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In this paper, squeezing transport of radiative water conveying aluminum alloys (i.e., AA7072 and AA7075) mobilized by entropy generation and dissipative energy is analyzed. Problem is formulated in a rotating frame with the consideration of magnetohydrodynamics and Joule heating aspects. Maxwell model for nanofluid has been used to incorporate the thermophysical properties of nanoelements. Formulated governing expressions have been transformed into system of ODEs by introducing similarity variables. The transformed system of ODEs is then numerically solved by Runge–Kutta–Fehlberg (RKF) method based on shooting background. The physical quantities (i.e., skin-friction coefficient, Nusselt and Bejan numbers) of scientific interest are formulated and illustrated via various plots. Graphical representations of squeezing function, temperature profile and velocity profile have been made to examine the effects of involved parameters. Streamlines and isotherms patterns have been formed and discussed. To authenticate the validity of model, skin-friction values have been compared with published literature for limited version of the model. Entropy and temperature of the system are improved with the involvement of aluminum alloys in water. Symmetrical behavior of streamlines is observed for positive approach of squeezing parameter. [ABSTRACT FROM AUTHOR]

Purpose: Nonlinear mixed-convective entropy optimized the flow of hyperbolic-tangent nanofluid (HTN) with magnetohydrodynamics (MHD) process is considered over a vertical slendering surface. The impression of activation energy is incorporated in the modeling with the significance of nonlinear radiation, dissipative-function, heat generation/consumption connection and Joule heating. Research in this area has practical applications in the design of efficient heat exchangers, thermal management systems or nanomaterial-based devices. Design/methodology/approach: Suitable set of variables is introduced to transform the PDEs (Partial differential equations) system into required ODEs (Ordinary differential equations) system. The transformed ODEs system is then solved numerically via finite difference method. Graphical artworks are made to predict the control of applicable transport parameters on surface entropy, Bejan number, Sherwood number, skin-friction, Nusselt number, temperature, velocity and concentration fields. Findings: It is noticed from present numerical examination that Bejan number aggravates for improved estimations of concentration-difference parameter a_2, Eckert number E_c, thermal ratio parameter ?_w and radiation parameter R_d, whereas surface entropy condenses for flow performance index n, temperature-difference parameter a_1, thermodiffusion parameter N_t and mixed convection parameter ?. Sherwood number is enriched with the amplification of pedesis-motion parameter N_b, while opposite development is perceived for thermodiffusion parameter. Lastly, outcomes are matched with formerly published data to authenticate the present numerical investigation. Originality/value: To the best of the authors' knowledge, no investigation has been reported yet that explains the entropic behavior with activation energy in the flowing of hyperbolic-tangent mixed-convective nanomaterial due to a vertical slendering surface. [ABSTRACT FROM AUTHOR]

In this study, an investigation is made to evaluate the heat transport properties of Casson fluid over an infinite flat plate. Initially, the plate accelerates within its plane, only to gradually decelerate until it comes to a complete stop. This variation in plate velocity introduces a dynamic component to the problem, enriching the understanding of heat transport phenomena. To accurately convert the governing partial differential equations, the study employs a mathematical transformation that converts them into a set of coupled nonlinear ordinary differential equations (ODEs). The numerical solution of these ODEs is carried out using the computational software MAPLE 2022, with a stringent convergence control threshold set at 10−6. This numerical approach ensures precision in analyzing the complex fluid dynamics and heat transfer phenomena under consideration. The study contributes to understanding heat transport in Casson fluids, especially in scenarios involving plate acceleration and deceleration. [ABSTRACT FROM AUTHOR]

Convective heat and mass transport of radiative Williamson hybrid (SWCNT + MWCNT) nanofluid (NF) by a Riga surface with the novel features of Cattaneo–Christov double-diffusion has been investigated. Thermal contributions of internal heat mechanism and Arrhenius energy in Darcy–Forchheimer medium have also been incorporated in the modeling. Mathematical modeling has been completed by using suitable mathematical expressions for thermophysical features of hybrid nanofluid (HNF). Transport partial differential equations (PDEs) have been transformed into ordinary differential equations (ODEs) by means of similarity variables. Numerical approximation of the transformed system has been obtained by using shooting-based Runge–Kutta–Fehlberg approach. Results have been presented through various graphs and discussed physically in detail. Solution is validated for limited cases. Concentration of the hybrid mixture is reduced for progressive concentration-relaxation parameter. Temperature is alleviated for developing thermal-relaxation parameter. Nusselt number is observed to be higher for Williamson HNF than simple ordinary NF. [ABSTRACT FROM AUTHOR]

The influence of thermal radiation and Joule heating on the entropy inception by triple diffusion over the permeable plate is examined, as well as its influence on other physical aspects of the problem. The radiative and Joules heating effects are being investigated using a mathematical model. The irreversibility caused variations in entropy inception due to fluid, heat fluxes, and solute concentration of salts utilized. The non-dimensioned modeled equations were interpreted numerically by shooting approach using Runge-Kutta-Fehlberg scheme. Numerical outcomes were plotted in the form of graphs for flow and thermal distributions, entropy inception rate, and Nusselt number because of suction/injection through the plate, and the results of concentration based parametric analysis were plotted out for local entropy inception rate, local Bejan number, local mass Bejan number and local irreversibility ratio based on assisting flow and opposing flow. Local mass Bejan number underwent some interesting aspects, such that it behaves opposite to local Bejan number to enhance for magnetic, radiation parameter in suction/injection situations. In the suction/injection flow conditions, the entropy inception rate gets enhanced for most of the flow and thermal parameters like magnetic, radiation, convective parameters, Eckert number, buoyancy parameters of solutes 1 and 2, and temperature ratio parameter. Because of influences of assisting and opposing flow, the entropy inception rate gets slowed down by the effects of Lewis numbers of solutes 1 and 2 and Darcy number. Reynolds number has the influence assisting the entropy rate to increase. [ABSTRACT FROM AUTHOR]

The present theoretical investigation is conducted on a micropolar fluid medium channel in the presence of mixed and nonlinear convection with the assumptions of thermal radiation and species reactive agents. The nonlinear governing equations, which describe the micropolar fluid flow and energy, are converted into ordinary differential equations using appropriate similarity variables. With the Runge–Kutta–Fehlberg method, the resultant equations are numerically solved. The physical characteristics of flow restrictions over velocity, microrotation, energy, and concentration profile are plotted and discussed. Further, the impact of several dimensionless parameters on Nusselt and Sherwood numbers is investigated and depicted graphically. In addition to observing flow patterns, contour plots of streamlines are plotted and discussed. It is demonstrated that the dimensionless velocity, temperature, and concentration of micropolar fluid have a maximum value at the center of the channel. However, the microrotation velocity of the micropolar fluid has both maxima and minima. The thermal and solutal properties of micropolar fluid influence heat and mass transport rates, that is, mixed convection and buoyancy parameter boost up the local heat transfer at the surface. Finally, Péclet number and chemically reactive parameters boost up the local mass transfer at the surface. [ABSTRACT FROM AUTHOR]

The numerical simulations are performed to investigate the electro-osmotic peristaltic flow of Prandtl fluid in the presence of tiny particles in a planner channel. The analysis is performed in the presence of slip effects, magnetic force and Joule heating. The governing nonlinear boundary value problem along with nonlinear boundary conditions is solved numerically using Keller Box method as well as numerical shooting technique by using the MATLAB tool. The solution validity is also ensured by computing the solution with BVP4C solver. The results claimed from analysis convey that concentration profile declined with concentration slip while an increasing trend for concentration has been noted for Soret number. The presence of slip factor reduces the magnitude of skin friction coefficient. With increasing the Grashof number and in the presence of electric forces, the temperature profile reduces. The Nusselt number increases with electro-osmotic parameter while reverse observations are predicted for Sherwood number. [ABSTRACT FROM AUTHOR]

In the current communication, three‐dimensional Williamson fluid flow past a bidirectional inclined stretching plate with novel Hall current, nonuniform heat source/sink, and nth‐order chemical reaction features are investigated. Rosseland's diffusion model is defined for the radiation heat transfer. The nonlinear governing derivative equations satisfying the flow are transmuted to the coupled derivative equations by employing the local similarity quantities and then solved numerically through the Runge–Kutta–Fehlberg method utilizing the shooting quadrature. An inclusive analysis is reported via graphs for the flow rate field, temperature, and concentration distributions for different evolving terms of immense concern. Wall dragging effect and wall heat gradient and wall concentration gradient have been examined, plotted, and described. The detailed geometry reveals that dimensionless velocity field is monotonically rising as the Hall parameter rises. The chemical reaction concentration for the Williamson fluid is enhanced with expanding values of the magnetic field parameter. Transitional values of wall stress components upturn with an increase in Hall parameter while the Williamson term is boosted. Nusselt number is reduced as the Williamson term rises and the Sherwood number enhances with a rising chemical reaction term. The results are verified for limiting cases by comparing with various investigations and found to have excellent accuracy. [ABSTRACT FROM AUTHOR]

The current paper on carbon nanotubes suspended magnetohydrodynamics micropolar dusty nanofluid impinging on a permeable extending sheet placed in a porous regime. The Darcy–Forchheimer scheme with heat source/sink and thermal radiation is taken into account. The shooting method is instrumental for obtaining numerical solutions of the transformed-converted system of nonlinear equations. The prescribed surface temperature (PST) and prescribed heat flux (PHF) boundary conditions are used. The impact of governing parameters on velocity, temperature, skin friction coefficient, Nusselt number, entropy generation rate and Bejan number are incorporated. The significant outcomes of the current investigation are that increment in the suction parameter decline the flow velocity and temperature (for both PST and PHF cases) while the injection uplift them. An enhancement in magnetic strength, the skin friction and heat transfer rate show the opposite trend for both SWCNT and MWCNT. Bejan number is increasing with the increase in nanoparticle volume fraction ϕ for both SWCNT and MWCNT. [ABSTRACT FROM AUTHOR]

The current investigation aims to explore the combined effects of heat and mass transfer on free convection of Sodium alginate-Fe3O4 based Brinkmann type nanofluid flow over a vertical rotating frame. The Tiwari and Das nanofluid model is employed to examine the effects of dimensionless numbers, including Grashof, Eckert, and Schmidt numbers and governing parameters like solid volume fraction of nanoparticles, Hall current, magnetic field, viscous dissipation, and the chemical reaction on the physical quantities. The dimensionless nonlinear partial differential equations are solved using a finite difference method known as Runge-Kutta Fehlberg (RKF-45) method. The variation of dimensionless velocity, temperature, concentration, skin friction, heat, and mass transfer rate, as well as for entropy generation and Bejan number with governing parameters, are presented graphically and are provided in tabular form. The results reveal that the Nusselt number increases with an increase in the solid volume fraction of nanoparticles. Furthermore, the rate of entropy generation and Bejan number depends upon the magnetic field and the Eckert number. [ABSTRACT FROM AUTHOR]

A numerical investigation has been conducted to investigate the steady forced convection boundary layer nanofluid flow past a horizontal circular cylinder placed in water-based copper (Cu) and alumina (Al 2 O 3 ) nanofluids. Using appropriate transformations, the system of partial differential equations is converted into an ordinary differential system of three equations, which is solved numerically using Keller box and Newton-Raphson methods. The effects of thermal and solutal convective boundary conditions are taken into account which makes the present analysis practically applicable. Numerical results are obtained for the dimensionless velocity, temperature and concentration as well as the skin-friction, Nusselt and Sherwood numbers for specific values of the governing parameters with fixed Prandtl number ( Pr = 6.2) and Schmidt number ( Sc = 0.68) for water. It is shown that, for a regular fluid ( ϕ = 0), a very good agreement exists between the present numerical results and those reported in open literature. [ABSTRACT FROM AUTHOR]

A theoretical study is presented for the coupled thermo-solutal free convection two-dimensional boundary layer flow of a of a magnetized fluid from an exponentially stretched magnetic sensor (Riga plate) surface. Heat generation/absorption, nonlinear thermal radiation and thermophoretic body force effects are included. Furthermore, thermal and solutal stratification are also featured in the boundary layer model. The derived nonlinear partial differential equation system with associated wall (sensor surface) and free stream boundary conditions is transformed to system of ordinary differential equations (ODE) via applicable similarity variables. A numerical solution is developed with the efficient Runge–Kutta–Fehlberg (RKF) technique with a shooting numerical method, in MATLAB software using the RKF-45 method. The graphical profiles were represented to examine the impacts of physically parameterics on the important physical stream features. Streamline and isotherm plots are also included for thermal buoyancy effect (Grashof number).Validation of solutions with earlier simpler models is included. A relatively well agreement is achived between model prediction and the benchmark value. Values for skin friction factor, Nusselt number and Sherwood numbers are also tabulated to quantify momentum, heat and mass (species) transfer characteristics at the sensor surface. The results indicate that the significant depletion in temperature accompanies accumulation in magnetization and thermal stratification parameters. Significant accumulation in mixed convection and Riga plate electrode width parameter enhance the concatenation profiles. Nusselt number grows substantially as thermal stratification and radiative parameter increases. Sherwood number grows substantially as solutal stratification, thermophoresis and Schmidt parameter increases. The present study generalizes previous models to include simultaneously exponential stretching, thermophoresis, thermal and solutal (mass) stratification and heat source/sink effects. • Mathematical model developed for a magnetized fluid through Exponentially stretching Riga Plate. • Characteristics of heat source (sink), non-linear radiation and thermophoretic are included in the model. • Utilizing Runge-Kutta 4th order with shooting solutions have been obtained. • Validation of present results is conducted with previous published results. • Stream lines and contour plots presented to study pattern of fluid flow. [ABSTRACT FROM AUTHOR]

Oblique stagnation point flow of incompressible Maxwell nanofluid past a stretching cylinder with active and passive controlled nanoparticles concentration condition is discussed numerically. The suitable coordinate decomposition reduce the governing boundary layer equations into the system of nonlinear ordinary differential equations which are approximated by Keller box procedure for several values of pertinent parameters. The Numerical results are compared and validated with existing ones as particular cases and found to be an excellent agreement. Velocity profile and lines of flow are sketched to discuss the Obliqueness of the flow. The temperature and concentration profiles drawn to illustrate the influence of involved parameters also variations in local Nusselt and Sherwood numbers are presented through tabular data. It is observed that the behavior of tangential velocity for the viscoelastic fluid and concentration of nanoparticles against thermophoresis diffusion over the cylinder are quite opposite when compared with the results over flat sheet. The temperature distribution and concentration of nanoparticles decreases with elasticity of the fluid. [ABSTRACT FROM AUTHOR]

Numerical analysis is performed for magnetohydrodynamics (MHD) couple stress nanofluid flow over a stretching sheet with melting and nonlinear radiation. The second law of thermodynamics is also incorporated with first-order slip. Nanofluid characteristics for thermophoresis and Brownian moments are encountered. The system that comprises differential equations of partial derivatives is remodeled into the system of differential equations via similarity transformations and then solved numerically through the Runge–Kutta–Fehlberg fourth-fifth (RKF-45) order technique. The physical parameters, which emerges from the derived system are discussed in graphical format. The significant outcomes of the current investigation are that the velocity field decays for a higher magnetic parameter. Another, important outcome of the study is both temperature and concentration are increasing functions of the first-order slip. Nusselt and Sherwood numbers are decreasing with an increase in magnetic strength. Further, Bejan number augment due to enhancement in the first-order slip and couple stress fluid parameters whereas a differing tendency is shown for magnetic and radiation parameters. [ABSTRACT FROM AUTHOR]

The study of fluid flow over a rotating disk is critically significant due to its applications in various industries and engineering and scientific fields. Ferrohydrodynamics of magnetic fluid experience the effects of magnetic fields incorporated with the walls of the rotating disk. The current investigation considers the ferrohydrodynamic flow of magnetic nanofluid caused by a rotating disk with temperature-dependent thermal conductivity and geothermal viscosity. The viscosity of magnetic nanofluid is directly proportional to the linear relation of depth and inversely proportional to temperature. The Navier–Stokes equations with the Maxwell equations of magnetization are modified to govern the fundamental partial differential equations and through transformations of similarity we obtained ordinary differential equations. It is inferred that rotation of the disk significantly boosts the radial movement of flow, and a loss is observed for other parameters such as variable viscosity, magnetic field parameter, and Reynolds number. Moreover, the heat transfer is enhanced considerably for increasing the Prandtl number, and the larger value of the rotation parameter depicts a weaker concentration phenomenon. Also, the Nusselt number show a decline curve for variable thermal conductivity parameter. Finally, the current findings can successfully fill a gap in the existing literature. [ABSTRACT FROM AUTHOR]

The present article aims to reports laminar, incompressible, electrically conducting two-dimensional non-Newtonian (power-law) liquid flow via exponentially stretching sheet with power-law slip velocity conditions. Transverse magnetic field, Hall current, viscous dissipation and radiative flux effects are incorporated in the formulation. Rosseland's diffusion model is defined for the radiation heat transfer. The non-linear partial derivation formulations satisfying the flow are transformed to the non-linear derivative equations by employing the local similarity quantities and then solved analytically through spectral quasi-linearization method (SQLM). The resultant solution is computed for different parameters in tables and graphical representation for clear understanding of the thermo-physical terms. Extensive visualization of primary and secondary velocities, temperature distributions for various emerging parameters presented for n = 0.7 (pseudo-plastic fluid) and n = 1,3 (dilatant fluid). The results are verified for limiting cases by comparing with various investigations and found excellent accuracy for Newtonian case. It is interesting to note that secondary flow rate is more dominant for both the cases of pseudo plastic and dilatant fluids for Hall parameter and Eckert number. Increasing Hall current leads suppress the fluid temperature but as Eckert number grows it leads grow the fluid temperature. Further, it is observed that as Hall parameter increases local Nusselt number strongly elevates. [ABSTRACT FROM AUTHOR]