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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.

The purpose of this paper is to make an analysis to study the non‐similar solution for unsteady water boundary layer flow over sphere with the influence of temperature‐dependent viscosity, Prandtl number, non‐uniform surface mass transfer and heat transfer.

The governing quasi‐linear partial differential equations have been solved numerically using an implicit finite difference scheme along with a quasi‐linearization technique. Non‐similar solutions have been obtained from the starting point of the stream‐wise coordinate to the point where the skin friction value vanishes.

It is observed that non‐uniform suction causes the point of vanishing skin friction to move downstream. The slot injection causes the vanishing skin friction to move upstream.

The effect of unsteadiness is more significant on the skin friction as compared to the heat transfer.

The main purpose of this study is to present a non-similar analysis of two-dimensional boundary layer flow of non-Newtonian nanofluid over a vertical stretching sheet with variable thermal conductivity. The Sisko fluid model is used for non-Newtonian fluid with an exponent (n* > 1), that is, shear thickening fluid. Buongiorno model for nanofluid accounting Brownian diffusion and thermophoresis effects is used to model the governing differential equations.

The governing boundary layer equations are converted into nondimensional coupled nonlinear partial differential equations using appropriate transformations. The resultant differential equations are solved numerically using implicit finite difference scheme in association with the quasilinearization technique.

This analysis shows that the temperature raises for thermal conductivity parameter and velocity ratio parameter while decreases for the thermal buoyancy parameter. The thermophoresis and Brownian diffusion parameter that characterizes the nanofluid flow enhances the temperature and reduces the heat transfer rate. Skin friction drag can be effectively reduced by proper control of the values of thermal buoyancy and velocity ratio parameter.

The wall heating and cooling investigation result in the analysis of the control parameters that are related to the designing and manufacturing of thermal systems for cooling applications and energy harvesting. These control parameters have practical significance in the designing of heat exchangers and solar thermal collectors, in glass and polymer industries, in the extrusion of plastic sheets, the process of cooling of the metallic plate, etc.

To the best of authors’ knowledge, it is found from the literature survey that no similar work has been published which investigates the non-similar solution of Sisko nanofluid with variable thermal conductivity using finite difference method and quasilinearization technique.

The purpose of this study is to provide a numerical investigation of Casson nanofluid along a vertical nonlinear stretching sheet with variable thermal conductivity and viscosity.

The boundary-layer equations are presented in the dimensionless form using proper non-similar transformations. The subsequent non-dimensional nonlinear partial differential equations are solved using the implicit finite difference technique. To linearize the nonlinear terms present in these equations, the quasilinearization technique is used.

The investigation showed graphically the temperature, velocity and nanoparticle volume fraction for particular included physical parameters. It is observed that the velocity profile decreases with an increase in the values of Casson fluid parameter while increases with an increase in the viscosity variation parameter. The temperature profile enhances for large values of velocity variation parameter and thermal conductivity parameter while it reduces for large values of thermal buoyancy parameter. Further, the Nusselt number and skin-friction coefficient are introduced which are helpful in determining the physical aspects of Casson nanofluid flow.

The immediate control of heat transfer in the industrial system is crucial because of increasing energy prices. Recently, nanotechnology is proposed to control the heat transfer phenomenon. Ongoing research in complex nanofluid has been fruitful in various applications such as solar thermal collectors, nuclear reactors, electronic equipment and diesel–electric conductor. A reasonable amount of nanoparticle when added to the base fluid in solar thermal collectors serves to deeper absorption of incident radiation, and hence it upgrades the efficiency of the solar thermal collectors.

The non-similar solution of Casson nanofluid due to a vertical nonlinear stretching sheet with variable viscosity and thermal conductivity is discussed in this work.

This paper looks into the rotating flow of an incompressible viscous fluid over an exponentially stretching continuous surface. The flow is governed by non‐linear partial differential equations. A non‐similar solution is developed after transforming the governing equations using two different numerical techniques namely Keller‐box and shooting methods. The influence of the non‐dimensional local rotating parameter Ω on the velocity fields and skin friction coefficients is analyzed and discussed.

In this paper, the authors have used the well‐known numerical methods, Keller‐box and shooting.

It is observed that for the increase in the rotation velocity of the frame there is a reduction in the boundary layer thickness and an increase in the drag force at the surface.

The present study is concerned with the boundary layer flow of a rotating viscous fluid over an exponentially stretching sheet. Numerical solutions are found. To the best of the authors' knowledge, this is the first investigation of the topic.

The problem of steady, laminar, heat and mass transfer by mixed convection from a semi‐infinite, isothermal, vertical and permeable plate embedded in a uniform porous medium in the presence of temperature‐dependent heat source or sink and magnetic field effects is considered. A mixed convection parameter for the entire range of free‐forced‐mixed convection is employed and non‐similar equations are obtained. These equations are solved numerically by an efficient implicit, iterative, finite‐difference scheme. The obtained results are checked against previously published work on special cases of the problem and are found to be in good agreement. Useful correlations for the local Nusselt number are obtained for various physical parameters. A parametric study illustrating the influence of the magnetic field, porous medium inertia effects, heat generation or absorption, concentration to thermal buoyancy ratio, and the Lewis number on the fluid velocity, temperature and concentration as well as the Nusselt and the Sherwood numbers is conducted. The obtained results are shown graphically and the physical aspects of the problem are discussed.

This paper aims to provide a detailed study on the influence of slip flow and thermal jump over mixed convection flow along an exponentially stretching surface. Also, impacts of suction/blowing, volumetric heat source/sink and velocity ratio parameter will be studied in this analysis.

The modeled governing equations for the assumed problem are dimensional nonlinear partial differential equations in nature. To reduce these equations, non-similar transformations are used to get the dimensionless nonlinear partial differential equations. Then, quasi-linearization technique is used to linearize these non-dimensional nonlinear partial differential equations. Finally, an implicit finite difference scheme is used to discretize the resulting equations.

The physical explanations are provided for the variations of various non-dimensional governing parameters over the velocity and temperature profiles. Also, the effects of these dimensionless parameters on skin friction coefficient and heat transfer rate are scrutinized in a manner which highlights their physical interpretation. The detailed discussion exhibits the fact that the streamwise co-ordinate velocity ratio parameter, partial slip parameter and the thermal jump parameter have significant influence over the flow and thermal fields.

This work has not been reported in the literature to the authors’ best of knowledge.

The purpose of this paper is to investigate the magnetohydrodynamics mixed convection flow over an exponentially stretching surface in the presence of non-uniform heat source/sink and cross-diffusion. Adequate non-similar transformations are used to transform governing mixed convection boundary layer equations to dimensionless form.

These dimensionless partial differential equations are solved by using implicit finite difference scheme in conjunction with Quasi-linearization technique.

The effects of admissible parameters such as Eckert number (Ec), the ratio of buoyancy forces parameter (N), non-uniform heat source/sink, Soret and Dufour numbers on flow, temperature and concentration distributions are discussed and analysed through graphs. In addition, the results for skin friction coefficient, Sherwood number and Nusselt number are presented and discussed graphically.

In literature, no research work has been found in similar to this research paper.

This study aims to investigate the unsteady magnetohydrodynamic mixed convective nanofluid flow by using Buongiorno two-phase model to achieve an appropriate mechanism to improve the efficiency of solar energy systems by mitigating the energy losses.

The transport phenomena occurring in this physical problem are modelled using nonlinear partial differential equations and are non-dimensionalised by using non-similar transformations. The quasilinearisation technique is used to solve the resulting system with the help of a finite difference scheme.

The study reveals that the effect of the applied transverse magnetic parameter is to increase the temperature profile and to reduce the wall heat transfer rate. The Brownian diffusion and thermophoresis parameters that characterise the nanofluids contribute to the reduction in wall heat transfer rate. The presence of nanoparticles in the fluid gives rise to critical values for the thermophoresis parameter describing the behaviour of the wall heat and mass transfer rates. Wall heating and cooling are analysed by considering the percentage increase or percentage decrease in the heat and mass transfer rates in the presence of nanoparticles in the fluid.

The investigation on wall cooling/heating leads to the analysis of control parameters applicable to the industrial design of thermal systems for energy storage, energy harvesting and cooling applications.

The analysis of the control parameters is of practical value to the solar industry.

In countries, such as South Africa, daily power cuts are a reality. Any research into improving the quality of energy obtained from alternate sources is a national necessity.

From the literature survey in the present study, it is found that no similar work has been reported in the open literature that analyses the time-dependent mixed convection flow along the exponentially stretching surface in the presence of the effects of a magnetic field, nanoparticles and non-similar solutions.

Concerns the laminar flows from a permeable heated surface which arise in fluids due to the interaction of the force of gravity and density differences caused by the simultaneous diffusion of thermal energy and of chemical species. Species concentration levels in air are assumed to be small in many processes in the atmosphere. Under the usual Boussinesque approximations, a set of non‐similar equations for combined buoyancy effects and the permeability of the surface are obtained. The resulting equations have been integrated by four distinct methods: perturbation method for small transpiration rate; asymptotic solutions for large transpiration rate; Keller‐box methods; and local non‐similarity method for any transpiration rate. Effects of various practical values of the Schmidt number, of the multiple buoyancy parameter and that of the transpiration rate of fluid through the surface on the local skin‐friction, the local Nusselt number and the local Sherwood number are shown graphically as well as in tabular form.