Search

This attempt demonstrates the nature of mass and heat transportation in non-Newtonian Reiner–Philippoff liquid flow over moving surface by considering zero and nonzero normal mass flux conditions and transverse magnetic field. Thermophoresis and Brownian movement is accounted due to the Buongiorno model of nanofluid. The expressions of flow are reframed through appropriate variables into pairs of self-similar expressions. Further, these self-similar expressions are executed numerically through the Shooting procedure (Runge–Kutta 4th order). Numerical benchmarks and graphical illustrations are prepared to visualize the role of influential constraints on interesting quantities. It is observed that Lorentz force is beneficial in obtaining effective velocity and heat transfer. Improvement in thermophoresis factor enriches temperature field in case of active control while reverse nature is observed in passive control situation. [ABSTRACT FROM AUTHOR]

Due to high sensitivity of fluid particles to temperature changes, the thermophysical characteristics of fluids are known to exhibit significant variations when exposed to temperature rise, which can impact the overall efficiency of conveying fluid substances in manufacturing processes across different surfaces and media. Industrial and mechanical processes such as aerodynamic extrusion in plastic sheets, fiber technology and biological dynamics as transpiration and muscle cramps exhibit different surface dynamics. The Reiner–Philippoff (RP) fluid model exemplifies shear-thinning, shear-thickening and Newtonian behavior. This study investigates the flow of a RP fluid over a stretching and shrinking surface with nonlinear thermal convection and variable thermophysical properties. The mathematical models describing the dynamical system are transformed through a similar group of transformations. Flow variables such as the fluid's velocity, temperature and solute concentration were numerically obtained through the spectral local linearization technique (SLLM). Subject to the validation and accuracy of the numerical results, the effects of pertinent parameters on the flow were investigated. The findings in this study reveal that the effects of the flow variables on stretching and shrinking sheets are not diametrically opposite. Moreover, the radiation negatively impacts the flow variables over a stretching sheet compared to the positive effect experienced at some point in flow over a shrinking sheet. [ABSTRACT FROM AUTHOR]

This study's main goal is to examine the advantages of a two-dimensional Reiner-Philippoff fluid flow via a stretched sheet. Furthermore, radiative heat transmission and magnetic dipole media are taken into account. It is now possible to have a comprehensive understanding of the rheological properties of non-Newtonian fluids by the use of the Reiner-Philippoff fluid, which distinguished the transport mechanisms of the fluid. The boundary layer method is used in the process of developing the model. Through the use of similarity variables, these equations are converted into a two-dimensional model. In order to achieve the numerical answers, the RKF-45 order is used first. A combination of numerical standards and visual representations is used in order to demonstrate them. An analysis of the features of the entangled flow, including the distributions of velocity and temperature, is carried out from a visual standpoint. According to the results of this study, the temperature field gets more prominent with a thicker λ0 and the temperature of the fluid goes down with more γ1. Aside from that, the decrease of hat transfer occurs more often with pseudo-plastic fluids than with Newtonian dilatant fluids.

Magneto-thermomechanical applications range from magnetic resonance imaging to electric diodes and the design of dielectric grease. To contribute significantly to the biomedical industry for proper prediction and treatment of diseases such as cancer, stenosis, and technological advancement in the design of electronic tools. This study presents the significance of magneto-thermomechanical modeling of Reiner–Philippoff fluid flow subject to thermal radiation influence. The Reiner–Philippoff fluid encapsulates the properties of shear-thinning, shear-thickening, and Newtonian fluids in different viscosity regimes. The main-stream velocity ue is considered in its generalized form as well as taking into account the influence of thermal radiation and thermal conductivity. To obtain the computational model analysis, a numerical tool via the bivariate spectral collocation method is deployed on the resulting transformed PDEs. Upon validation of the method, the profile distributions of respective boundary layers with respect to the Bingham number, magneto-thermomechanical parameter, and Reiner–Philippoff fluid parameter are analyzed and discussed. The results of the engineering quantities of skin friction and Nusselt number are presented in graphical and tabular form. Among the findings of this study is that the Newtonian fluid is a turning point for skin drag force and heat transfer rate. Besides, the ferrohydrodynamic parameter recedes the velocity of shear-thinning fluid the most, although, boosts its (shear-thinning fluid) heat transfer coefficient. [ABSTRACT FROM AUTHOR]

The non-Newtonian liquid scheme is created to address the limitations of the classical (Newtonian) scheme in terms of accurately reflecting real-world fluid flow behavior in industrial applications and improving operational efficiency. The Reiner–Philippoff model, one of the many extant models, modeling non-Newtonian fluids, is of concern because it only captures a few features in some circumstances. Thus, this study aims to investigate the theoretical aspects of Cattaneo–Christov for heat diffusion fusion of Reiner–Philippoff liquid stream in the presence of Darcy–Forchheimer media. Furthermore, the procedure of heat transport is taken out in the occurrence of nonlinear heat radiative, viscous dissipation and Ohmic heating. The partial derivatives of nonlinear differential equations are changed into similarity equations of a certain form by using appropriate similarity transformations. Furthermore, the Runge–Kutta–Fehlberg method with shooting approach is utilized to solve the dimensionless model. The influence of pertinent fluid flow parameters is illustrated graphically. The further engineering curiosity of a local Nusselt number is illustrated and analyzed. It is found that velocity curve is boosted with the augmenting scales of Reiner–Philippoff liquid parameter and Forchheimer number. Further, it is analyzed that increasing the thermal relaxation parameter and Eckert number reduces the heat transport rate at the surface. [ABSTRACT FROM AUTHOR]

In this study, by considering the effects of joule heating and viscous dissipation, we analyzed the Reiner-Philippoff fluid flow along a stretching sheet. Velocity slip of first order is taken into account. Using the Shooting method, the transformed governing equations are numerically solved. Graphical analysis is used to examine how new parameters affect the fields of temperature and velocity. The obtained results are compared to the results that have been published and are found to be in strong agreement. Examples of this kind of flow on a stretching sheet include the extrusion of polymers, liquid coatings, and other procedures. [ABSTRACT FROM AUTHOR]

The aim of this paper is to highlight the output of the investigation on the MHD and radiative flow and thermal characteristics of a non-Newtonian Reiner–Philippoff nanofluid with Brownian and thermophoresis diffusion effects. The model studied is embedded in the Buongiorno theory. This unique model is designed to observe both shear thickening and shear thinning properties on that particular fluid with embedded Brownian and thermophoresis diffusion implications. The proposed model consists of continuity, momentum, energy, and concentration equations constructed using the theoretical assumptions and are reduced to a set of ordinary differential equations (ODEs) before solving it using the bvp4c function in MATLAB software. Two solutions are observed, and their physical significance is justified using the temporal stability analysis. From the standpoint of the Reiner–Philippoff fluid parameter, the skin friction coefficient as well as the heat and mass transfer rates are at maximum for the shear-thickening fluid followed by the Newtonian and shear-thinning fluids. The thermophoresis parameter is noticed to decline the heat and mass transfer rate whereas the Brownian motion parameter boosts the mass transfer rate but decreases the heat transfer rate.

Heat transfer is an important process in many engineering, industrial, residential, and commercial buildings. Thus, this study aims to analyse the effect of MHD and viscous dissipation on radiative heat transfer of Reiner–Philippoff fluid flow over a nonlinearly shrinking sheet. By adopting appropriate similarity transformations, the partial derivatives of multivariable differential equations are transformed into the similarity equations of a particular form. The resulting mathematical model is elucidated in MATLAB software using the bvp4c technique. To determine the impact of physical parameters supplied into the problem, the results are shown in the form of tables and graphs. The findings reveal that the heat transfer rate reduces as the Eckert number and radiation parameter are introduced in the operating fluid. However, increasing the magnetic parameter raises both the skin friction coefficient and the local Nusselt number, which impulsively improves the heat transfer performance. The suction effect has a noticeable influence on the Reiner–Philippoff fluid, since increasing the suction parameter's value is seen to enhance the skin friction coefficient and the heat transfer performance. The dual solutions are established, leading to the stability analysis that supports the first solution’s validity.

The aim of this paper is to highlight the output of the investigation on the MHD and radiative flow and thermal characteristics of a non-Newtonian Reiner–Philippoff nanofluid with Brownian and thermophoresis diffusion effects. The model studied is embedded in the Buongiorno theory. This unique model is designed to observe both shear thickening and shear thinning properties on that particular fluid with embedded Brownian and thermophoresis diffusion implications. The proposed model consists of continuity, momentum, energy, and concentration equations constructed using the theoretical assumptions and are reduced to a set of ordinary differential equations (ODEs) before solving it using the bvp4c function in MATLAB software. Two solutions are observed, and their physical significance is justified using the temporal stability analysis. From the standpoint of the Reiner–Philippoff fluid parameter, the skin friction coefficient as well as the heat and mass transfer rates are at maximum for the shear-thickening fluid followed by the Newtonian and shear-thinning fluids. The thermophoresis parameter is noticed to decline the heat and mass transfer rate whereas the Brownian motion parameter boosts the mass transfer rate but decreases the heat transfer rate. [ABSTRACT FROM AUTHOR]

This paper aims to examine the MHD effects on Reiner–Philippoff fluid flow over a permeable shrinking wedge. The partial derivatives of multivariable differential equations are transformed into similarity equations by adopting appropriate similarity transformations. The resulting equations are solved in MATLAB using the bvp4c technique. The findings reveal that the existence of the magnetic field is proven to improve the friction factor and heat transfer performance. Similar effects are observed with the rise of the suction strength. However, increasing the Reiner–Philippoff fluid parameter lowers the heat transfer rate but increases the friction factor. Moreover, the Lorentz force created by the magnetic field essentially slows the fluid motion, thereby delaying the separation of the boundary layer. The dual solutions are established, leading to the stability analysis that supports the first solution's validity. [ABSTRACT FROM AUTHOR]

The field of magnetohydrodynamics (MHD) encompasses a wide range of physical objects due to their stabilising effects. Thus, this study concerns the numerical investigation of the radiative non-Newtonian fluid flow past a shrinking sheet in the presence of an aligned magnetic field. By adopting proper similarity transformations, the governing partial derivatives of multivariable differential equations are converted to similarity equations of a particular form. The numerical results are obtained by using the bvp4c technique. According to the findings, increases in the suction parameter resulted in higher values of the skin friction and heat transfer rate. The same pattern emerges as the aligned angle and magnetic parameter are considered. On the other hand, the inclusion of the Bingham number, the Reiner–Philippoff fluid, and the thermal radiation parameters deteriorate the heat transfer performance, evidently. The dual solutions are established, which results in a stability analysis that upholds the validity of the first solution.

Heat transfer is an important process in many engineering, industrial, residential, and commercial buildings. Thus, this study aims to analyse the effect of MHD and viscous dissipation on radiative heat transfer of Reiner–Philippoff fluid flow over a nonlinearly shrinking sheet. By adopting appropriate similarity transformations, the partial derivatives of multivariable differential equations are transformed into the similarity equations of a particular form. The resulting mathematical model is elucidated in MATLAB software using the bvp4c technique. To determine the impact of physical parameters supplied into the problem, the results are shown in the form of tables and graphs. The findings reveal that the heat transfer rate reduces as the Eckert number and radiation parameter are introduced in the operating fluid. However, increasing the magnetic parameter raises both the skin friction coefficient and the local Nusselt number, which impulsively improves the heat transfer performance. The suction effect has a noticeable influence on the Reiner–Philippoff fluid, since increasing the suction parameter's value is seen to enhance the skin friction coefficient and the heat transfer performance. The dual solutions are established, leading to the stability analysis that supports the first solution's validity. [ABSTRACT FROM AUTHOR]

The thermodynamics modeling of a Reiner–Philippoff‐type fluid is essential because it is a complex fluid with three distinct probable modifications. This fluid model can be modified to describe a shear‐thinning, Newtonian, or shear‐thickening fluid under varied viscoelastic conditions. This study constructs a mathematical model that describes a boundary layer flow of a Reiner–Philippoff fluid with nonlinear radiative heat flux and temperature‐ and concentration‐induced buoyancy force. The dynamical model follows the usual conservation laws and is reduced through a nonsimilar group of transformations. The resulting equations are solved using a spectral‐based local linearization method, and the accuracy of the numerical results is validated through the grid dependence and convergence tests. Detailed analyses of the effects of specific thermophysical parameters are presented through tables and graphs. The study reveals, among other results, that the buoyancy force, solute and thermal expansion coefficients, and thermal radiation increase the overall wall drag, heat, and mass fluxes. Furthermore, the study shows that amplifying the space and temperature‐dependent heat source parameters allows fluid particles to lose their cohesive force and, consequently, maximize flow and heat transfer. [ABSTRACT FROM AUTHOR]

Using magnetohydrodynamics (MHD), the thermal energy and mass transport boundary layer flow parameters of Reiner–Philippoff fluid (non-Newtonian) are numerically investigated. In terms of energy and mass transfer, non-linear radiation, Cattaneo–Christov double diffusions, convective conditions at the surface, and the species reaction pertaining to activation energy are all addressed. The stated governing system of partial differential equations (PDEs) is drained into a non-linear differential system using appropriate similarity variables. Numerical solutions are found for the flow equations that have been determined. Two-dimensional charts are employed to demonstrate the flow field, temperature and species distributions, and rate of heat and mass transfers for the concerned parameters for both Newtonian and Reiner–Philippoff fluid examples. The stream line phenomenon is also mentioned in this paper. A table has also been utilized to illustrate the comparison with published results, which shows that the current numerical data are in good accord. The findings point to a new role for heat and mass transfer. According to the findings, increasing values of solutal and thermal relaxation time parameters diminish the associated mass and thermal energy layers. The current study has significant ramifications for chemical engineering systems. [ABSTRACT FROM AUTHOR]

The thermo-dynamical modeling is a powerful tool for predicting the optimal melting of heat transfer; this is because there is a good correlation between numerical and analytical heattransfers via thermodynamic predicted results. A mathematical model is constructed underflow of a non-Newtonian (Reiner-Philippoff) fluid based on certain assumptions. Such mathematical model flow is handled by invoking similarity solutions for governing equations. The obtained system of nonlinear equations is solved numerically by utilizing fourth-fifth order Runge-Kutta-Fehlberg method. The consequences of distinguished parameters onfluid flow are analyzed in details through the plotted graphic visuals. Physical quantities are also considered numerically by tables. The claimed results reveal that the velocity profile reduce due to Forchheimer parameter and porosity parameter. The growing nature of temperature field is observed against temperature ratio parameter. The numerical values of local Nusselt number decline with radiation parameter and surface heating parameter. The obtained results presents novel role in the heat transfer phenomenon, electronic cooling, microheat pipes, electronic cooling, reaction processes, nuclear reactors etc.

The nanofluids are more practical to enhance the heat transfer compared to regular fluids. Such effectiveness in mind causes this communication's concern to investigate the Darcy–Forchheimer flow of Reiner–Philippoff nanofluid with heat source/sink, thermal conductivity in the occurrence of motile microorganisms over the stretching surface. The melting phenomenon is also considered. For this purpose, the set of nonlinear partial differential equation (PDE) is converted into ordinary differential equation (ODE) using the required translation of similarities. These obtained simple ordinary differential equations are solved using the built‐in MATLAB computational tool bvp4c method. The graphical outcomes are delineated for velocity, temperature, concentration, and motile microorganisms profiles via Lewis number, fluid parameter, radiation parameter, thermophoresis parameter, Brownian motion parameter, Prandtl number, bioconvection Lewis number, Reynolds number, Peclet number, and bioconvection Rayleigh number, respectively. The numerical data confirm that the coefficient of wall heat transfer reduces for the greater values of the Schmidt number and thermophoresis parameter. The heat profile is reduced for the higher magnitude of the Prandtl number while boosted up for the higher estimations of thermal radiation parameter. The mass transfer of microorganisms is boosted via the Peclet and bioconvection Lewis number. [ABSTRACT FROM AUTHOR]

Using magnetohydrodynamics (MHD), the thermal energy and mass transport boundary layer flow parameters of Reiner–Philippoff fluid (non-Newtonian) are numerically investigated. In terms of energy and mass transfer, non-linear radiation, Cattaneo–Christov double diffusions, convective conditions at the surface, and the species reaction pertaining to activation energy are all addressed. The stated governing system of partial differential equations (PDEs) is drained into a non-linear differential system using appropriate similarity variables. Numerical solutions are found for the flow equations that have been determined. Two-dimensional charts are employed to demonstrate the flow field, temperature and species distributions, and rate of heat and mass transfers for the concerned parameters for both Newtonian and Reiner–Philippoff fluid examples. The stream line phenomenon is also mentioned in this paper. A table has also been utilized to illustrate the comparison with published results, which shows that the current numerical data are in good accord. The findings point to a new role for heat and mass transfer. According to the findings, increasing values of solutal and thermal relaxation time parameters diminish the associated mass and thermal energy layers. The current study has significant ramifications for chemical engineering systems.

Currently, researchers across the world achieved theoretical and experimental works to investigate the significance of nanofluid due to their diverse application in heat transport phenomena. Nanofluids are actually the suspension of nanoparticles in the base liquid. Embedding nanoparticles in the base fluid enhances thermal conductivity and heat transfer rate. The present article shed light on the influence of gold nanoparticles along with oxytactic microorganisms on radiative Reiner–philippoff fluid due to extendable sheet. Suitable transformation convert the partial differential equations (PDEs) are renovated into nonlinear ordinary differential equations (ODEs) and furthermore tackled these equations numerically via bvp4c Matlab builtin scheme. Further the investigations are carried out in the presence of molecular diffusivity, oxytactic microorganisms and nonlinear thermal radiation. The effect of influential parameters on heat transfer, mass transfer, motile density of microorganisms profile are investigated with the assistance of tables and graphs. Embedding the nanoparticles and nonlinear thermal radiation amplifies the heat transfer process and motile density profile depreciates owing to an augmentation in Peclet number. The novel outcomes of this investigation will advance the field of nanomaterials. [ABSTRACT FROM AUTHOR]

The main focus of the present research work is to elaborate the Reiner–Philippoff fluid flow over a stretching sheet along with thermal radiation effect. A Darcy–Forchheimer medium was imposed and a linear stretching surface was used to generate the flow. Application of appropriate transformation yields nonlinear ordinary differential equation through nonlinear Navier–Stokes equations and solved by Runge–Kutta–Fehlberg shooting technique. Importance of influential variables such as velocity and temperature was elaborated graphically. It is envisaging that the boost up values of γ declines the both velocity and temperature profiles. [ABSTRACT FROM AUTHOR]

• Flow problem of Reiner-Philippoff fluid with A A 7072 , A A 7075 , Ti 6 Al 4 V , Ti 5 Al 2.5 S n is analyzed. • Cattaneo-Christov heat flux and Forchheimer velocity are considered. • Variable heat source (sink) and thermal radiative heat flux is taken into consideration. • Numerical treatment is accomplished in collaboration with the Galerkin finite element method. • The heat transfer rate magnifies extra in tetra hybridity nanofluid in disparity to tri and di hybridity nanofluid. Scientists across the world have tried to explore the effect of non-Newtonian fluids moving over a symmetric stretchable sheet with the presence of diverse influences revealed in this study due to its tremendous applications in various engineering and industrialized sectors like aerodynamics extrusion of plastic surfaces, condensation procedure of metal symmetric plate in a refrigeration immersion, and extrusion of a polymeric surface from a dye. Proposed model Reiner-Philippoff fluids flowing related to a symmetric stretch surface with the inclusion of effects like Forchheimer velocity, thermal radiative, and Cattaneo Christov heat fluxing are considered in the momentum and temperature equation. Novel tetra hybrid nanoparticles are considered to check the thermo physical behaviour of the proposed model. The showed PDEs are transformed into ODEs with the utilization of symmetric and self-similarity variables and further attempted numerically with the assistance of the Galerkin finite element methodology (G-FEM). The obtained findings are scrutinized in the form of figures and tables. Findings From obtained outcomes, it is perceived that the heat transfer Nusselt magnifies extra in the instance of tetra hybrid nanofluids (THNFs) in disparity to tri and di hybrid nanoparticles. Darcy Forcheeimer effect Fr diminishes the fluid velocity and the temperature outline amplifies owed to amplification in thermal radiative variable Rd. The insertion of nanoparticles supports in the stabilizating of a nanofluid's flow and provides the symmetric of the structure. Error in heat transfer Nusselt number diminishes by the virtue of magnification in Rd and the heat deliverance phenomenon magnifies as a consequence of enlargement in the thermal relaxation constraint. Practical application of the proposed model Due to its particle use in manufacturing and engineering for shells that expand and contract, like stretchable (shrinkable) packaging, bundle wrapping, hot roll, sheet material extrusion, wire roll, glass fiber manufacturing, metallic packags, and aluminum bottles manufacturing, parabolic tough surface collectors, cooling of thermal reactors, polymer production, etc., the examination of two-dimensional flowing over an extending shallow has attracted attention. The proposed model outcomes are utilized in order the enhance heat transfer of the various liquids by utilizing tetra hybrid nanoparticles and effects like nonlinear based thermal radiation, Cattaneo-Christov heat flux and heat source/sink phenomenon. Novelty The effort is novel in its sagacity that no nanofluid model has been developed yet to examine the effect of tetra hybrid nanoparticles on liquid moving over any sort of surface. [ABSTRACT FROM AUTHOR]

In this article flow of a classical non-Newtonian fluid, Reiner–Philippoff fluid, in the presence of nano-particles over a non-linear stretching sheet is studied numerically. The mathematical model incorporates the non-linear stress-deformation behavior for Reiner–Philippoff fluid and Brownian motion and thermophoresis effects due to nanoparticles. The correlation expressions for skin friction, Nusselt number and Sherwood number are developed by performing linear regression on the obtained numerical data. The effects of nano-particles and Reiner–Philippoff fluid are discussed on the skin friction, Nusselt number and Sherwood number. It is observed that skin friction for dilatant fluids is higher than pseudoplastic fluids and temperature and nanoparticles concentration fluxes at the surface increase with an increase in Reiner–Philippoff fluid parameter. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a numerical analysis of the steady boundary-layer flow of a Reiner–Philippoff fluid induced by a 90° stretching wedge in a variable free stream. The governing partial differential equations are converted into a set of two ordinary differential equations by the use of a similarity transformation. The flow is therefore governed by a stretching velocity parameter λ and two non-Newtonian fluid parameters γ and . The variation of the skin friction, as well as other flow characteristics, as a function of the governing parameters is presented graphically and tabulated. A stability analysis has also been performed for this self-similar flow based on linear disturbances to the steady similarity solutions. The results presented in this paper reveal that there are no multiple (dual) solutions for the present problem and the unique solution is stable. [Copyright &y& Elsevier]

Reiner–Philippoff fluid flow over a heated surface through theory of Cattaneo–Christov for heat diffusion is executed in this work. The impacts of Cattaneo–Christov heat flux, Ohmic heating and transverse magnetic field are also considered. The Transformations are used to reduce system of partial differential equations into ordinary ones and are solved numerically by using RKF-45 method. The dimensionless numbers on velocity and temperature are elaborated. Further engineering curiosity of local Nusselt are tabulated, depicted and interpreted. • Reiner–Philippoff fluid flow over a heated surface is modeled. • Theory of Cattaneo–Christov for heat diffusion is executed for energy expression. • The impacts of ohmic heating and transverse magnetic field are considered. • The dimensionless numbers on velocity and temperature are elaborated. [ABSTRACT FROM AUTHOR]