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To study quantitatively the effects of combined temperature dependent thermodynamics and transport fluid properties on the heat transfer rate, heat function fields and profiles in a fluid filled square enclosure.

Navier‐Stokes equations in two‐dimensions, which are the flow governing equations, were transformed into stream function and vorticity transport equations. These equations together with the energy and heat function equations were cast into their non‐dimensional forms. Numerical solutions of the resulting equations were done by the use of finite‐difference method.

The numerical investigations conducted covered the Rayleigh and Prandtl numbers in the range 10³≤Ra≤10⁶ and 0.01≤Pr≤450, respectively, and expansion parameter ε=(T_h−T_c)/T_R in the range 0.05≤ε≤1. Results show that Boussinesq‐approximation is not sufficient to simulate natural convective flow when the difference between T_h and T_c is high and close to the reference state temperature. The effects of the other fluids properties other than density can be disregarded in computation without significant loss of accuracy. Combined fluid properties have very strong effects on the heat transfer, heat function fields and profiles.

The results of this study will serve as baseline information to designers of heat transfer or process equipment in which fluid at very high temperature occurs.

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.

Spiral-wound heat exchangers (SWHEs) are widely used in different industries. In special applications, such as cryogenic (HEs), fluid properties may significantly depend on fluid temperature. This paper aims to present an analytical method for design and rating of SWHEs considering variable fluid properties with consistent shell geometry and single-phase fluid.

To consider variations of fluid properties, the HE is divided into identical segments, and the fluid properties are assumed to be constant in each segment. Validation of the analytical method is accomplished by using three-dimensional numerical simulation with shear stress transport k-ω model, and the numerical model is verified by using the experimental data. Moreover, the HE cost is selected as the main criterion in obtaining the proper design, and the most affordable geometry is selected as the proper design.

The accuracy of different heat transfer and pressure drop correlations is investigated by comparing the analytical and numerical results. The average errors in the calculation of effectiveness, shell-side pressure drop and tube-side pressure drop using the analytical method are 2.1%, 13.9% and 13.3%, respectively. Moreover, the effect of five main geometrical parameters on the SWHE cost is investigated. The results indicate that the effect of longitudinal pitch ratio on the SWHE cost can be neglected, whereas other geometrical parameters have a significant impact on the total cost of the SWHE.

This work contains a versatile and low-cost analytical method to design and rating the SWHEs considering the variable fluid property with consistent shell geometry. The previous studies have introduced complex methods and have not considered the consistency of shell geometry.

The interaction of variable property convection and surface radiation in a differentially heated square cavity is considered. Effect of surface radiation on natural convection has been studied from the point of view of flow structure and isotherm patterns. Wherever possible, a comparative study has been invoked between the outcome of the present work and the constant property formulation. The finite element method has been used in the present work and associated formulation schemes have been described in detail.

The generalized integral transform technique (GITT) is an hybrid numerical‐analytical method that has been successfully applied in convection‐diffusion problems, where the original potentials are replaced by eigenexpansion series, and the system of partial differential equations is transformed into a finite system of ordinary differential equations, allowing to obtain an error controlled solution without any kind of grid generation. This paper aims at the application of GITT to the transient version of the classical differentially heated square cavity problem, considering fluid properties as functions of temperature. Comparing results to some previously reported data for constant fluid properties validates the computational procedure. The solution for variable fluid properties with Boussinesq approximation is presented for several values of inclinations, at Rayleigh number of 10³ and a Prandtl number of 0.71, demonstrating GITT capability of capturing circulating cells formation and evolution at a low Rayleigh number. New correlations for leaning angle and aspect ratio are presented.

The effect of non-linear thermal radiation and variable thermo-physical properties are investigated in the Falkner-Skan flow of a Casson nanofluid in the presence of magnetic field. The paper aims to discuss this issue.

Selected bunch of similarity transformations are used to reduce the governing partial differential equations into a set of non-linear ordinary differential equations. The resultant equations are numerically solved using Runge-Kutta-Fehlberg fourth-fifth-order method along with shooting technique.

The velocity, temperature and concentration profiles are evaluated for several emerging physical parameters and are analyzed through graphs and tables in detail.

This study only begins to reveal the research potential and pitfalls of research and publishing on boundary-layer flow, heat and mass transfer of Casson nanofluid past and the moving and static wedge-shaped bodies.

It is found that the presence of non-linear thermal radiation and variable properties has more influence in heat transfer. Furthermore, temperature profile increases as the radiation parameter increases.

The purpose of this paper is to examine the effects of thermophoresis and magnetic field on steady two‐dimensional laminar hydrodynamic flow with heat and mass transfer over a semi‐infinite permeable flat surface in the presence of viscous dissipation and thermal radiation effects. The fluid viscosity and thermal conductivity are assumed to vary as a function of temperature.

The boundary layer equations are transformed to non‐linear ordinary differential equations using scaling group of transformations and these equations are solved numerically by using the fourth order Runge‐Kutta method with shooting technique for some values of physical parameters.

Some of the results obtained for a special case of the problem are compared to the results published in previous work and are found to be in excellent agreement. Many results are obtained and a representative set is displayed graphically to illustrate the influence of the physical parameters involved in the problem on the velocity, temperature and concentration profiles, as well as the local skin‐friction coefficient, the wall heat transfer and the particle deposition rate.

One valuable, important observation is that the effect of the variable viscosity parameter is to increase the effect of all studied parameters in the boundary‐layer's flow field. Also, the skin‐friction coefficient, wall heat transfer and wall deposition flux in a fluid of uniform viscosity are higher than in a fluid of non‐uniform viscosity when the surface is permeable.

The paper presents a numerical solution for two‐dimensional boundary‐layer flow with heat and mass transfer over a semi‐infinite permeable flat surface. Numerical results indicate that the combining effects of magnetic field and radiation strongly controls flow and mass transfer characteristics for the thermophoretic hydrodynamic flow. This problem is interesting from the physical point of view and also for its applications in engineering sciences.

The purpose of this paper is to investigate the unsteady magnetohydrodynamic (MHD) Couette flow of an electrically conducting incompressible non-Newtonian third grade reactive fluid with temperature-dependent variable viscosity and thermal conductivity properties under isothermal surface conditions.

The coupled non-linear partial differential equations for momentum and energy balance governing the transient problem are obtained and tackled numerically using a semi-discretization finite difference technique.

The effects of various embedded thermophysical parameters on the velocity and temperature fields including skin friction, Nusselt number and thermal stability conditions are presented graphically and discussed quantitatively.

The approach is applicable to modelling the complex physical phenomenon in MHD lubrications that occurs in numerous areas of engineering and industrial processes.

This paper may be of industrial and engineering interest especially in understanding the combined effects of unsteadiness, variable thermophysical properties and magnetic field on the thermal stability condition for a reactive non-Newtonian third grade fluid under Couette flow scenario.

This paper aims to explore the variable properties of a flow inside the thin film of a unsteady Maxwell fluid and to analyze the effects of shrinking and stretching sheet.

The governing mathematical model has been developed by considering the boundary layer limitations. As a result of boundary layer assumption, a nonlinear partial differential equation is obtained. Later on, similarity transformations have been adopted to convert partial differential equation into an ordinary differential equation. A well-known homotopy analysis method is implemented to solve the problem. MATHEMATICA software has been used to visualize the flow behavior.

It is observed that variable viscosity does not have a significant effect on velocity field and temperature distribution either in shrinking or stretching case. It is noticed that Maxwell parameter has no dramatic effect on the flow of thin liquid fluid. It has been seen that heat flow increases by increasing the conductivity with temperature in both cases (shrinking/stretching). As a result, fluid temperature goes down when than delta = 0.05 than delta = 0.2.

To the best of authors’ knowledge, nobody has conducted earlier thin film flow of unsteady Maxwell fluid with variable fluid properties and comparison of shrinking and stretching sheet.

The steady two-dimensional laminar boundary layer flow, heat and mass transfer over a flat plate with convective surface heat flux was considered. The governing nonlinear partial differential equations were transformed into a system of nonlinear ordinary differential equations and then solved numerically by Runge–Kutta method with the most efficient shooting technique. Then, the effect of variable viscosity and variable thermal conductivity on the fluid flow with thermal radiation effects and viscous dissipation was studied. Velocity, temperature and concentration profiles respectively were plotted for various values of pertinent parameters. It was found that the momentum slip acts as a boost for enhancement of the velocity profile in the boundary layer region, whereas temperature and concentration profiles decelerate with the momentum slip.

Numerical Solution is applied to find the solution of the boundary value problem.

Velocity, heat transfer analysis is done with comparing earlier results for some standard cases.

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