniform heat generation. In addition, the Prandtl number can vary inside the boundary layer and is an effective way to manage heat transfer and fluid flow. Furthermore, slip effects and suction at the boundary have been considered, and the hybrid nanofluid flow is also influenced by variations in viscous forces and viscous dissipation effects. The governing partial differential equations can be discretized into dimensionless ordinary differential equations using similarity transformations. The various important physical parameters have been presented in detail using diagrams. It is also observed that the skin friction of hybrid nanofluids is increased by up to 4.07% compared to nanofluids with suction. The presence of thermal radiation can enhance the energy Nusselt number of hybrid nanofluids by as much as 6.5%. Moreover, the variable Prandtl number is more effective than the constant Prandtl number in enhancing the heat transfer rate.

This article describes the significance of ‘Stefan suction/blowing’ on the forced flow of nanoliquid past the surface of a ‘plate’ with temperature-obeying ‘thermal conductivity’ and ‘fluid viscosity’ with ‘zero nanoparticle flux’ at the ‘plate’ that has not till been attended by anyone and thus it points to the originality of present investigation and here lies the novelty of our work. Nanofluid flow is modeled with the help of ‘Buongiorno's two-phase model’ which contains the instantaneous virtue of thermophoresis diffusion and Brownian movement. This investigation shows that the speed of heat transport is remarkably augmented by the variable ‘thermal conductivity’ and variable ‘viscosity parameters’ which is the main contribution of this research. Due to changeable viscosity, reducing nature of velocity as well as the reducing nature of concentration of the nanoparticles near the ‘plate’ are observed. Due to Stefan's blowing parameter, fluid velocity augments but ‘temperature’ is observed to reduce for mounting values of Stefan's blowing parameter. 3.2 % reduction in skin-friction coefficient is noted when variable viscosity parameter reduces from -6 to -8. Moreover, 7.1 % reduction in heat transfer as well as mass transfer is noted when the variable thermal conductivity parameter rises from 0.2 to 0.4. The consequence of this inspection exposes a variation of exciting diversity which claims extra exploration of the present study.

This study simulates the peristalsis mechanism using non-Newtonian third-grade fluid and considers variable fluid characteristics along with electroosmosis, slip, and chemical reactions. The governing equations are designed to account for low Reynolds numbers and long wavelengths. Considering the diverse variables involved, the study delves into the effects of liquid property variations on velocity, temperature, concentration, and trapping. The graphical depiction of velocity and temperature profiles serves to elucidate the consequences of diverse fluid characteristics, demonstrating a significant reduction in these parameters.

In this study, we considered the flow of a micropolar fluid over a vertical Riga sheet. The non linear stretching sheet is considered. The effects of variable thermal conductivity and radiation on the Riga sheet are taken into account. Additionally, we also debated the Brownian motion and thermophoretic. To simplify the partial differential equations, we converted them into dimensionless ordinary differential equations using suitable similarity variables and solved dimensionless system numerically using the bvp4c function. The impact of some intended parameters on the dimensionless velocity, microrotation, temperature, and concentration distributions graphically are presented and the numerical outcomes of physical quantities like skin friction, Nusselt number, Sherwood number, and couple stress have been presented in tabular form. The micropolar parameter increased which increased the couple stress and friction at surface. Because, the fluid rotation increased which increased friction at surface and also increased the couple stress. The transfer of mass decayed and transfer of heat heightened by larger values of variable thermal conductivity. Thermal conductivity improved which improved the heat transfer phenomena, so transfer of heat at surface becomes larger while also reducing the transfer of mass.

The suspension of non-Newtonian materials with nanoparticles is important to enhance the thermal phenomenon in various engineering and industrial processes. The versatile research in nanomaterials provide different applications in thermal processes, heat exchangers, thermoelectric devices, HVAC systems, energy processes etc. Following to such novel motivations in mind, current research endorsed the enhancement in heat transfer due to suspension of Jeffrey nanofluid comprising the variable thermal conductivity. The cause of flow is associated to two disks attaining fixed distance. The modified developed relations for Fourier's hypothesis are utilized to model the problem. The flow problem is modeled with appliance of fundamental novel laws. By applying suitable transformations, corresponding differential equations are renovated into dimensionless forms which are solved with applications of analytic homotopic algorithm. The behavior of temperature and velocity due to various parameters is discussed. The numerical calculations have been done for wall shear force and Nusselt number. The results show that the velocity profile boosted due to variation of stretching ratio constant. The enhancement in heat transfer is observed due to Reynolds number. Moreover, the increasing observations for wall shear force in upper and lower disk surfaces are obtained against larger material parameter. The simulated results may find applications in improving heat transfer phenomenon, manufacturing systems, recovery processes, cooling systems, chemical phenomenon, fuel cells etc.

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.

Owing to high thermal predictions, the scientists have utilized multidisciplinary contributions of nanofluids in various engineering and scientific problems. Based on exclusive heat transfer results, the contributions of nanomaterials are commonly addressed in thermal devices, chemical reactions, vehicle engines, fusion processes, energy outcomes and many industrial systems. Recently, it is emphasized that the suspension of nanoparticles with microorganisms show valuable applications in the fertilizers, petroleum sciences and bio-fuels. Based on such novel applications, in current research work, a mathematical model is developed for viscoelastic nanofluid under the suspension of microorganisms. The analysis is further updated with applications of magnetic force, chemical reaction and radiative influence. Unlike to tradition research approach, here the modified expression of thermal heat flux via Cattaneo–Christov (CC) relations are adopted for modeling the problem. Furthermore, the nature of thermal conductivity is considered to be variable. The oscillating surface with stretching velocity is assumed to be source of flow. The whole problem is expressed in terms of complicated and nonlinear PDE's for which analytic process is adopted. Onset of parameters are addressed physically and various applications are suggested. It is noticed that presence suction/injection parameter and permeability of porous space enhanced the heat transfer rate. The concentration phenomenon declined with viscoelastic parameter.

In this study, a partial velocity slip of the boundary layer flow and an analysis of the MHD two-dimensional ternary hybrid nanofluid with fluid based on polymers with variable thermal conductivity are conducted. On a stretching sheet with a convective boundary condition, the investigation was conducted. Model equations with boundary conditions were transformed into a set of ODEs in order to study the flow. The resulting system of equations was solved by using the Runge-Kutta fourth-order method in conjunction with the shooting method. A numerical analysis was done to determine the impact of several key factors on the system's heat transfer characteristics and flow field velocity. Computed the flow field's velocity and heat transfer properties by varying these physical parameters, then graphically displayed the results. Additionally, tables covered the local shear stress and rate of heat transfer respectively, describe the flow's resistance to motion and the rate of local heat transfer of ternary hybrid nanofluid. For a thorough comparison, the results were compiled in tables. Additionally, the results were compared to data already available for regular fluids, and it was discovered that there was a very high degree of agreement between the two sets of results. This raises confidence in the precision of their numerical computations. New findings: The explicit formulas that have been derived make it simple to understand how changes in temperature-dependent thermal conductivity and nanoparticle volume fraction affect significant parameters, such as sk.fsdain friction and heat transfer rate, in the study of ternary hybrid nanofluids.

The classical viscous theory is limited to illustrating the characteristics of several materials like pseudoplastic and dilatant fluids. Sutterby fluid has the features of shear thinning and shear thickening fluids because of its Power law index. Therefore, this study considered an incompressible, time-independent and electrically conducting Sutterby fluid flow across a rotating and stretchable disk. The disk experiences the effect of porous space. The energy equation has variable conductivity, heat source and thermal relaxation time features while mass equation exploits the influence of chemical reaction. The aspects of Buongiorno nanofluid theory are also examined in the Sutterby flow model. The phenomenon of Stefan blowing is analysed through mass transfer rate at the surface of disk. The flow expressions are first transferred into a new system of single independent variable and then treated numerically via Runge–Kutta–Fehlberg (RKF) method combined through shooting process. The behaviour of distinguished physical quantities is discussed graphically on momentum, mass species and thermal fields. The numeric data of drag force, Sherwood number and Nusselt number is calculated against several physical parameters.

This article employs the Cattaneo-Christov double diffusion concept to examine thermal and solute energy transfer processes in Maxwell liquid movement. The irregular two-dimensional movement of a Maxwell liquid with changing heat conductivity across an extended cylinder is investigated, together with thermal radioactivity and velocity slip. We develop partial differential equations for heat and mass transmission in Maxwell liquid using the Cattaneo-Christov pattern instead of Fourier's and Fick's law. Numerical shooting solves ordinary differential equations obtained from controlling partial differential equations via similarity transformations. We noticed that unstable factor should be no more than one for optimal outcomes. Greater Maxwell values minimize the movement field and increase liquid energy transfer. Heat and concentration diffusions in Maxwell liquids decline as thermal and concentration relaxation times approach maximum. In addition, a low thermal conductivity characteristic improves the temperature field.

Micro polar fluids have a wide variety of applications in biomedical, manufacturing, and technical activities, such as nuclear structures, biosensors, electronic heating and cooling, etc. The aim of this study is to investigate the properties of heat transfer on a magnetohydrodynamic free convection movement of micro polar fluid over an exponentially stretchable curved surface. The flow is non-turbulent and steady. The effects of Joule heating, varying thermal conductivity, irregular heat reservoir, and non-linear radiation are anticipated. The modelled PDEs are converted to ODEs via transformation, and the integration problems are then addressed using ND-Solve method along with bvp4c package. It is observed that velocity is reduced and the micro rotation field is increased as the micro rotation parameter is increased. It is witnessed that the temperature of the fluid enhances as the Eckert number is augmented. The velocity is increasing function of the curvature parameter while the decreases with increasing magnetic factor. The distribution of temperature is improved by a rise in temperature-dependent thermal conductivity characteristic. It is investigated that as the values of temperature ratio, Prandtl number, and the Biot number are increased the temperature distribution is enhanced. For the stability of the numerical results, the mean square residue error (MSRE) and total mean square residue error (TMSRE) are computed. For the confirmation of the present analysis, a comparison is done with the published study and excellent settlement is found.

This investigation is related to this study of entropy generation during Carreau nanofluid flow under variable thermal conductivity conditions. The heat and mass transfer phenomena are observed in the presence of thermal radiation and activation energy. The flow is induced by a porous stretching surface. Appropriate variables are used in order to simplify the problem into dimensionless form. The numerical simulations are performed by using the shooting technique. The physical aspects of the problem in view of different flow parameters are reported. It is observed that consideration of variable fluid thermal conductivity enhances heat transfer. An enhancement in heat and mass transfer phenomena is observed with increasing the Weissenberg number. Moreover, entropy generation increases with Weissenberg and Brinkman numbers. Current results present applications in thermal processes, heat exchangers, energy systems, combustion and engine design, chemical processes, refrigeration systems, etc. [ABSTRACT FROM AUTHOR]

Thermal analysis of serrated fins which are consist of annular and plain sections are investigated. Serrated fin's thermal conductivity is assumed to change linearly with temperature. Nonlinear differential equations are obtained by applying the energy balance equation for both sections of the serrated fin and these equations are solved by applying homotopy perturbation method. Insulated fin tip, constant fin base temperature and common boundary conditions between the interface of two sections are considered. Serrated fin radii ratio (𝜀), segment height ratio (𝛿), thermo-geometric fin parameter (𝜓) and thermal conductivity parameter (𝛽) effecting the thermal performance and temperature distribution are investigated. The results showed that the homotopy perturbation is a reliable method for the solutions of such nonlinear differential equations. A very good agreement with the homotopy perturbation method and the numerical finite difference method are obtained. It is seen that, serrated fin efficiency lays between annular and rectangular fins and increases with the increase of segment height ratio and thermal conductivity parameter. Such as, fin efficiency values under the condition of 𝜀 = 2, 𝜓1 = 1.0 and 𝛽 = 0 for 𝛿 = 0, 0.5, and 1 are 0.692, 0.718, and 0.762, respectively. [ABSTRACT FROM AUTHOR]

This paper mainly analyzes the heat transfer of Carreau fluid over an infinite rotating disk, and two models with variable thermal conductivity are considered. Firstly, the governing partial differential equations (PDEs) are transformed into ordinary differential equations (ODEs) by similarity transformation. Then, the boundary value problem is solved by improved bvp4c method, which reduced sensitivity to the initial values. For shear-thinning and shear-thickening fluids, the effects of Carreau fluid index n and Prandtl number Pr on velocity and temperature fields are shown and analyzed when 0.5 ≤ n ≤ 1.5 , 1 ≤ P r ≤ 10. Furthermore, the thermal conductivity is computed under two cases. [ABSTRACT FROM AUTHOR]