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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.

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. [ABSTRACT FROM AUTHOR]

AbstractThis article analyses the flow across a moving surface using the magnetohydrodynamic (MHD) Williamson fluid model in detail, accounting for the effects of diffusion, nonlinear convection, and variable thermal conductivity. The heat transmission within the system is impacted by the changing thermal conductivity, which can also significantly alter the flow behavior. The effects of the moving surface on flow forms in porous media are explained here using the Darcy model. The similarity transformations are used to convert the underlying nonlinear partial differential equations into a collection of ordinary differential equations. The work uses a numerical RK4 technique to examine the complex incompressible fluid flow behavior on a moving surface. The study’s conclusions provide insight into the intricate flow patterns and shear layer forms brought on by the interaction of fluid and surface motion while taking varied thermal conductivity into account. The findings give important information for the design and optimization of engineering applications involving changeable thermal characteristics and advance our understanding of fluid dynamics in geophysical and atmospheric systems. Physical descriptions are used to depict how flow parameters behave in relation to velocity, temperature, and concentration distributions. [ABSTRACT FROM AUTHOR]

This work objective focuses on studying the combined influences of variable thermal conductivity, chemical reaction, and magnetohydrodynamics (MHD) on the flow of a tangent hyperbolic nanofluid flow over an exponentially stretching surface, considering a first-order velocity slip condition. Additionally, thermophoresis and Brownian motion impacts are taken into account. The phenomena of heat transfer are analyzed considering several factors such as thermal radiation, Joule heating and nonlinear heat source. On the other hand, mass transfer is explored under the effect of chemical reaction. Tangent hyperbolic fluid is an important branch of non-Newtonian fluids known for its ability to describe shear thinning effects. Understanding fluid flow on exponentially stretched surfaces is of great significance due to its applications in various industrial processes. These applications include fluid film condensing methods, plastic production for making plastic covers, fiber manufacturing (where it is used to spin fibers), glass blowing, metallurgical procedures, and the paper industry. The concept of magnetohydrodynamics (MHD) is significant due to its various engineering applications, such as MHD generators, flow meters, heat reservoirs, small components in different devices, and cooling systems for nuclear reactors. To analyze the system, using similarity transformations, the governing equations of continuity, velocity, and concentration are transformed into non-dimensional differential equations. The numerical solution is obtained using the shooting technique. The study presents the physical significance of all the fluid parameters involved, focusing on the velocity, temperature, and concentration profiles. These profiles are presented graphically and discussed in detail. The results show that the fluid velocity profile increases with enhancing values of the We and the magnetic number M. The thermal profile increases with higher Nt and Rd The concentration profile decreases with higher values of Q t and Nb. [ABSTRACT FROM AUTHOR]

In many engineering systems, hybrid and nanofluids are influenced by their respective thermophysical characteristics. Lately, several models have been envisaged to foresee the hybrid and nanofluid attributes. The properties of hybrid nanofluids (HNFs) as potential heat transfer fluids are controlled by numerous aspects such as solid part size, volume fraction, and temperature. Considering the interesting facts of the hybrid and nanofluid flows, we in this exploration examined the thermal performance comparison of both types of fluid flows. The nanofluid and HNF are composed of molybdenum disulfide (MoS2)/kerosene oil and silicon dioxide–molybdenum disulfide (SiO2–MoS2)/kerosene oil, respectively. The flows are taken in a canonical gap between the cone and the disk. Both the cone and the disk may be rotating or stationary. The novelty of the computational model is enhanced by discussing the effects of viscous dissipation, Joule heating, and the variable thermal conductivity with convective condition. The Tawari and Das model is designed to analyze the heat transfer performance of the assumed fluid flows. The assumed fluid model is transmuted into the set of differential equations that are dealt numerically with the bvp4c MATLAB approach. The results are displayed in tables and graphical forms. For elevating estimations of the Eckert number, the heat transmission rate is found to be more significant in the disk than cone. It is also learned that hybrid nanoliquid heat transfer performance outperforms nanoliquid. The fluid velocity increases by raising the nanoparticle volume fraction ϕmol, and is decreasing for a higher magnetic field parameter. With the elevating estimates of thermal conductivity, it is shown that the cone transmits heat more quickly whereas the disc transmits heat more slowly. The thermal conductivity parameter increases the probability of collision of the liquid particles, that ultimately upsurges fluid heat transmission rate. [ABSTRACT FROM AUTHOR]

The article focuses on studying the effect of variable thermal conductivity on the reflection of waves propagating through a medium. Considered solid is half space with semiconductor properties. Additionally, we have also introduced the concept of non-local thermoelasticity to develop a stress-strain relation. Using the Helmholtz decomposition principal, we have determined that three longitudinal waves and one transverse wave propagate through the medium after reflection. To account for the thermal signals generated by the elastic vibration, we have used a three-phase lag (3PL) heat conduction model. The numerical computation of the theoretical results is presented graphically for a specific medium. The study of elastic waves passing through the human body is used for diagnosis and treatment. Nature and characteristics of the materials can also be detected by evaluating the behavior of waves reflected and transmitted through them. [ABSTRACT FROM AUTHOR]

This paper addresses the melting of phase change solid sphere, which motivates researchers to develop new thermal energy storage (TES) systems techniques. Phase change materials can store or release large amounts of heat in short intervals of time, thus improving the thermal performance of cooling and heating systems in buildings and regulate the temperature of PV systems, batteries and other electronic components. We have considered a convective spherical Stefan problem with thermal conductivity as a function of time and temperature. The heat balance integral method (HBIM) is used to find the problem's solution numerically. The temperature profile is approximated by using n degree polynomial. The influence of governing parameters on the location of melting front and temperature profile is discussed thoroughly. The parameters depict that transition from solid to liquid phase becomes fast for higher values of Stefan number while the transition rate slows down for larger values of Peclet number. The melting rate increases from 20% to 80% when Stefan number rises from 0.1 to 1.0 at a particular time. Moreover, a comparative study of the proposed model with some existing models is being done. It is observed that moving melting front for the assumed problem undergoes a fast melting process. [ABSTRACT FROM AUTHOR]

Slip condition plays a significant role in many heat transfer phenomena such as cleaning microheat exchangers, mechanical heart valve cleaning, and inner cavity polishing. The present study is carried out on the numerical analysis of steady mixed convection (SWCNT + MWCNT/ H2O) hybrid nanofluid flow with slip boundary conditions in the presence of variable thermal conductivity, heat generation and thermal radiation via an exponentially extending sheet. By using the proper exponential similarity transformations, a nonlinear coupled ordinary system is obtained from the coupled partial differential system. The generated ordinary differential systems are resolved using the MATLAB software. Physical characteristics, such as the mixed convection parameter (λ), the velocity slip (A), the thermal slip (B), and the heat generation (QH), that have an impact on temperature, Nusselt number, and velocity field, are shown in graphical and tabular representations. The enhancement of suction and velocity slip causes a reduction in the velocity profile. The findings of the thermal slip test against stretching sheet show that hybrid nanofluid improves the rate of heat transmission by 4.33% when compared to nanofluid. [ABSTRACT FROM AUTHOR]

The importance of thermal efficiency in major industrial and engineering sectors cannot be overstated. Numerous processes within these domains require substantial heat transfer, and conventional fluids often fall short in generating the necessary amount of heat for these operations. Recognizing this limitation, there arose a need to enhance the thermal conductivity of ordinary liquids. In response to this challenge, researchers and scientists proposed a groundbreaking idea: the introduction of metallic and non-metallic nano additives into the base fluid to improve its thermal effectiveness. This innovative approach gave rise to a new category of liquids known as hybrid nanofluids. In this article, we delve into the analysis of the 2D steady flow of SWCNT-Fe3O4/H2O and MWCNT-Cu/H2O-based hybrid nanofluid over a stretching and shrinking sheet, taking into account factors such as suction/injection and thermophysical impacts. The utilization of similarity variables enables the reduction of partial differential equations to a more manageable system of ordinary differential equations. To solve these transformed ordinary differential equations, a numerical technique, specifically the shooting algorithm with the bvp4c solver, is employed. The results are presented and elucidated through graphical representations, providing valuable insights into the behavior of the system under consideration. [ABSTRACT FROM AUTHOR]

Non-Newtonian fluids have industrial and technical applications. Several liquids in nature do not have Newtonian viscosities. These fluids include applesauce, polymer mixtures, colloidal and fermented mixtures, clay glazes, paints, lubricants, cement, slush, shampoos, mud, foodstuffs, paper paste, aqueous froths, etc. This study considers stratified flow and variable heat transmission across a stretched surface. The magnetic hydrodynamics and slips' impacts are illustrated. On the basis of flow assumptions, the mathematical model was created using the Navier–Stokes equation. The boundary layer approximation approach is provided PDEs by working on the Navier–Stokes equation under flow assumptions. This system is converted into ODEs through similarity transformations. Dimensionless system is elucidated by means of RKF-45 technique. The concerning physical parameter effects are elaborated numerically as well as graphically. Based on the findings of the comparison, it was determined that Williamson fluid had superior performance in terms of fluid velocity compared to Maxwell fluid. Furthermore, the temperature of the fluid is greater for booming values of both e 1 and ε parameters. [ABSTRACT FROM AUTHOR]

AbstractPeristaltic flow of nanofluid with temperature-dependent thermal conductivity is investigated. Variation of effective thermal conductivity of nanofluids with temperature is addressed. Mathematical modeling of momentum and energy equation is considered in a symmetric channel. Viscous dissipation, Ohmic heating, and mixed convection are accounted. Applied magnetic field and convective boundary conditions are imposed. Dimensionless expressions are simplified under long wavelength approximation. The relevant problems are solved by numerical technique. Velocity, temperature, pressure, and heat transfer characteristics are studied graphically. Heat transfer rate rapidly increases by increasing the concentration of nanomaterial. Therefore, nanomaterial is used for the cooling process in engineering and biomedical devices. [ABSTRACT FROM AUTHOR]

In this work, the effect of hydrostatic initial stress is studied with the exited semiconductor material. Electrons are exited at the free surface of the elastic semiconductor medium using the photo-thermal-elastic theory during the transport (diffusion) process. The thermal memories are due to the dual-phase-lag (DPL) relaxation times of the heat conduction equation with a novel model. In this model, the thermal conductivity is chosen as a linear dependent function of the thermal temperature impact which is variable. The effect of gravitational field is taken into account during the two-dimensional (2D) elastic deformation under the impact of an internal heat source. The Kirchhoff transformation mapping is used. The harmonic wave (normal mode) method is applied for the 2D governing equations to obtain the main physical fields analytically. Some thermal and mechanical forces are applied with other elastic-plasma conditions at the free surface of the semiconductor material to get the complete solutions. Some comparisons used a novel parameters which depend on the DPL model and the differences in the thermal conductivity parameters and they are illustrated graphically and discussed. [ABSTRACT FROM AUTHOR]

The current study explores two-dimensional disturbances in a nonlocal photothermoelastic semiconducting medium with two temperatures by implementing the Green Naghdi-II theory. The thermal conductivity of the medium is assumed to be varying with temperature changes. The formulation is subjected to an inclined mechanical load. A lot of research has been carried out in recent years on photothermoelastic medium, but not much attention has been given to study the dynamical interactions in a nonlocal photothermoelastic medium with two temperatures and variable thermal conductivity under the effect of inclined mechanical load. The analytical solutions of physical field variables such as temperatures, stresses, carrier density and displacement are obtained by using the normal mode analysis method. For a specific material, numerical computations are performed to illustrate the results. The results that were obtained through numerical analysis for the physical quantities are displayed graphically. The comparisons are made among the results obtained by taking into account the different values of time, inclination angle, two temperature parameter, nonlocal parameter, variable thermal conductivity and photothermal elastic constants. Some special cases of interest have been inferred from the present study for validation. [ABSTRACT FROM AUTHOR]

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.

This investigation aims to analyze the effects of heat transport characteristics in the unsteady flow of nanofluids over a moving plate caused by a moving slot factor. The BRS variable is utilized for the purpose of analyzing these characteristics. The process of mathematical computation involves converting the governing partial differential equations into ordinary differential equations that have suitable similarity components. The Keller-Box technique is employed to solve the ordinary differential equations (ODEs) and derive the corresponding mathematical outcomes. Figures and tables present the relationship between growth characteristics and various parameters such as temperature, velocity, skin friction coefficient, concentration, Sherwood number, and Nusselt number. The results are assessed by comparing them to previous findings. The observation reveals that higher dimensionless reference temperature and variable values of the moving slot parameter have a suppressing effect on the velocity and temperature patterns of nanofluids. Higher values of the dimensionless reference temperature and moving slot parameter lead to enhancements in the Sherwood number, skin friction coefficient, and Nusselt number. The conductivity of the nanofluid is ultimately affected by these enhancements. [ABSTRACT FROM AUTHOR]

In the current research, a thorough examination unfolds concerning the attributes of magnetohydrodynamic (MHD) boundary layer flow and heat transfer inherent to nanoliquids derived from Sisko Al2O3-Eg and TiO2- Eg compositions. Such nanoliquids are subjected to an extending surface. Consideration is duly given to slip boundary conditions, as well as the effects stemming from variable viscosity and variable thermal conductivity. The analytical approach applied involves the application of suitable similarity transformations. These conversions serve to transform the initial set of complex nonlinear partial differential equations into a more manageable assembly of ordinary differential equations. Through the utilization of the FEM, these reformulated equations are solved, considering the specified boundary conditions. The outcomes attained are graphically depicted by means of plots and tables. These visual aids facilitate a comprehensive exploration of how diverse parameters exert influence over the distributions of velocity, temperature, and concentration. Furthermore, detailed scrutiny is directed towards the fluctuations characterizing pivotal parameters, viz., Nusselt number, skin-friction coefficient, and Sherwood number. It is identified that the Nusselt number showcases a diminishing trend coinciding with increasing values of the volume fraction parameter (φ). This trend remains consistent regardless of whether the nanoliquid under consideration is Al2O3-Eg or TiO2-Eg based. In contrast, both the skin-friction coefficient and Sherwood number assume lower values as the volume fraction parameter (φ) escalates. This pattern remains congruent across both classifications of nanoliquids. The findings of the study impart valuable insights into the complex interplay governing the characteristics of HMT pertaining to Sisko Al2O3-Eg and TiO2-Eg nanoliquids along an extending surface. [ABSTRACT FROM AUTHOR]

In this research paper, we numerically analyze the flow and heat transfer rate of non-Newtonian pseudo-plastic nanofluid with variable apparent viscosity and thermal conductivity effects, respectively, through annular sector duct. Concentric pipes annular sector duct of an apex angle, 2 β and ratio of radii, R ̂ , is filled with saturated porous media. For this purpose, we utilize the power law Darcy–Brinkman flow model along with Forchheimer term. Also, the contribution of nanoparticles is accounted in carboxy methyl cellulose (CMC)-water, which has been taken as base fluid. Finite volume method (FVM) is utilized to discretize the governing mathematical model, whereas algebraic equations are solved numerically by using strongly implicit procedure (SIP). With the help of graphs, the impacts of nanoparticles' contribution and porosity factor have been discussed by giving physical interpretation. Results are also found in the limiting sense and show the good agreement with already published data. At β = π / 3 , ϕ = 0. 1 0 , D a = 0. 0 1 and R ̂ = 0. 2 5 , we can observe down in f Re and Nu upto 5. 6 5 8 % and 1 0. 0 1 % , respectively, when n decreases from 1 to 0. 9 1 , whereas 1 3. 4 7 % and 2 3. 5 7 % , respectively, by decreasing the value of n from 1 to 0. 7 6. For both cases of nanoparticles' contribution, the downs in Nu have been observed same by decreasing the value of n. [ABSTRACT FROM AUTHOR]

AbstractIn this study, the flow, thermal transfer, and mass transport of Casson-Maxwell hybrid nanofluids are explored. The governing PDEs are converted into nonlinear ODEs using similarity transformations and then solved using MATLAB's Bvp4c scheme. Various non-dimensional parameters’ influences on fluid behaviour and transport are investigated. Results indicate that higher curvature parameter values boost velocity, temperature, and concentration fields, enhancing mass and heat transfer as well as fluid motion. The unsteadiness parameter affects velocity profiles and heat/mass transfer processes. Thermal and mass relaxation times, alongside parameters like thermophoresis, Brownian motion, variable thermal conductivity, Arrhenius activation energy, chemical reaction, and temperature difference ratio, significantly shape temperature and concentration profiles and optimise heat and mass transfer rates. Additionally, combining the Casson and Maxwell hybrid nanofluid models shows marked changes in skin friction performance: absolute skin friction rises by 30%, while heat transmission increases by almost 11% compared to the Casson-Maxwell nanofluid model. [ABSTRACT FROM AUTHOR]

The current study focuses on nonlinear convective nanofluid (MoS2 − vacuum pump oil) flow with different shapes in an annular region across coaxial cylinders in a permeable media. At the interface of coaxial cylinders velocity slip and temperature jump conditions are incorporated. The phenomenon of thermal transport is enhanced by amalgamating generalized Fourier law with variable thermal conductivity. The Hamilton-Crosser nanofluid flow model is adopted here. The nonlinear equations that govern the flow are simplified via a similarity transformation. For the numerical solution, the bvp4c algorithm is utilized. Graphical analysis is employed to illustrate how important factors affect the temperature and velocity fields. Computational values of the drag force coefficient and Nusselt number are summarized in tabular form. The study reveals that the velocity field upsurges on enhancing the nonlinear convective and radii ratio parameters. On amplifying the rarefaction and thermal conductivity parameters, the thermal field upsurges. Skin friction coefficient exhibits a decreasing behavior on incrementing the porosity parameter. Heat flux diminishes more rapidly by boosting the concentration of nanoparticles. A considerable correlation is apparent graphically and in tabular form by comparing the results of the current investigation with published studies. [ABSTRACT FROM AUTHOR]

In many engineering applications, it is important to consider the temperature dependence of a material's properties, such as its viscosity and thermal conductivity. Aiming the same, here, in the existing exploration, viscosity and thermal conductivity are taken as variables instead of constant. This study discusses the flow of a viscous fluid over a rotating disk with a surface catalyst. The homogeneous-heterogeneous reactions are supplemented by surface catalysis that boosts the chemical reaction rate in the minimum possible time. The novelty of the problem is enhanced by the incorporation of the variable diffusion coefficients of both chemical species. The Von Karman transformation is used and the system is scrutinized by the bvp4c function of the MATLAB software. The results are portrayed in the form of illustrations and tables. The outcomes divulged that the mass diffusion rate and wall concentration for the porosity and surface catalyzed parameter show a decreasing behavior. [ABSTRACT FROM AUTHOR]

The key function of lubricants is to reduce the friction, wear, and heat between the parts that are in contact with each other. The main applications of the lubricants are to control temperature, and reduction in wear and corrosion of the machinery. Keeping in mind the importance of lubrication and its applications in varied machines. The goal of this research is to inspect the heat transmission impact in the magnetohydrodynamic flow of Jeffrey liquid near a stagnation point through a lubricated surface. Lubrication is accomplished by a shear-thinning liquid. The velocity, continuity, and shear stress, amalgamated with power-law fluids, are used to develop interfacial conditions. The exclusivity of the anticipated model is the inclusion of variable thermal conductivity and diffusion coefficients in the existence of homogeneous-heterogeneous reactions. Using the Keller–Box finite-difference approximation approach, the numerical results are accomplished. The outcomes are portrayed and tabulated in the form of diagrams and tables, respectively. It is witnessed that a greater magnetic field affects the fluid flow velocity and the drag force coefficient. Moreover, it is also inferred that the heat transfer rate dwindled for the greater thermal conductivity parameter. Authentication of the presented model is also part of this investigation. [ABSTRACT FROM AUTHOR]

The present article describes the impact of variable thermal conductivity on the flow of ternary hybrid nanofluid with cylindrical shape nanoparticles over a stretching surface. Three nanoparticles combine in base fluid polymer. The assumption made will be used to model an equations. Modeled equations are in the form of a system of partial differential equations are difficult to solve can be converted to system of an ordinary differential equations, through resemblance substitutions, and will be solved numerically. Numerical scheme of Runge–Kutta order four is coupled with the shooting method to solve the resulting equations. The graphs in the study illustrate how physical quantities, such as magnetic field, injection/suction, nanoparticles volume fraction, and variable thermal conductivity, affected the velocity, skin friction, temperature, and local Nusselt number. The velocity profiles deflate as the volume fraction rises. While the temperature rises with an increase in the volume fraction of nanoparticles for both injection and suction, the velocity profiles also decline as the injection and suction parameter increases. Furthermore, as the magnetic field increases, the temperature profile rises while the velocity profile falls. The temperature curves increase as thermal conductivity increases. Finally, as the magnetic field is strengthened, the Nusselt number and skin friction decrease. The combination of mathematical modeling, numerical solution techniques, and the analysis of physical quantities contributes to the advancement of knowledge in this ternary hybrid nanofluid. [ABSTRACT FROM AUTHOR]

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.

Abstract In this study, forced convective squeezing flow between two rotating parallel plates has been examined. The thermal conductivity depends on the distributions of the temperature and the flow, electric and magnetic fields are considered as time dependent. The worked suspension is ternary hybrid nanofluids which consist of water as a base fluid and graphene, Al2O3 and MWCNT as nanoparticles. The energy equation consists of viscous dissipation, radiation, and Joule heating terms. Suitable transformations are introduced as a first step of the solution methodology and fourth order differential equations are obtained. The resulting system is solved, numerically, and various validation tests are performed. The main outcomes revealed that profiles of the stream function are lower when the squeezing parameter, electric field parameter, or magnetic parameter increases. Also, there is an enhancement in values of the temperature gradients up to 16.78% at the lower plate when the Joule heating parameter is varied from 0 to 6. [ABSTRACT FROM AUTHOR]

Owing to novel thermos-physical properties, various applications of nanofluids are noted in thermal systems, solar energy, extrusion framework, industrial processes, cooling system, heating devices and biomedical applications. In order to attain more thermal impact of nanofluids, various features are endorsed by researchers. However, the thermal applications of nanofluids with interaction of induced magnetic field intended less attention. The aim of this study is to report the significance of induced magnetic force for non-Newtonian nanofluid containing microorganisms. The thixotropic non-Newtonian fluid model is used to classify the distinct rheological impact. The bioconvective thermal model is presented in view of variable thermal conductivity. The problem is further entertained with thermal radiation impact and activation energy. The convective boundary conditions are used to simulate the computations. The governing system is first reduced into dimensionless models which are numerically treated with implementation of shooting technique. The physical parameters report high fluctuation in the thermal phenomenon which are carefully evaluated. [ABSTRACT FROM AUTHOR]

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]

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

In this study, we numerically explore the impact of varying viscosity and thermal conductivity on a magnetohydrodynamic flow problem over a moving nonisothermal vertical plate with thermophoretic effect and viscous dissipation. The boundary conditions and flow‐regulating equations are converted into ordinary differential equations with the aid of similarity substitution. The MATLAB bvp4c solver is used to evaluate the numerical solution of the problem and it is validated by executing the numerical solution with previously published studies. The impacts of several factors, including the magnetic parameter, Eckert number, heat source parameter, thermal conductivity parameter, stratification parameter, Soret, Dufour, Prandtl number, and Schmidt number are calculated and shown graphically. Also, the skin friction coefficient, Nusselt number, and Sherwood number are calculated. Fluid velocity, temperature, and concentration significantly drop as the thermophoretic parameter and thermal stratification parameter increases. As thermal conductivity rises, it is seen that the velocity of the fluid and temperature inside the boundary layer rise as well. Also, the Soret effect drops temperature and concentration profile. The applications of this type of problem are found in the processes of nuclear reactors, corrosion of heat exchangers, lubrication theory, and so forth. [ABSTRACT FROM AUTHOR]