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Generally, in computational thermofluid dynamics, the thermophysical properties of fluids (e.g. viscosity and thermal conductivity) are considered as constant. However, in many applications, the variability of these properties plays a significant role in modifying transport characteristics while the temperature difference in the boundary layer is notable. These include drag reduction in heavy oil transport systems, petroleum purification and coating manufacturing. The purpose of this study is to develop, a comprehensive mathematical model, motivated by the last of these applications, to explore the impact of variable viscosity and variable thermal conductivity characteristics in magnetohydrodynamic non-Newtonian nanofluid enrobing boundary layer flow over a horizontal circular cylinder in the presence of cross-diffusion (Soret and Dufour effects) and appreciable thermal radiative heat transfer under a static radial magnetic field.

The Williamson pseudoplastic model is deployed for rheology of the nanofluid. Buongiorno’s two-component model is used for nanoscale effects. The dimensionless nonlinear partial differential equations have been solved by using an implicit finite difference Keller box scheme. Extensive validation with earlier studies in the absence of nanoscale and variable property effects is included.

The influence of notable parameters such as Weissenberg number, variable viscosity, variable thermal conductivity, Soret and Dufour numbers on heat, mass and momentum characteristics are scrutinized and visualized via graphs and tables.

Buongiorno (two-phase) nanofluid model is used to express the momentum, energy and concentration equations with the following assumptions. The laminar, steady, incompressible, free convective flow of Williamson nanofluid is considered. The body force is implemented in the momentum equation. The induced magnetic field strength is smaller than the external magnetic field and hence it is neglected. The Soret and Dufour effects are taken into consideration.

The variable viscosity and thermal conductivity are considered to investigate the fluid characteristic of Williamson nanofluid because of viscosity and thermal conductivity have a prime role in many industries such as petroleum refinement, food and beverages, petrochemical, coating manufacturing, power and environment.

This fluid model displays exact rheological characteristics of bio-fluids and industrial fluids, for instance, blood, polymer melts/solutions, nail polish, paint, ketchup and whipped cream.

The outcomes disclose that the Williamson nanofluid velocity declines by enhancing the Lorentz hydromagnetic force in the radial direction. Thermal and nanoparticle concentration boundary layer thickness is enhanced with greater streamwise coordinate values. An increase in Dufour number or a decrease in Soret number slightly enhances the nanofluid temperature and thickens the thermal boundary layer. Flow deceleration is induced with greater viscosity parameter. Nanofluid temperature is elevated with greater Weissenberg number and thermophoresis nanoscale parameter.

This study aims to analyze the Prandtl fluid flow in the presence of better mass diffusion and heat conduction models. By taking into account a linearly bidirectional stretchable sheet, flow is produced. Heat generation effect, thermal radiation, variable thermal conductivity, variable diffusion coefficient and Cattaneo–Christov double diffusion models are used to evaluate thermal and concentration diffusions.

The governing partial differential equations (PDEs) have been made simpler using a boundary layer method. Strong nonlinear ordinary differential equations (ODEs) relate to appropriate non-dimensional similarity variables. The optimal homotopy analysis technique is used to develop solution.

Graphs analyze the impact of many relevant factors on temperature and concentration. The physical parameters, such as mass and heat transfer rates at the wall and surface drag coefficients, are also displayed and explained.

The reported work discusses the contribution of generalized flux models to note their impact on heat and mass transport.

The purpose of this paper is to perform an analytical approximation for the flow of magnetohydrodynamic Carreau fluid with the association of nanoparticles over a rotating disk. The disk is moving with a constant uniform speed. Governing equations are obtained by using these assumptions in the form of partial differential equations with boundary conditions. These coupled, highly nonlinear equations are transformed into a coupled system of ordinary differential equations by engaging similarity transformation in the rotating frame of reference.

An efficient and reliable scheme, namely optimal homotopy asymptotic method, is used to obtain the solutions of the arising physical problem, which is further analyzed graphically. After computing the solutions of the arising problem, plots of velocities, temperature and concentration are discussed briefly.

It has been observed that dimensionless velocity reduced due to magnetic effect between the boundary layer and escalating values of the magnetic parameter upsurges the temperature and concentration profiles. Contour plots and numerical results are given for local numbers like skin friction coefficient, Nusselt number and Sherwood number.

The work presented in this manuscript is neither published nor submitted anywhere for the consideration/publications. It is a novel work.

The purpose of this study, thermal radiation and viscous dissipation impacts on double diffusive convection on peristaltic transport of Williamson nanofluid due to induced magnetic field in a tapered channel is examined. The study of propulsion system is on the rise in aerospace research. In spacecraft technology, the propulsion system uses high-temperature heat transmission governed through thermal radiation process. This study will help in assessment of chyme movement in the gastrointestinal tract and also in regulating the intensity of magnetic field of the blood flow during surgery.

The brief mathematical modelling, along with induced magnetic field, of Williamson nanofluid is given. The governing equations are reduced to dimensionless form by using appropriate transformations. Numerical technique is manipulated to solve the highly nonlinear differential equations. The roll of different variables is graphically analyzed in terms of concentration, temperature, volume fraction of nanoparticles, axial-induced magnetic field, magnetic force function, stream functions, pressure rise and pressure gradient.

The key finding from the analysis above can be summed up as follows: the temperature profile decreases and concentration profile increases due to the rising impact of thermal radiation. Brownian motion parameter has a reducing influence on nanoparticle concentration due to massive transfer of nanoparticles from a hot zone to a cool region, which causes a decrease in concentration profile· The pressure rise enhances due to rising values of thermophoresis and thermal Grashof number in retrograde pumping, free pumping and copumping region.

To the best of the authors’ knowledge, a study that integrates double-diffusion convection with thermal radiation, viscous dissipation and induced magnetic field on peristaltic flow of Williamson nanofluid with a channel that is asymmetric has not been carried out so far.

The purpose of this paper is to focus on the influence of multiple slips on MHD Williamson nanofluid flow embedded in porous medium towards a linearly stretching sheet that has been investigated numerically. The whole analysis has been carried out considering the presence of nth-order chemical reaction between base fluid and nanoparticles.

A similarity transformation technique has been adopted to convert non-linear governing partial differential equations into ordinary ones and then they are solved by using both the RK-4 method and Laplace transform homotopy perturbation method. The consequences of multiple slip parameters on dimensionless velocity, temperature and concentration and heat and mass transfer rates have been demonstrated using tabular and graphical outline.

The investigation explores that the Nusselt number reduces for escalating behaviour of velocity slip and thermal slip parameter. Fluid’s temperature rises in the presence of generative reaction parameter.

A fine conformity of the current results has been achieved after comparing with previous literature studies. Considering destructive chemical reaction, reduced Nusselt number is found to decrease, but reverse consequence has been noticed in the case of generative chemical reaction. Mass transport diminishes when the order of chemical reaction amplifies for both destructive and generative reactions.

Present investigation based on the flow of electrically conducting Williamson nanofluid embedded in a porous medium past a linearly horizontal stretching sheet. In addition to that, the combined effect of thermophoresis, Brownian motion, thermal radiation and chemical reaction is considered in both energy and solutal transfer equation, respectively.

With suitable choice of nondimensional variables the governing equations for the velocity, temperature, species concentration fields, as well as rate shear stress at the plate, rate of heat and mass transfer are expressed in the nondimensional form. These transformed coupled nonlinear differential equations are solved semi-analytically using variation parameter method.

The behavior of characterizing parameters such as magnetic parameter, melting parameter, porous matrix, Brownian motion, thermophoretic parameter, radiation, Lewis number and chemical particular case present result validates with earlier established results and found to be in good agreement. Finally reaction parameter is demonstrated via graphs and numerical results are presented in tabular form.

The said work is an original work of the authors.

The purpose of this paper is to examine the influence of magnetic field on Williamson nanofluid embedded in a porous medium in the presence of non-uniform heat source/sink, chemical reaction and thermal radiation effects.

The governing physical problem is presented using the traditional Navier–Stokes theory. Consequential system of equations is transformed into a set of non-linear ordinary differential equations by means of scaling group of transformation, which are solved using the Runge–Kutta–Fehlberg method.

The working fluid is examined for several sundry parameters graphically and in a tabular form. It is noticed that with an increase in Eckert number, there is an increase in velocity and temperature along with a decrease in shear stress and heat transfer rate.

A good agreement of the present results has been observed by comparing with the existing literature results.

The current determination is committed to characterize the boundary layer flow of Williamson nanofluid prompted by nonlinear strained superficial under heat and mass transport mechanisms. Buongiorno model is presented to view the influence of nanoparticles in fluid flow. Scrutiny has been conceded under the action of the transversely smeared magnetic field. Heat and mass relocation exploration are conducted in the companionship of radiation effects and actinic compensation.

Similarity variable is designated to transmute nonlinear partial differential equations of conservation laws of mass, momentum, energy and species into ordinary dimensional expressions. These constitutive and complicated ordinary differential expressions assessing the flow situation are handled efficaciously by manipulating Runge–Kutta–Fehlberg procedure (RK-5) with shooting routine.

The graphical demonstration is deliberated to scrutinize the variation in velocity, temperature and concentration profiles with respect to flow regulating parameters. Numerical data are displayed through tables in order to surmise variation in skin friction coefficient and Nusselt number. The augmenting values of fluid parameter and magnetic parameter reduces the horizontal fluid velocity, whereas normal velocity upsurges for mounting values of stretching ratio parameter. Moreover, mounting values of radiation parameter and thermophoresis parameter upsurges the temperature profile, whereas, growing values of Prandtl number lessen the temperature field.

The current exploration is used in many industrial and engineering applications in order to discuss the transport phenomenon.

Flow over a nonlinear stretched surface has numerous applications in the industry. The present attempt examines the combined influence of various physical characteristics for the flow of Williamson fluid and no such attempt exist in the available literature.

The study aims to numerically examine the impact of nanoparticles on an unsteady flow of a Williamson fluid past a permeable convectively heated shrinking sheet.

In sort of the solution of the governing differential equations, suitable transformation variables are used to get the system of ODEs. The converted equations are then numerically solved via the shooting technique.

The impacts of such parameters on the velocity profile, temperature distribution and the concentration of nanoparticles are examined through graphs and tables. The results point out that multiple solutions are achieved for certain values of the suction parameter and for decelerating flow, while for accelerating flow, the solution is unique. Further, the non-Newtonian parameter reduces the fluid velocity and boosts the temperature distribution and concentration of nanoparticles in the first solution, while the reverse drift is noticed in the second solution.

The current results may be used in many applications such as biomedicine, industrial, electronics and solar energy.

The authors think that the current results are new and significant, which are used in many applications such as biomedicine, industrial, electronics and solar energy. The results have not been considered elsewhere.

The purpose of this paper is to consider the simultaneous flow of Casson Williamson non Newtonian fluids in a vertical porous medium under the influence of variable thermos-physical parameters.

The model equations are a set of partial differential equations (PDEs). These PDEs were transformed into a non-dimensionless form using suitable non-dimensional quantities. The transformed equations were solved numerically using an iterative method called spectral relaxation techniques. The spectral relaxation technique is an iterative method that uses the Gauss-Seidel approach in discretizing and linearizing the set of equations.

It was found out in the study that a considerable number of variable viscosity parameter leads to decrease in the velocity and temperature profiles. Increase in the variable thermal conductivity parameter degenerates the velocity as well as temperature profiles. Hence, the variable thermo-physical parameters greatly influence the non-Newtonian fluids flow.

This study considered the simultaneous flow of Casson-Williamson non-Newtonian fluids by considering the fluid thermal properties to vary within the fluid layers. To the best of the author’s knowledge, such study has not been considered in literature.