Thermal Biot Number Research Articles

Effect of Variable Viscosity on Entropy Generation Analysis Due to Graphene Oxide Nanofluid Convective Flow in Concentric Cylinders

Aggregated studies of graphene nanoparticles is important for the effective utilization of their striking thermophysical properties and extensive industrial applications. This investigation is one such computational study to explore the flow of graphene oxide nanofluids with temperature dependant viscosity between two concentric cylinders. Buongiorno model is used to develop the flow of graphene nanofluids including the impacts of Soret and Dufour effects and the effects of nanoparticle characteristics such as thermophoresis and Brownian motion. The modelled equations are transformed and are numerically solved using linearization method together with Chebyshev’s spectral collocation method under convective conditions. The impacts of embedded parameters on temperature, concentration and skin friction profiles of the chosen nanofluid and their consequent impacts on the predominant cause for the generated entropy are studied. From the tabulated values of Nusselt number and Sherwood number, it is observed that convective heat transfer can be enhanced by thermal Biot number whereas Soret number enhances diffusive mass transfer and variable viscosity parameter preferably reduces the skin friction. A comparison table is presented and it shows that the values obtained from the present method are in good agreement with existing literature. Also, the obtained results are depicted and interpreted in detail. Furthermore, entropy generation is analysed and its irreversibilty is calculated.

A semi-analytical solution of the magnetohydrodynamic blood-based ternary hybrid nanofluid flow over a convectively heated bidirectional stretching surface under velocity slip conditions

This work inspects the thermal transportation of the magnetohydrodynamic Casson trihybrid nanofluid flow over a convectively heated bidirectional elongating sheet. The flow is considered as three dimensional passing over the sheet, which is placed in a porous medium. The effects of thermal radiations and space- and thermal-dependent heat sources are used in energy equations, while magnetic effects are used in momentum equations. Appropriate variables have been used to convert the modeled equations into a dimensionless form, which have then been solved using the homotopy analysis method. In this work, it is uncovered that both the primary and secondary velocities are weakened with an upsurge in porosity and magnetic factors. The thermal transportation is augmented with growth in thermal- and space-dependent heat source factors and the thermal Biot number. The convergence of the method used in this work is ensured through ℏ-curves. The results of this investigation have also been compared with the existing literature with a fine agreement among all the results that ensured the validation of the model and method used in this work.

Numerical illustration of diffusive flow of blood-based tri-hybrid nanofluid generated by a curved stretching sheet using law of porosity

The study of flow of blood through the blood vessels carries nanoparticles which opens new ways in the research. This study explores one such flow of trihybrid nanoparticles suspended in blood over a curved stretching surface which undergoes the Darcy-Forchheimer porosity model. The analysis employs Cattaneo-Christov heat flux model along with chemical reaction, linear heat source allowing the surface to slip with heat and mass convection. The trihybrid nanofluids consist of a mixture of titanium dioxide, iron oxide, and silica nanoparticles mixed with base fluid (blood) to generate TiO 2 - Fe 3 O 4 - SiO 2 /blood hybrid nanofluids. Runge-Kutta-Fehlberg 4th–5th order technique, a robust numerical technique, was employed to obtain mathematical solutions. Throughout the numerical process, all parameters, except those under examination, were kept at their default values. Additionally, various plots were generated based on numerical results to illustrate the obtained data. The findings indicate that an increase in the Forchheimer number and porosity results in a reduction in the velocity profile. Furthermore, an increase in the radiation parameter and thermal Biot number leads to an increase in the temperature profile, while the temperature profile decreases with an increase in the thermal relaxation parameter. Additionally, an increase in the chemical reaction parameter and concentration Biot number results in an increase in the concentration profile. Moreover, higher Brinkman and Prandtl numbers enhance the Nusselt number.

Irreversibility estimation of MHD thermosolutal convection of Powell–Eyring fluid flow through an inclined microchannel

ABSTRACT Due to the impressive utility of the mass transport phenomena on microscales for various miniaturised devices, the theoretical and experimental studies in microchannel flows to analyse heat and mass transport find enormous interest in researchers. Investigations in microchannel flows have gigantic applications in biochips, drug delivery, and cooling of microchips. This article examines the combined heat and mass transport of Powell–Eyring fluid through a permeable inclined microchannel considering magnetism, thermo-diffusion, and Navier's slip effects under convective boundary conditions. To solve the nonlinear system numerically MATLAB bvp4c solver is employed. This analysis reveals that the entropy generation due to thermosolutal irreversibility is enhanced strictly with the thermo-diffusion effect and solutal Biot number. The Bejan number profile shows a dominating character of Reynold's number close to the upper channel wall and deteriorates with the immense solutal Grashoff number. Also, it achieves maximum and minimum values for the supreme thermal Biot number and Eckert number, respectively in the middle of the channel. The outcome of the study may provide significant insight into controlling flows through microchannels as well as manipulating microfluidic and biomedical devices for minimising energy loss and designing an efficient model for better thermal performance and transmission of chemical species.

Applications of Soret and Dufour effects for Maxwell nanomaterial by convectively heated surface

The intension of recent analysis is to discuss the radiated magnetized flow of Maxwell nanoliquid. Flow is induced due to stretching the surface. Convective and zero mass flux conditions are taken into account. Influence of Soret and Dufour are under consideration. Internal heat source, magnetic field and thermal radiation are discussed in energy expression. Random diffusion and thermophoresis characteristics in presence of chemical reaction are deliberated. Thermal conductivity and viscosity depend upon temperature. Similarity transformation is utilized to transform nonlinear partial differential systems into ordinary systems. ND-solve technique is used to get the numerical solutions for nonlinear nondimensional system. Graphical analysis for flow, concentration and thermal distribution versus emerging variables are examined. Computational outcomes for solutal transport rate and Nusselt number via sundry variables are explored. Velocity profile declines against magnetic field, whereas reverse trend found for temperature profile. Thermal field has increasing trend for thermal Biot and Dufour numbers. Larger Maxwell variable has opposite effect on flow field.

Irreversibility analysis of radiative Williamson nanofluid flow with higher order chemical reaction and quadratic drag force over an extended surface: Non-similar computations

This study aims to present non-similar solutions for the radiative Williamson nanofluid flow with a quadratic drag force effect over a horizontally extended surface. The sheet is extended along the X-axis, and the magnetic field is applied along the Y-axis, perpendicular to the flow. The Buongiorno nanofluid model is employed to incorporate the random dispersion and thermal characteristics of the nanofluid. The innovation in the proposed model lies in its consideration of the effects of viscous and ohmic dissipation, Robin boundary conditions, and higher-order chemical reactions. The governing equations for the flow are scaled down to the second level using an appropriate transformation combined with a non-similarity technique and computationally assessed using the MATLAB bvp4c algorithm. The significant influences of the dimensionless parameters on the velocity, thermal, and solutal fields are depicted graphically. The findings reveal that the fluid velocity diminishes with increasing Weissenberg and Hartmann numbers. The solutal field experiences a reduction with variations in the chemical reaction parameter, while it rises with an increase in the higher-order chemical reaction parameter. The wall heat transfer rate is augmented with higher Eckert and thermal Biot numbers. The mass transfer rate rises with higher values of the chemical reaction parameter, Schmidt number, and solutal Biot number. A comparison of the results from this study with previous research demonstrates strong agreement, affirming the validity of the proposed model. For the value of the Williamson parameter [Formula: see text], the percentage error of the present analysis with established studies is 0% and 0.096770%.

Darcy-Forchheimer chemically reactive bidirectional flow of nanofluid with magneto-bioconvection and Cattaneo-Christov properties

Since the last two decades, researchers have paid significant attention to nanofluid because of their high rates of thermal conduction. Due to the widespread usage of these materials in several types of thermal transport devices, including nuclear reactor cooling, car generators, petrochemicals, industrial heating and cooling needs, as well as heat transfer technology. Applications for non-Newtonian liquid can be found in a wide range of fields, notably chemical nuclear reactor, paper manufacturing, petroleum engineering, processes, food processing, geophysics, biological sciences and many others. To determine the properties at different shear rates When the shear rate is significantly increased, a cross fluid model was developed to help with the difficulty. Main theme of existing work is to scrutinize the magneto-bioconvection aspects for 3D nonlinear material with triple stratification phenomenon. Additionally, we have examined heat-mass efficacy utilizing time-dependent thermal relaxation phenomenon and Buongiorno nanofluid model. It has been proposed that the horizontal stretching sheet has been inserted in Darcy-Forchheimer porous medium. Features of magnetohydrodynamics and activation energy are considered in cross fluid model. Furthermore, to improving the fluid's thermal properties, the combination of microorganisms (microbes) in nanofluids also causes the flow to be stable. With the implantation of similarity variables, we have transformed non-linear PDEs into non-linear ODEs. Utilizing bvp4c scheme (MATLAB pregame), the governing system of ODEs are solved. The tabular and graphical representations are used to illustrate the results. By raising the concentration relaxation and Brownian motion parameters, a considerable decrease in concentration profile is seen. The development of thermal Biot number and Forchheimer number approximations has advanced the temperature field, which is an interesting observation. The fluid's microorganism profile is assumed to be deteriorating based on Lb and δ1.

HARK formulation for entropy optimized convective flow beyond constant thermophysical properties

Background and objectiveOhmic heating has a pivotal role in food processing industry. For example, Ohmic heating in chocolate industry for cocoa beans shell is significant substrate for bioactive compounds recovery sustainability. In addition, the Soret and Dufour effects have importance in chemical and petroleum processes involving separation treatments, convective movements in lakes and solar ponds, solidification, humidity migration in building, drying processes, crystal growth and many others. In view of such applications here we discuss the hydromagnetic mixed convection flow with variable thermophysical properties. Formulation for Reiner-Rivlin material is made. Entropy generation in presence of dissipation, magnetohydrodynamics and radiation are discussed. Thermal relation consists of heat generation and dissipation. Soret and Dufour outcomes are under consideration. Ohmic heating is attended. Binary chemical reactive flow has been accounted. Convective conditions are implemented. MethodologyBy utilization of appropriate variables, we get the ordinary differential equations. ND-solve method is implemented to provide computations. ResultsEvaluation of different variables for flow, concentration, entropy rate and temperature are studied. Analysis of surface drag force and solutal and thermal transport rates via influential variables are examined. An augmentation in velocity is noted for variable viscosity and material parameters. Reverse effect holds for thermal field and flow with variation in magnetic variable. An intensification in thermal distribution and entropy is found through radiation and thermal Biot number. A reverse impact is observed for concentration through Schmidt and Soret numbers. Higher variable mass diffusivity parameter correspond to improves concentration and entropy rate. Brinkman number has increasing trend for entropy rate.

Time-independent three-dimensional flow of a water-based hybrid nanofluid past a Riga plate with slips and convective conditions: A homotopic solution

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

Mixed convection phenomenon for hybrid nanofluid flow exterior to a vertical spinning cylinder with binary chemical reaction and activation energy

The study of hybrid nanofluids over spinning cylindrical configurations is widely used in numerous engineering and technological applications. Compared to conventional coolants, nanofluids explore superior thermal conductivities and thereby promote outstanding heat transport capabilities. In this study, hybrid nanofluid flow and thermal transmission across a vertical spinning cylinder are examined in the presence of an externally applied transverse magnetic field. The working fluids used are Ag/water nanofluid and Al2O3-Ag/water hybrid nanofluid. The analysis of heat transmission is carried out in the presence of slip and convective conditions, nonlinear thermal radiation, activation energy, and viscous dissipation. Partial differential equations (PDEs) are used to model the physical situation and are subsequently transformed into ordinary differential equations (ODEs). Through the use of MATLAB's bvp4c technique for ODEs, graphical and computational results are produced and validated with previously reported studies. The important findings are that the flow field diminishes as the magnetic field parameter and Reynolds number increase. Further, for larger levels of nano particle's fraction and thermal Biot number, the thermal features increase. Moreover, it is noted that the mass diffusion rate is lowered by the system's activation energy.

Bioconvection analysis for convectively heated radiative flow of Sutterby fluid involving efficacy of ferromagnetic nanoparticles

In this article explained about the study 2-D Sutterby fluid model with suspension of microorganisms in ferrofluid, while radiation aspect is also considered here. Basic purpose of using microorganism is to obtain more stability in suspension. Here the important characteristics of thermophoresis parameter, viscous dissipation, magnetic interaction parameter and Brownian motion parameter are examined. Now, the system of non-linear P.D.Es is changed into set of O.D.Es then we solved these equations by using famous mathematical scheme bvp4c. Graphical results showed that temperature of Sutterby ferrofluid intensifies with increase in the estimations of thermal Biot number as well as radiation effects whereas results in reduction of Prandtl number. The density of microorganism reduces for greater values of Peclet number.

Entropy optimized flow subject to variable fluid characteristics and convective conditions

Background and objectiveNanofluids possess significant enhancement in nanomaterial properties such as convective heat transfer coefficient, thermal conductivity (which increases volumetric fraction of nanoparticles) and diffusivity at reasonable nanoparticle concentration. Nanofluids provide interesting new opportunities to develop nanotechnology-based operative coolants for different kinds of innovative applications. Hydromagnetic radiative flow of nanomaterial by curved stretched sheet is addressed in presence of Darcy-Forchheimer relation. Heat generation and dissipation are deliberated. Variable mass diffusivity and thermal conductivity behaviors are under consideration. Convective conditions are taken into account. Random diffusion and thermophoresis behaviors are considered. Dufour and Soret behaviors are taken. Binary chemical reaction and thermal radiation are explored. Entropy rate is taken into consideration. MethodologyNonlinear formulation is reduced to ordinary differential system. Convergent solutions for nonlinear ordinary systems are developed invoking Optimal homotopy analysis method (OHAM). ResultsImpacts for influential parameters regarding fluid flow, pressure, thermal distribution, entropy and concentration are discussed. Larger magnetic variable has reverse behavior on entropy rate and pressure. Higher magnetic field intensifies thermal distribution whereas reverse effect noted for liquid flow. Thermal distribution has increasing trend for Dufour number and variable thermal conductivity. Concentration reduces for random motion and Schmidt number. Concentration has increasing behavior for Soret number and variable mass diffusivity parameter. Larger estimation of thermal Biot number has same impact on thermal distribution and entropy. Increasing behaviors of entropy rate and concentration for solutal Biot number are observed. Bejan number reduces against Brinkman number whereas opposite trend holds for radiation parameter.

Heat transfer optimization and rheological features of Buongiorno nanofluid in a convectively heated inclined annulus with nonlinear thermal radiation

The theoretical analysis of the mixed convective Buongiorno nanofluid flow in an inclined annular microchannel with convectively heated walls subjected to the effects of nonlinear thermal radiation, exponential heat source (EHS), thermal dependent heat source (THS) is carried out. The description of the Buongiorno nanofluid is implemented to analyze the Brownian diffusion and thermo-migration mechanisms. The general boundary conditions for the velocity, thermal, and nanoparticle volume fraction (NVF) are considered. Numerical solutions for fully developed governing equations are obtained using bvp5c solver and verified with FEM. The optimization of heat transport rates is made by using the Box-Behnken design-based response surface method. It is found that the Lorentz force and the inclination angle of the annulus significantly affect the rheological characteristics of the nanofluid. Nanoparticles increase thermal energy in the system through Brownian diffusion and thermophoresis, resulting in increased temperature field. Internal heat sources would serve as an important tool for modulating the thermal field in microchannel, as they are directly associated. At low-level values of the thermal Biot number, the exponential heat source, and the thermal radiation parameter, it is possible to attain the maximum Nusselt number on both walls of the annulus.

Convective heat and mass transfer analysis on Casson nanofluid flow over an inclined permeable expanding surface with modified heat flux and activation energy

Due to the enormous advantages of nanofluid technology, the study of various nanofluid flows under different assumptions became an important research topic. Furthermore, Fourier proposed the basic heat flux law, and it has some initial disturbances. Later, Cattaneo and Christov modified the Fourier model by including the relaxation term and rectified the conflicts in the Fourier model. Current research explores the influence of activation energy on a chemically reactive Casson nanofluid over a stretching surface. Cattaneo–Christov heat and mass flux are considered for the investigation. The governing PDEs (partial differential equations) along with the boundary constraints are transformed into ODEs (ordinary differential equations) with the aid of suitable similarity variables and then solved numerically by the bvp5c MATLAB package. We have drawn the velocity, temperature, and concentration profiles. Also, plotted the isotherms and streamlines, and analyzed the effects of all the influential parameters on the flow regime. The increasing Casson fluid parameter leads to a decrease in the fluid velocity. Larger value of the Casson fluid parameter () recovers the results for the Newtonian fluid. The results obtained from the study show that the temperature shoots up for intensifying values of the magnetic parameter, radiation parameter, Eckert number, thermal Biot number, Brownian motion parameter, and the thermophoresis parameter; meanwhile the increase in the thermal relaxation parameter drops the temperature. The positive values of the heat source parameter decreases the rate of heat transfer by 10%. Also, we noticed that the effect of the growing values of the Schmidt number and the chemical reaction parameter is to decrease the concentration field. Moreover, a rise in the Reynolds and Brinkmann numbers pushes up the entropy generation.

Magneto-Bio-Convection Enhanced heat transfer in Prandtl hybrid nanofluid with inclined magnetization and microorganism migration

Keeping in view the applications of the hybrid nanofluids in the engineering and industries such as heating and cooling, food processing and heat generation, the focus of this investigation is to explore the effect of mixture base hybrid nanofluid with bio convection effect over linearly convectively heated stretched surface due to the motile micro organisms. The high thermal conductivity of the hybrid nanofluid play significant role in heat transmission. The effect of inclined magnetization on heat transfer of the hybridized bioconvective flow is also examined in this study. Prandtl hybrid nanofluid is used along with silver and magnetite nano-particles. The flow governing equations have been converted into dimensionless form through a suitable similarity transfer. The flow governing model equations are highly non linear and can’t be tackled analytically. Therefore, the formulated problem has been addressed using the BVP-4C technique. It was observed that when inclination angle of the magnetization is kept at 60 degrees and magnetic force is in the range of 0.5<M≤4, the velocity profile increase. Raising the level of bioconvection impact decline microorganism migration, on contrary high levels of Peclet number reverse this effect. Significant improvement has been observed in heat transfer shift and shear stress by raising thermal Biot number. The outcomes of the present study have been validated with already published results, the outcomes of our results were found in good agreement with previously published results.

Investigating effects of Lorentz forces and convective heating on ternary hybrid nanofluid flow over a curved surface using homotopy analysis method

Abstract This work investigates the ternary hybrid nanofluid flow over an extending curved surface. The surface is impermeable and convective with hot working fluid water. Additionally, TiO 2 {\text{TiO}}_{\text{2}} , CoFe 2 O 4 {\text{CoFe}}_{\text{2}}{\text{O}}_{\text{4}} , and MgO \text{MgO} nanoparticles are suspended with water to form a tri-hybrid nanofluid. The modeled equations are presented in the partial differential equation form and are then converted to ordinary differential equations with appropriate similarity variables. The semi-analytical solution is determined by homotopy analysis method. The impacts of magnetic field, Joule heating, chemical reaction, Brownian motion, and thermophoresis on flow profiles, Nusselt number, and Sherwood number are determined using tables and figures. The findings of this study demonstrated that as the magnetic parameter upsurges, the velocity distribution shrinkages, while the temperature distribution escalates. The greater curvature factor boots the velocity, thermal, and volumetric fraction distribution. The thermal and volumetric fraction distributions are the increasing functions of thermophoresis factor. The higher magnetic factor, Eckert number, and thermal Biot number increase the Nusselt number, while they reduce the higher Brownian and thermophoretic factors. The higher thermophoresis and Brownian motion factors heighten the Sherwood number. Furthermore, it has been noted that using nanofluid (TiO2-water) and hybrid nanoliquid (TiO2-CoFe2O4/water), the transfer of energy rate increases by up to 17.31 and 31.72% as the nanoparticle parameter increases from 0.01 to 0.04, respectively. However, the energy transference rate in case of ternary hybrid nanoliquid (TiO2-MgO-CoFe2O4/water) is 47.972%.

Unsteady Prandtl nanofluidic flow through stretching sheet due to mixed convection, first-order slip, and chemical reaction

This article explores the unsteady flow, heat, and mass transport of a Prandtl nanofluid flow over a stretching sheet due to the existence of mixed convection, first-order slip, and chemical reaction. The flow characteristics are analysed for the interaction of thermal and solutal Biot numbers. The system of coupled non-linear leading partial differential equations (PDEs) is converted into non-linear ordinary differential equations (ODEs) with the facilitation of given similarity transformations. Furthermore, these equations are solved by applying a semi-analytical method termed the “Optimal Homotopy Analysis Method” (OHAM) using the computational software MATHEMATICA. The tables and Figures present the numerical computations of the pertinent parameters of the flow problems. The essential findings of this study are for the growing values of the Prandtl parameter, the velocity profile is enhanced, and the temperature profiles show the opposite behaviour. Unsteady parameters reduced the thickness of the heat and moving boundary layers. The temperature profiles are enhanced as the thermal Biot number grows, and similar characteristics can be observed in the solutal Biot number on concentration profiles.

Oblique stagnation point flow of magnetized Maxwell fluid over a stretchable Riga plate with Cattaneo-Christov heat flux and convective conditions

The current work deals with the oblique stagnation point flow phenomenon of a rate-type Maxwell fluid with the significance of the Cattaneo-Christov double diffusion theory. The Cattaneo-Christov theory is illustrated through the modified form of Fourier’s and Fick’s laws. The steady magnetized flow mechanism is observed in two dimensions through a stretchable convective Riga plate. In the mass and heat transfer analysis, the consequences of chemical reactions and thermal radiation are also incorporated. With the contribution of relevant dimensionless quantities, the setup of dimensionless equations is acquired which further takes the form of nonlinear equations. The physical significance of the numerous parameters on different features of the flow phenomenon is graphically exhibited. The interesting physical quantities are computed and numerically evaluated relative to the pertinent parameters. This study reveals that the thermal relaxation time parameter lowers the rate of heat transfer, and the thermal Biot number enhances the rate of heat transport. Moreover, the Deborah number minimizes the flow field of both tangential and axial velocities.

Chemically reactive MHD convective flow and heat transfer performance of ternary hybrid nanofluid past a curved stretching sheet

One of the topmost challenges of today’s industry age is to find an efficient heat transfer fluid because heat transfer rate in common fluids is unable to provide an efficient heating and cooling process in the industries. Ternary hybrid nanofluids are considered as next generation heat transfer fluids, which are prepared by suspension of three different type of nanoparticles in the base fluids. This novel class of nanofluids, due to its unique and dynamic thermophysical properties, has diverse applications in numerous arenas of nanotechnology and heat transfer appliances. This research article examines an electrically conducting and magnetically influenced 2D flow of modified hybrid nanofluid past a curved stretching sheet. The considered trihybrid nanofluid contains nanometer sized particles of three different materials (CuO, Al2O3, TiO2) suspended in the water. The preliminary assumptions in this numerical investigation include the exponential heating, Brownian motion, chemical factor, and thermophoresis effects. At boundary, convective mass and heat flux constraints are employed. This pragmatic investigation with the aforementioned presumption is conducted for the first time to evaluate heat and mass transference properties of ternary nanofluid past a curved stretchable surface. The problem is mathematically modelled by using the fundamental momentum and energy equations and modified to cater the solid additives concentration in the base fluid. The modelled Partial Differential Equations (PDEs) are subsequently transformed into Ordinary Differential Equations (ODEs) by employing suitable similarity transformation and subsequently solved by the MATLAB software bvp4c to demonstrate role of important controlling parameters in tabular and graphical form. The research concludes that the enhancement of curvature factor enhances the velocity profile while the impact is opposite for magnetic factor. The most important and an interesting aspect of this innovative study is that the rate of heat transfer increases for all embedding parameters (ie M,K,Nb,Nt,Ec,Δt,β,BiT,BiCandQe), which is the basic purpose of using nanofluids for their promising use in nanotechnology. The study reveals that frictional force at the stretching surface decreases by reducing curvature of surface. However, converse trend is observed for increasing magnetic factor. Moreover, said impact of curvature is more prominent for ternary hybrid nanofluid whereas M has greater impact for unitary nanofluid. The greater heat source factor, activation energy, concentration and thermal Biot numbers, temperature difference and thermophoresis factors increase the concentration boundary layer while decreasing trend is observed for Brownian motion, Schmidt number and chemical reaction factor. The Nusselt number increases for higher values of thermal Biot number, thermophoresis parameter and the heat source factor.

ATSS model based upon applications of Cattaneo-Christov thermal analysis for entropy optimized ternary nanomaterial flow with homogeneous-heterogeneous chemical reactions

ATSS model for magnetohydrodynamic Darcy-Forchheimer radiative ternary nanoliquid flow by curved stretched sheet is constructed. Ternary nanoliquid consists of three different nanoparticles (gold (Au), zinc oxide (ZnO) and multi-walled carbon nanotube (MWCNT)) in ordinary liquid (Carboxymethylcellulose water (CMC-H2O)). Cattaneo-Christov heat flux and convective condition are discussed. Thermal equation has Ohmic heating, heat generation/absorption and radiation. Entropy production along with cubic autocatalysis chemical reaction is discussed. The obtained differential nonlinear systems are numerically computed by using ND-solve method. Graphical discussion for liquid flow, entropy rate and temperature via influential parameters for nanomaterial (Au/CMC-H2O), hybrid nanomaterial (Au+ZnO/CMC-H2O) and ternary nanomaterial (Au+ZnO+MWCNT/CMC-H2O) is organized. Computational outcomes for coefficient of skin friction and Nusselt number are studied. Opposite trend of velocity and skin friction for curvature is noticed. Velocity reduces against higher magnetic field. Augmentation for temperature against Eckert and thermal Biot numbers is noticed. Entropy production enhancement for radiation and diffusion parameter is observed. Thermal transport rate for radiation and thermal relaxation time has an increasing effect.