Thermal Biot Number Research Articles

A Comprehensive Analysis on Thermally Enhanced Electro-Magneto-Hydrodynamic Micropolar Flow Mixture Comprising Water (70%) and Ethylene-Glycol (30%) with Alumina Nanoparticles over a Riga Plate

In this research paper, a two-dimensional flow of an electro-magneto-hydrodynamic water-ethylene glycol-based nanofluid over a Riga plate has been presented. The nanofluid mixture has micropolar and electrical behaviors. Furthermore, the effects of chemical reaction and activation energy are imposed in the present investigation. It is important to mention that the nanofluid mixture is composed of alumina nanoparticles (Al2O3) and base fluid as water-ethylene glycol (70:30). It is important to mention that the significance of this study lies in engineering cooling systems, drug delivery, and microfluidic devices. The main equations of problem have converted to dimension-free form using similarity variables. The transformed ODEs are then converted into first-order differential equations and solved numerically by executing the shooting method. The validation on the modeled equations is confirmed by validating the present analysis with the results available literature. From this analysis, it is obtained that the greater micropolar parameter and modified Hartmann number enhanced the streamwise velocity profile while reducing micro-rotational velocity. The greater micro-gyration constraint reduced streamwise velocity profile while enhancing micro-rotational velocity. The greater thermophoresis factor and thermal Biot number enhanced both thermal and concentration profiles. The greater activation energy factor enhanced the concentration distribution, and the greater Brownian motion factor and Schmit number reduced the concentration distribution. The higher thermophoresis factor reduced the heat transfer rate, and the higher heat source factor and thermal Biot number enhanced heat transfer rate.

Bioconvection flow of Carreau nanomaterial invoking Soret and Dufour impacts

Background and objectiveThermal transport enhancement through nanomaterial flow has gained much attention of the investigators recently. Such attention is for applications in engineering, petroleum industries, geothermal engineering and pharmaceutical developments such as X-ray imaging, welding process, semiconductor material production, thermal storage system, electric cooling devices, drug delivery, magma solidification etc. In view of such interest here we analyze the bioconvective stretched flow of Carreau nanoliquid. Thermal, microorganism and mass convective constraints are considered. Gyrotactic microorganisms within presence of chemical reaction is considered. Variable thermal conductivity is considered. Dufour and Soret features are under consideration. Thermophoresis diffusion and random movement features are considered. Energy relation comprises heat generation and radiation. MethodologyNonlinear dimensionless expressions are developed by employing suitable transformations. Numerical computations are obtained by implementation of Newton built in-shooting technique. ResultsPerformance of liquid flow, concentration, microorganism field, and thermal field is studied. Numerical values of quantities of engineering performance via influential parameters are explored. Larger Weissenberg number yield velocity increase. Reduction in velocity through bioconvection Rayleigh number is witnessed. Concentration and thermal field through solutal thermal Biot numbers have similar effect. An increment in thermal distribution and Nusselt number for Dufour number is detected. Increasing values of Soret number and chemical reaction correspond to decay in concentration. An augmentation in thermal transfer rate and temperature through radiation is noticed. An increment in density number against Peclet and bioconvection Lewis numbers is noticed.

Heat transfer enhancement in magnetohydrodynamic hybrid nanofluids over a Bi-directional extending sheet with slip and convective conditions

The hybrid nanofluids can enhance cooling systems in microelectronics by enhancing heat dissipation from processes which makes them vital for maintaining optimal performance. They are also beneficial in solar systems where efficient heat transfer is essential for exploiting the energy detention. Thus, this study has studied the three-dimensional flow of a water-based hybrid nanofluid comprising of Fe3O4 and CuO nanoparticles on a bi-directional extending sheet. The bi-directional extending sheet is subjected to thermal convective and velocity slip conditions. In addition, the effects of heat source, magnetic field, thermal radiation, viscous dissipation, and Joule heating are employed. The partial differential equations (PDEs) that represent the mathematical model are subsequently converted to ordinary differential equations (ODEs) by applying the appropriate similarity variables. The shooting technique is incorporated to determine the computational solution of the converted ODEs. The effectiveness of the current study is confirmed by published results, which also validate the current outcomes. Based on the results, it is concluded that CuO and Fe3O4 solid nanoparticle volume fractions improved the thermal distribution while decreasing the velocity distributions along x and y-axes. The thermal distribution is improved by the thermal heat source, thermal radiation, thermal Biot number, and thermal Eckert numbers. CuO-water nanofluid has a higher velocity panel than CuO-Fe3O4/water hybrid nanofluid. Conversely, the CuO-Fe3O4/water hybrid nanofluid has a higher thermal profile than the CuO-water nanofluid. CuO-water nanofluid flow has higher surface drags than CuO-Fe3O4/water hybrid nanofluid flow. CuO-water nanofluid has a lower heat transfer rate than CuO-Fe3O4/water hybrid nanofluid.

Blood Based Magnetohydrodynamic Casson Hybrid Nanofluid Flow on Convectively Heated Bi-Directional Porous Stretching Sheet with Variable Porosity and Slip Constraints

Abstract Fluid flow through porous spaces with variable porosity has wide-range applications, notably in biomedical and thermal engineering, where it plays a vital role in comprehending blood flow dynamics within cardiovascular systems, heat transfer and thermal management systems improve efficiency using porous materials with variable porosity. Keeping these important applications in view, in current study blood based hybrid nanofluid flow has considered on a convectively heated sheet. The sheet exhibits the properties of a porous medium with variable porosity and extends in both the x and y directions. Blood has used as base fluid in which the nanoparticles of Cu and CuO have been mixed. Thermal radiation, space-dependent, and thermal-dependent heat sources have been incorporated into the energy equation, while magnetic effects have been integrated into the momentum equations. Dimensionless variables have employed to transform the modeled equations into dimensionless form and facilitating their solution using bvp4c approach. It has concluded in this study that, both the primary and secondary velocities augmented with upsurge in variable porous factor and declined with escalation in stretching ratio, Casson, magnetic and slip factors along x- and y-axes. Thermal distribution has grown up with upsurge in Casson factor, magnetic factor, thermal Biot number and thermal/space dependent heat sources while has retarded with growth in variable porous and stretching ratio factors. The findings of this investigation have been compared with the existing literature, revealing a strong agreement among present and established results that ensured the validation of the model and method used in this work.

Entropy generation minimization and activation energy in magneto-thermo-solutal stratified Ellis hybrid nanofluid flow through a stretching stenotic artery: Insights into cardiovascular disease

This article explores the impact of binary chemical reactions with activation energy on the flow of magnetized mono and hybrid nanofluids within a porous artery under the effects of viscous dissipation, nonlinear thermal radiation, and Joule heating. The main novelty of this study lies in considering a non-Newtonian Ellis fluid model of blood through a stretching stenotic artery consisting of gold (Au) and silver (Ag) nanoparticles. Additionally, velocity slip, convective temperature, and concentration boundary conditions are applied at the arterial surface. The proposed model compares the performance of Ag/Blood nanofluid and Au-Ag/Blood hybrid nanofluid models. The governing equations are solved using the bvp4c built-in solver in MATLAB, which employs advanced numerical techniques and algorithms tailored for BVPs, ensuring quicker convergence with minor errors and accurate solutions. Graphs are plotted for concentration, temperature, velocity, entropy minimization, skin friction coefficient, Nusselt number, and Sherwood number for various physical parameters. The results show that with increased nonlinear thermal radiation (0.1≤Nr≤2.0), thermal Biot number (0.1≤Bi1≤0.3), and Eckert number (0.01≤Ec≤0.2), the thermal distribution profile exhibits a rising trend. In contrast, with increasing fluctuations in the chemical reaction rate parameter (0.1≤Rc≤0.3) and Schmidt number (1.0≤Sc≤3.0), the concentration distribution profile exhibits a decreasing trend. In terms of mass and heat transfer efficiency, the Au-Ag/Blood hybrid nanofluid flow outperforms the Ag/Blood nanofluid model. More entropy is observed for Au-Ag/Blood compared to Ag/Blood in the stenotic artery. Heat energy may be created by targeting the injured area and avoiding harm to nearby tissues. Localized heating can widen arteries and increase blood flow to the affected locations, potentially aiding cardiovascular health management and personalized therapy. This study has various implications for the design of drug delivery systems, biophysical models, innovative materials, and our knowledge of fluid dynamics and heat transfer. However, nanofluid/hybrid nanofluid stability is challenging for current researchers since this modeled flow can be considered over a shrinking artery or in the trihybrid model in future studies.

A thermal performance study on magnetic dipole based viscoplastic nanomaterial deploying distinct rheological aspects

Magnetic nanoliquids stand inimitable when compared with conventional liquids as their distinctive magnetic attributes can be regulated utilizing magnetic fields. For this reason, heat transference can be stimulated or regulated subjected to externally imposed magnetic fields. Magnetic nanoliquids are useful in comparison to orthodox or non-magnetic nanoliquids. These encompasses, energy conversion, electronics, hydraulics, thermal engineering and bioengineering. This study elaborates the magnetic dipole impact on convectively heated rheological nanomaterial confined by stretchy surface. Mathematical modeling is based on thermally radiative viscoplastic (Casson) model. Porous medium features are scrutinized through Darcian Forchheimer (DF) relation. Two-component Buongiorno nanomaterial model which captures Brownian diffusive together with thermophoretic diffusion is under consideration. Energy and solutal transportation expressions capture thermal source and chemical reaction effects. The dimensionalized nanomaterial flow model for stretching flow is obtained by deploying similarity variables. Numerical solutions are computed through Bvp4c scheme. The physical outcomes are elucidated graphically and arithmetically on dimensionless quantities (i.e., Nusselt number, temperature, skin-friction, velocity, Sherwood number and concentration streams). A benchmark is reported to authenticate the acquired numeric solutions. It is further visualized that nanomaterial temperature escalates subject to higher estimations of thermal Biot number, Curie temperature factor, radiation factor, thermophoresis parameter, heat source, ferrohydrodynamic interaction factor and Brownian diffusive parameter while it diminishes with Prandtl number and dissipation factor.

A comparative analysis on the dynamics of solid-liquid interfacial layer and nanoparticle diameter of magnetohydrodynamic nanofluid flow containing spherical and cylindrical-shaped alumina nanoparticles over a stretching curved surface

In this work, a comparative analysis on magnetohydrodynamic nanofluid flow containing spherical and cylindrical-shaped alumina nanoparticles over a stretching curved surface is mainly focused. The effects of Brownian motion, Joule heating, thermophoresis, chemical reaction and activation energy are taken into consideration in this work. It is important to mention that this analysis considers a 4 % volume fraction of the alumina nanoparticles. A thermal convective and zero-mass flux conditions are imposed to scrutinize the heat transfer analysis. The leading equations are transformed into dimensionless form by using suitable similarity variables. A numerical solution is obtained using the shooting technique. The acquired outcomes depict that greater magnetic factor enhances the skin friction coefficient. The greater magnetic factor, thermal Biot number, Eckert number, and interfacial layer thickness augment the heat transfer rate, while a greater nanoparticle diameter diminishes the thermal transfer rate. A higher magnetic factor has an increasing impact on thermal distribution and a reducing impact on velocity distribution. A greater curvature factor enhances both the velocity and thermal distributions. The concentration distribution is enhanced by the higher interfacial layer thickness and activation energy factor, while it is reduced by a higher nanoparticle diameter, Brownian motion factor, and chemical reaction factor. From the comparative analysis, it is found that the velocity, thermal, and concentration distributions are higher for the cylindrical-shaped nanoparticles compared to spherical-shaped nanoparticles.

Thermal transport analysis for ternary hybrid nanomaterial flow subject to radiation and convective condition

Ternary nanomaterials are now recognized as useful not only for thermal efficiency importance but also to enhance physical characteristics of liquids. Insertion of three nanoparticles in base liquid is characterized as ternary hybrid nanomaterial. Such materials have better magnet properties, electrical conducting and mechanical resistance. Here we discuss three-dimensional magnetized stretched flow of ternary nanofluid through porous space is addressed. Porous space is scrutinized by Darcy-Forchheimer relation. Convective condition is imposed. Nanoparticles here include copper, polyphenol coated and aluminum oxide and water as conventional liquid. Energy equation consists of radiation, magnetohydrodynamics, dissipation and heat generation. Resulting dimensionless system is computed by Newton built in-shooting technique. Outcomes of velocity, temperature, skin friction and Nusselt number for emerging parameters of interest are organized. Comparison of results for ternary nanofluid (CoFe2O3+Cu+Al2O3/H2O), hybrid (CoFe2O3+Cu/H2O) and nanofluid (CoFe2O3/H2O) is examined. It is found that temperature and velocity against Hartman number have reverse trends. Temperature and Nusselt number for radiation have increasing features. Similar characteristics for temperature through heat generation and Eckert number is noticed. Larger thermal Biot number corresponds to rise the Nusselt number and temperature. An increase in temperature through Forchheimer number is witnessed while reverse trend holds for velocity.

The impact of double‐diffusive convection on electroosmotic peristaltic transport of magnetized Casson nanofluid in a porous asymmetric channel

AbstractThe primary objective of the present article is to investigate the heat and mass transfer in mixed convection peristaltic flow of Casson nanofluid through an asymmetric permeable channel filled with a porous medium in the presence of electroosmosis. Magnetohydrodynamics and radiative heat transfer are also considered. The study is motivated by industrial micro‐pumping systems utilizing multi‐functional nanomaterials. Researchers have investigated the distinct temperature and rheological properties of Casson nanofluids. Solutal molecular diffusion and nanoparticle diffusion are both examined. Mixing nanoparticles with Casson fluid alters its flow characteristics and heat transmission, amalgamating different properties that are useful in a wide range of industrial and scientific applications. Buongiorno's two‐component nanoscale model is deployed for simulating nanofluid transport, and the Rosseland diffusion flux is utilized for optically thick electromagnetic liquids. Heat generation or absorption and cross‐diffusion (Soret and Dufour) effects are also incorporated in the model. An efficient analytical approach known as the long wavelength‐low Reynolds number lubrication approximation (LWL‐LRN) is utilized to solve the non‐dimensional boundary value problem. Validation of the solutions with previous studies is included. Graphs are presented using MATLAB 2022b to visualize the influence of key parameters including permeability, magnetic field, thermal radiation, Grashof number, Brownian motion, thermophoresis, electrical field and Prandtl number on transport characteristics (velocity, temperature, concentration), and trapping phenomena associated with peristaltic propulsion. As thermophoresis and Brownian parameters are intensified, there is a strong response in nanoparticles which induces axial acceleration, as observed at locations y = 0.15, where u = 0.191, and y = 0.33, where u is elevated to 0.14. An increase in radiation parameter () results in a depletion in axial velocity magnitudes along the left half of the wall and also modifies velocity distribution in the right section of the microchannel. An increase in the thermal radiation parameter (Rn) and heat absorption (sink) is found to suppress temperatures. Increasing heat generation, thermal Grashof number (Gr), and solutal Grashof number (Gc) decelerate axial flow in the left half space but accelerate flow in the right half space of the micro‐channel. Increasing radiation parameters and thermal Biot number boost temperatures when heat sink is present but reduce them when heat source (generation) is present. Increasing radiation parameter boosts nanoparticle volume fraction (concentration) whereas an elevation in heat generation and thermal Biot number both induce the opposite effect. Increasing the magnetic field damps the flow and reduces the number of boluses present. However, bolus volume increases with greater thermal Grashof Number , Darcy (permeability) number , and Helmholtz‐Smoluchowski velocity , that is, stronger axial electrical field.

Mixed convective magneto flow of nanofluid for the Sutterby fluid containing micro-sized selfpropelled microorganisms with chemical reaction: Keller box analysis

The current work aims to scrutinize the bioconvection Sutterby nanofluid flow of the Cattaneo-Christov heat and mass flux over a rotating disk. The effects of thermophoresis and Brownian motion receive considerable consideration. The process of analyzing heat and mass transfer phenomena involves taking into account the impacts of thermal radiation and chemical reactions that are susceptible to convective boundary conditions. Firstly, we reduce the PDEs of the physical model to ODEs through alter transformation and then numerically solved the transformed ODEs using Keller Box technique. An analysis of numerical data follows to ascertain the role of numerous flow variables on the flow profiles. Based on the findings, it is evident that an increase in the fluid variable Δ and the porous variable K leads a decrease in the, radial F'(ζ), axial F'(ζ) and tangential G(ζ) velocities. Furthermore, we find that the growing values of the thermal radiation Rd variable and the thermal Biot number B T greatly aid in raising the fluid’s temperature. Concentration profile shows decreasing behavior for rising values of Schmidt number Sc but upsurge for solutal Biot number B C . The microorganism is decayed with greater Lewis number Lb and Peclet number Pe.

A numerical investigation of the magnetized water-based hybrid nanofluid flow over an extending sheet with a convective condition: Active and passive controls of nanoparticles

Abstract This study presents a numerical investigation of a viscous and incompressible three-dimensional flow of hybrid nanofluid composed of Ag and Al2O3 nanoparticles over a convectively heated bi-directional extending sheet with a porous medium. The main equations are converted into dimensionless form by using appropriate variables. The effects of magnetic field, porosity, Brownian motion, thermophoresis, and chemical reaction are investigated. Furthermore, the mass flux and zero-mass flux constraints are used to study heat and mass transfer rates. The obtained data show that the growing magnetic factor has reduced the velocity profiles while increasing the thermal profile. The increased porosity factor has decreased the velocity profiles. The increased thermal Biot number has increased the concentration and thermal profiles. When compared to passive control of nanoparticles, the hybrid nanofluid flow profiles are strongly influenced by the embedded factor in the active control of nanoparticles.

A homotopic analysis of the blood-based bioconvection Carreau–Yasuda hybrid nanofluid flow over a stretching sheet with convective conditions

Abstract The time-independent and incompressible blood-based hybrid nanofluid flow, including Au and Cu nanoparticles across an expanding sheet, has been studied. To illustrate the non-Newtonian performance of the blood-based hybrid nanofluid flow, a non-Newtonian model known as the Carreau–Yasuda model is used. The hybrid nanofluid flow is studied under the influence of magnetic effects, thermal radiation, Brownian motion, thermophoresis, and chemical reactivity. Homotopy analysis method (HAM) is employed to evaluate the modeled equations. A study is conducted on the convergence analysis of HAM, and the HAM and numerical analyses are compared. From the present analysis, the velocity profile increases with an increase in Weissenberg number and decreases with increasing magnetic factor. The temperature, concentration, and microorganisms profiles increase in tandem with the higher thermal Biot, concentration Biot, and microorganism Biot numbers. The thermal and concentration profiles, respectively, have decreased due to the larger thermal and concentration relaxation time factors. The microorganism profiles have decreased due to the increased bioconvection of Lewis and Peclet populations. The modeled equations can be solved by both the HAM and the numerical approaches, validating both approaches to solution.

Nanoparticle aggregation kinematics and nanofluid flow in convectively heated outer stationary and inner stretched coaxial cylinders: Influenced by linear, nonlinear, and quadratic thermal radiation

The consequence of nanoparticle aggregation and convective boundary condition on the nanofluid stream past the co-axial cylinder with radiation impact is investigated in the present examination. The influence of linear, nonlinear, and quadratic thermal radiation on the nanofluid flow is analyzed. The outer cylinder stays stable, while the inner cylinder deforms horizontally in the axial direction, allowing fluid to flow. By using similarity variables, the governing equations are transformed into ordinary differential equations (ODEs). Subsequently, the Runge–Kutta–Fehlberg fourth-fifth order (RKF-45) method is employed to solve the reduced ODEs. The upshot of several nondimensional terms on the temperature and velocity profiles is displayed with graphical representation. The comparison of linear, quadratic, and nonlinear thermal radiation on the thermal profile is illustrated. The upsurge in curvature parameter increases velocity and thermal profile. The increase in radiation parameter intensifies the temperature profile. The thermal profile improves with a rise in the values of radiation parameter. The radiation parameter generates thermal energy in the flow zone, which is why the temperature field has improved. The thermal Biot number exhibits an increasing response with temperature and thermal boundary layer thickness. The linear thermal radiation shows better heat transfer compared to quadratic and nonlinear thermal radiation.

Soret and Dufour impacts in entropy optimized MHD flow by third-grade liquid involving variable thermal characteristics

Soret and Dufour impacts for third-grade liquid flow are examined. MHD (magnetohydrodynamics), Joule heating, and thermal radiation are studied. Properties beyond constant thermophysical characteristics are discussed. Convective condition of mass and heat transfer is addressed. First-order chemical reaction with entropy generation is deliberated. Finite difference method is implemented. Analysis for involved variables about quantities of interest is organized. The findings show that velocity for material parameters of fluid has increasing trend. Suction variable yields to decay in velocity. Radiation and suction variables reveal enhancement in temperature whereas higher Dufour number lower thermal field. Higher thermal Biot number improved temperature. Higher magnetic field and radiation variables enhance entropy generation rate. Nusselt number against radiation has deceasing behavior whereas Sherwood number for reaction rate shows opposite trend.

Simulation of hybrid boiling nano fluid flow with convective boundary conditions through a porous stretching sheet through Levenberg Marquardt artificial neural networks approach

In the domain of artificial neural networks, the Levenberg-Marquardt technique stands out for its innovative approach and convergent stability. It generates a numerical approach for the progression of a hybrid Cu–Al2CO3/water nanofluid on a porous stretched sheet (HNF-PSS), employing regression plots, state transition measures, histogram representations, and mean squared errors. This work explores the analysis of the fluid flow problem associated with HNF-PSS, introducing a novel application of an intelligent computing system that utilizes the effectiveness of neural networks trained by the Levenberg-Marquardt algorithm (NN-TLMA). The initial mathematical expression, expressed in terms of partial differential equations (PDEs) for HNF-PSS, undergoes transformation into dimensionless nonlinear ordinary differential equations (ODEs). The collection of data for the envisioned NN-TLMA involves parameters influencing the velocity of the HNF-PSS system model, generated using the Lobatto IIIa formula. The efficacy of the suggested NN-TLMA for solving the HNF-PSS is robustly verified by examinations of state transition dynamics, regression analyses, mean square error, and error histogram studies. The consistent alignment of the obtained results with corresponding solutions attests to the legitimacy of the structure, achieving a high level of accuracy within the range of 10–6 to 10–8. Insightful findings demonstrate that the thermal Biot number contributes significantly to an upsurge in fluid temperature. Furthermore, an augmentation in nanofluid concentration and thermal profile is found to increase the porosity strength of the medium. Nevertheless, an attenuation in the velocity profile is noted under these conditions. The application of this simulation work can be found in optimizing the designs of heat exchanger, in biomedical application and in renewable energy processes.

Radiative bioconvective flow with non-uniform heat source and Soret and Dufour impacts

Background and objectiveThe stretched flow with heat transfer has pivotal role in geothermal energy system, oil extraction, continuous casting, metal spinning and electronic cooling. Owing to this fact, the current analysis focuses on non-linear thermal radiation effect in bio-convective stagnation point flow by a stretchable wedge. Darcy relation is used to discuss the porous space. Convective conditions are deliberated. Non-uniform heat source is addressed. Soret and Dufour outcomes are analyzed. Dissipation and magnetohydrodynamics are discussed. Presence of gyrotactic microorganisms along with chemical reaction is considered. MethodologyRelated non-linear partial differential equations (PDEs) are reduced into dimensionless ordinary differential equations (ODEs) through adequate transformations. Optimal homotopy analysis method (OHAM) is adopted for the computations of related nonlinear differential systems. ResultsFlow, microorganism field, concentration and temperature distribution are graphically explored. Numerical analysis for coefficient of skin friction, microorganism density number and Sherwood and Nusselt numbers against emerging parameters are discussed. It is noted that velocity and skin friction coefficient have similar scenario for modified Hartman number. Thermal transport rate and temperature have reverse trends for non-uniform heat source variable. An augmentation in thermal distribution is seen through thermal Biot number. Larger Dufour number has increasing trend for temperature. An increasing trend for solutal Biot number for concentration is noticed. Larger Soret number leads to concentration enhancement. Microorganism field and motile density number against Peclet number have opposite response. There is reduction for bio-convective Lewis number in motile density number.

Bödewadt flow of thermally radiative hybrid nanofluid under the implication of horizontal magnetic field

It is a known fact that the implication of uniform magnetic field in transversal direction to fluid flow concerns the stabilization of velocity field and deterioration of heat transfer rate. It is now recognized that the applied uniform horizontal magnetic field is useful for stabilizing/destabilizing the flow rate, which is principally rely upon the direction angle such as cooling/heating the disk surface. Considering this, the present study investigates an incompressible three-dimensional Bödewadt flow above a stretchable with an implication of horizontal magnetic field. The Bödewadt flow defines a uniform and stable angular movement of fluid at sufficient large distance from the stationary surface. Such flow is balanced by the Centrifugal forces and is featured through radial pressure gradient. The radiative heat transfer attributes are characterized by the hybrid nanofluid, which is composition of Copper ( Cu ) and Titanium Dioxide ( Ti O 2 ) with water ( H 2 O ) as base fluid. A well-known approach of similarity variables is adopted to first normalize the flow model and then the resultant system of coupled non-linear ordinary differential equations is solved by Runge-Kutta-Fehlberg (RKF) MATLAB built-in package. The graphical results on flow and thermal fields are sketched for different values of dimensionless quantities. It is observed that direction angle in terms of horizontally applied magnetic field has stabilizing impact along radial axis close to the 0 ° or 90 ° , whereas destabilizing influence of direction angle is noticed between 30 ° − 60 ° . The temperature field is enhanced by the enlarged parametric values of thermal Biot number and solid volume fractions. Local Nusselt-number is increased at the disk surface by the radiation parameter.

Enhancing thermal efficiency in MHD kerosene oil-based ternary hybrid nanofluid flow over a stretching sheet with convective boundary conditions

The increasing demand for thermal management due to the high heat density heat exchangers for different technological and industrial processes draw the attention of researchers in heat transfer analysis to investigate the simultaneous solution to this problem. Keeping this in mind, the current work addressed the utilization of ternary hybrid nanofluid, a mixture of graphene oxide with silver and copper, to examine the heat and mass transfer enhancement of MHD Maxwell fluid. In the current model, the author discussed heat and mass transfer analysis of Maxwell MHD ternary hybrid nanofluid flow across a porous medium over an extending sheet. The energy and concentration equations are expressed to include the effects of Brownian motion and thermophoretic diffusion. Additionally, the effects of thermal radiation, activation energy, chemical reactions, and convective boundary conditions are considered. The similarity transformations are used to convert the nonlinear PDEs into ODEs. The impact of embedded factors on velocity, temperature, and concentration profiles is perceived graphically and mathematically by using the HAM technique. The convergence of computed solutions is ensured by h-curves. The significant outcomes from the analysis expressed that the flow distribution increases with slip and suction/injection factors. The concentration of the ternary hybrid nanofluid increases with an increase in thermophoretic diffusion (0.1–0.5), thermal biot number, and solutal biot number (0.1–0.5), however, a declining behavior is perceived with rising quantity of Schmidt number (0.6–0.8) and Brownian motion (0.1–0.5) parameters. Nusselt number shows a dominant behaviour with a higher magnetic factor. Similarly, the skin friction increases with an increase in thermal biot number and thermophoresis factor. It is revealed that the skin friction along x− direction increases from (0.78138, 0.833702, 0.897022, and 0.972526) for ternary hybrid nanofluid. Nusselt number increases from 2 to 5% (0.208936, 0.214288, 0.219799, 0.22555) when the volume fraction varies from 0.01 to 0.04 respectively.

Mathematical Simulation for MHD Casson Convective Nanofluid Flow Induced by 3D Permeable Sheet with Chemical Effect

Objectives: Current manuscript focuses on examination of chemical reaction and heat generation impacts on 3D MHD non-Newtonian nanofluid flow with convective boundary conditions induced by permeable sheet. Additionally, Brownian motion, non-Newtonian heating and thermophoretic processes as used for this study. Methods: A computational programme, MATLAB has been used for solving the system of O.D.Es with the help of ODE45 solver. The Runge Kutta Fehlberg approach is implemented to calculate the answer to the expression for temperature, velocity, and nanoparticle concentration after the shooting process. Findings: For a variety of fluid parameters, the temperature, concentration of nanoparticles, and dimensionless velocities are shown and examined, including permeability parameter , magnetic , stretching ratio parameter , Lewis number , Brownian motion and Prandtl number , thermal Biot number , Casson fluid parameter , chemical reaction parameter . The temperature is found to increase with an enhance in the thermal Biot number and to reduce with a greater Prandtl number and stretching ratio parameter. Novelty: Although the immense significance and frequent use of nanofluids in industries and technology, no effort has been made to explore the chemical influence on MHD Casson fluid flow using a three-dimensional permeable sheet. Through similarity transformations, the Runge-Kutta Fehlberg technique converts mass, momentum, and energy conservation equations into ODEs and incorporates boundary conditions. Skin friction and the heat transmission rate past an extending surface, which have an impact on technology and production, can be predicted using the results of this study. Keywords: Chemical reaction, Buongiorno's model, Nanofluid, Biot numbers, 3D permeable sheet

Study of Nano-Powell-Erying fluid flow past a porous stretching sheet by the effects of MHD, thermal and mass convective boundary conditions

The object of this research is to examine the combined effects of mass and thermal Biot numbers on the properties of a Powell-Erying fluid flow that is two-dimensional, constant, viscous, incompressible, and non-Newtonian. In the direction of the flow is an extending sheet encircled by a porous medium. Further consideration is given to the existence of a chemical reaction, thermophoresis, Brownian motion, and velocity lapse, among other factors. Utilizing the Powell-Erying Cauchy non-Newtonian model, the viscoelastic effect is accounted for. When establishing concentration and temperature boundary conditions, thermal and mass Biot numbers are incorporated. By utilizing graphs, one can examine the impacts of a variety of engineering parameters on concentration profiles, velocity, and temperature. This is accomplished through the implementation of numerical solutions derived via the Runge–Kutta method. By utilizing graphs, one can examine the impacts of a variety of engineering parameters on concentration profiles, velocity, and temperature. This is accomplished through the implementation of numerical solutions derived via the Runge–Kutta method. Furthermore, the Nusselt number, Skin-friction, and Sherwood number coefficients are evaluated and shown in a tabular format utilizing the same parameters. In the end, the numerical outcomes obtained from this investigation are substantiated and considered to be highly consistent with the findings that were previously documented.