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Non‐linear reaction‐diffusion processes with cross‐diffusion in two‐dimensional, anisotropic media are analyzed by means of an implicit, iterative, time‐linearized approximate factorization technique as functions of the anisotropy of the heat and species diffusivity tensors, the Soret and Dufour cross‐diffusion effects, and five types of boundary conditions. It is shown that anisotropy and cross‐diffusion deform the reaction front and affect the front velocity, and the magnitude of these effects increases as the magnitude of the off‐diagonal components of the heat and species diffusivity tensors is increased. It is also shown that the five types of boundary conditions employed in this study produce similar results except when there is either strong anisotropy in the species or heat diffusivity tensors and there are no Soret and Dufour effects, or the species and heat diffusivity tensors are isotropic, but the anisotropy of the Soret and Dufour effects is important. If the species and heat diffusivity tensors are isotropic, the effects of either the Soret or the Dufour cross‐diffusion effects are small for the cases considered in this study. The time required to achieve steady state depends on the anisotropy of the heat and diffusivity tensors, the cross‐diffusion effects, and the boundary conditions.

Some functional properties of engineering materials, i.e. physical, mechanical and thermal ones, depend directly on the microstructure, which is a result of processes occurring in the material during the forming and thermomechanical processing. The proper microstructure can be obtained in many cases by the phase transformation. This phenomenon is one of the most important processes during hot forming and heat treatment. The purpose of this paper is to develop a new comprehensive hybrid model for modeling diffusion phase transformations. A problem has been divided into several tasks and is carried out on several stages. The purpose of this stage is a development of the structure of a hybrid model, development of an algorithm used in the diffusion module and one-dimensional heat flow and diffusion modeling. Generally, the processes of phase transformations are studied well enough but there are not many tools for their complex simulations. The problems of phase transformation simulation are related to the proper consideration of diffusion, movement of phase boundaries and kinetics of transformation. The proposed new model at the final stage of development will take into account the varying grain growth rate, different shape of growing grains and will allow for proper modeling of heat flow and carbon diffusion during the transformation in many processes, where heating, annealing and cooling can be considered (e.g. homogenizing and normalizing).

One of the most suitable methods for modeling of microstructure evolution during the phase transformation is cellular automata (CA), while lattice Boltzmann method (LBM) suits for modeling of diffusion and heat flow. Then, the proposed new hybrid model is based on CA and LBM methods and uses high performing parallel computations.

The first simulation results obtained for one-dimensional modeling confirm the correctness of interaction between LBM and CA in common numerical solution and the possibility of using these methods for modeling of phase transformations. The advantages of the LBM method can be used for the simulation of heat flow and diffusion during the transformation taking into account the results obtained from the simulations. LBM creates completely new possibilities for modeling of phase transformations in combination with CA.

The studies are focused on diffusion phase transformations in solid state in condition of low cooling rate (e.g. transformation of austenite into ferrite and pearlite) and during the heating and annealing (e.g. transformation of the ferrite-pearlite structure into austenite, the alignment of carbon concentration in austenite and growth of austenite grains) in carbon steels within a wide range of carbon content. The paper presents the comprehensive modeling system, which can operate with the technological processes with phase transformation during heating, annealing or cooling.

A brief review of the modeling of phase transformations and a description of the structure of a new CA and LBM hybrid model and its modules are presented in the paper. In the first stage of model implementation, the one-dimensional LBM model of diffusion and heat flow was developed. The examples of simulation results for several variants of modeling with different boundary conditions are shown.

The purpose of the current flow configurations is to bring to attention the thermophysical aspects of magnetohydrodynamics (MHD) Williamson nanofluid flow under the effects of Joule heating, nonlinear thermal radiation, variable thermal coefficient and activation energy past a rotating stretchable surface.

A mathematical model is examined to study the heat and mass transport analysis of steady MHD Williamson fluid flow past a rotating stretchable surface. Impact of activation energy with newly introduced variable diffusion coefficient at the mass equation is considered. The transport phenomenon is modeled by using highly nonlinear PDEs which are then reduced into dimensionless form by using similarity transformation. The resulting equations are then solved with the aid of fifth-order Fehlberg method.

The rotating fluid, heat and mass transport effects are analyzed for different values of parameters on velocity, energy and diffusion distributions. Parameters like the rotation parameter, Hartmann number and Weissenberg number control the flow field. In addition, the solar radiation, Joule heating, Prandtl number, thermal conductivity, concentration diffusion coefficient and activation energy control the temperature and concentration profiles inside the stretching surface. It can be analyzed that for higher values of thermal conductivity, Eckret number and solar radiation parameter the temperature profile increases, whereas opposite behavior is noticed for Prandtl number. Moreover, for increasing values of temperature difference parameter and thermal diffusion coefficient, the concentration profile shows reducing behavior.

This paper is useful for researchers working in mathematical and theoretical physics. Moreover, numerical results are very useful in industry and daily-use processes.

A fundamental principle of materials engineering is that the microstructure of a material controls the properties. The phase transformation is an important phenomenon that determines the final microstructure. Recently, many analytical and numerical methods were used for modeling of phase transformation, but some limitations can be seen in relation to the choice of the shape of growing grains, introduction of varying grain growth rate and modeling of diffusion phenomena. There are also only few comprehensive studies that combine the final microstructure with the actual conditions of its formation. Therefore, the objective of the work is a development of a new hybrid model based on lattice Boltzmann method (LBM) and cellular automata (CA) for modeling of the diffusional phase transformations. The model has a modular structure and simulates three basic phenomena: carbon diffusion, heat flow and phase transformation. The purpose of this study is to develop a model of heat flow with consideration of enthalpy of transformation as one of the most important parts of the proposed new hybrid model. This is one of the stages in the development of the complex model, and the obtained results will be used in a combined solution of heat flow and carbon diffusion during the modeling of diffusion phase transformations.

Different values of overheating/overcooling affect different values in the enthalpy of transformation and thus the rate of transformation. CA and LBM are used in the hybrid model in part related to heat flow. LBM is used for modeling of heat flow, while CA is used for modeling of the microstructure evolution during the phase transformation.

The use of LBM and CA in one numerical solution creates completely new possibilities for modeling of phase transformations. CA and LBM in comparison with commonly used approaches significantly simplify interface and interaction between different parts of the model, which operates in a common domain. The CA can be used practically for all possible processes that consist of nucleation and grains growth. The advantages of the LBM method can be well used for the simulation of heat flow during the transformation, which is confirmed by numerical results.

The developed heat flow model will be combined with the carbon diffusion model at the next stage of work, and the new complex hybrid model at the final stage will provide new solutions in numerical simulation of phase transformations and will allow comprehensive modeling of the diffusional phase transformations in many processes. Heating, annealing and cooling can be considered.

The paper presents the developed model of heat flow (temperature module), which is one of the main parts of the new hybrid model devoted to modeling of phase transformation. The model takes into account the enthalpy of transformation, and the connection with the model of microstructure evolution was obtained.

The classical integer derivative diffusionmodels for fluid flow within a channel of parallel walls, for heat transfer within a rectangular fin and for impulsive acceleration of a quiescent Newtonian fluid within a circular pipe are initially generalized by introducing fractional derivatives. The purpose of this paper is to represent solutions as steady and transient parts. Afterward, making use of separation of variables, a fractional Sturm–Liouville eigenvalue task is posed whose eigenvalues and eigenfunctions enable us to write down the transient solution in the Fourier series involving also Mittag–Leffler function. An alternative solution based on the Laplace transform method is also provided.

In this work, an analytical formulation is presented concerning the transient and passage to steady state in fluid flow and heat transfer within the diffusion fractional models.

From the closed-form solutions, it is clear to visualize the start-up process of physical diffusion phenomena in fractional order models. In particular, impacts of fractional derivative in different time regimes are clarified, namely, the early time zone of acceleration, the transition zone and the late time regime of deceleration.

With the newly developing field of fractional calculus, the classical heat and mass transfer analysis has been modified to account for the fractional order derivative concept.

The purpose of this paper is to consider unsteady free convection flow of a dissipative fluid past an exponentially accelerated infinite vertical porous plate in the presence of Newtonian heating and mass diffusion.

The problem is governed by coupled non-linear partial differential equations with appropriate boundary conditions. A Galerkin finite element numerical solution is developed to solve the resulting well-posed two-point boundary value problem. It is a powerful, stable technique which provides excellent convergence and versatility in accommodating coupled systems of ordinary and partial differential equations.

It is found that the skin friction coefficient increases with increases in either of the Eckert number, thermal Grashof number, mass Grashof number or time whereas it decreases with increases in either of the suction parameter, Schmidt number or the acceleration parameter for both air and water. The skin friction coefficient is also found to decrease with increases in the values of the Prandtl number. In addition, it is found that the rate of heat transfer increases with an increase in the suction parameter and decreases with an increase in the Eckert number for both air and water. Lastly, it is found that the rate of heat transfer increases with increasing values of the Prandtl number and decreases with increasing time for all values of the Prandtl number.

The present study has considered only Newtonian fluids. Future studies will address non-Newtonian liquids.

A very useful source of information for researchers on the subject of free convective flow over the surface when the rate of heat transfer from the surface is proportional to the local surface temperature.

This paper is relatively original and illustrates the effects of viscous dissipation on free convective flow past an exponentially accelerated infinite vertical porous plate with Newtonian heating and mass diffusion.

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 article is primarily concerned with those metallic diffusion coatings that are applied for the protection of iron and steel. It will be presented in three parts: 1. Aluminium coatings. 2. Chromium coatings. 3. Zinc coatings. Special reference is made in each part to the available methods of application, the coatings' composition and structure, their physical properties, and their corrosion and oxidation resistance.

The purpose of this study is to examine the radiation effect on the natural convective heat transfer of an alumina–water nanofluid in a square cavity in the presence of centered nonuniformly heated plate.

The square cavity filled with alumina–water nanofluid has a nonuniformly heated plate placed horizontally or vertically at its center. The plate is heated isothermally with linearly varying temperature. The vertical walls are cooled isothermally with a constant temperature, while the horizontal walls are insulated. The governing equations have been discretized using finite volume method on a uniformly staggered grid system. Simulations were carried out for different values of the heated plate nonuniformity parameter (λ = –1, 0 and 1), the nanoparticles solid volume fraction (Φ = 0.01 − 0.04) and the radiation parameter (R_d = 0 – 2) at the Rayleigh number of Ra = 1e+07.

It is found that the total heat transfer rate is enhanced with an increase in the radiation parameter for both the horizontal and vertical plates. The role of nanoparticles addition to the base fluid can have dual effects on the heat transfer rate by augmenting and dampening for the absence of radiation while it dampens the heat transfer rate for the presence of radiation.

The originality of this work is to analyze steady natural convection in a square cavity filled with a water-based nanofluid in the presence of centered nonuniformly heated plate. The results would benefit scientists and engineers to become familiar with the analysis of convective heat and mass transfer in nanofluids, and the way to predict the properties of nanofluid convective flow in advanced technical systems, in industrial sectors including transportation, power generation, chemical sectors, electronics, etc.

The purpose of this paper is to employ the Generalized Integral Transform Technique in the analysis of conjugated heat transfer in micro-heat exchangers, by combining this hybrid numerical-analytical approach with a reformulation strategy into a single domain that envelopes all of the physical and geometric sub-regions in the original problem. The solution methodology advanced is carefully validated against experimental results from non-intrusive techniques, namely, infrared thermography measurements of the substrate external surface temperatures, and fluid temperature measurements obtained through micro Laser Induced Fluorescence.

The methodology is applied in the hybrid numerical-analytical treatment of a multi-stream micro-heat exchanger application, involving a three-dimensional configuration with triangular cross-section micro-channels. Space variable coefficients and source terms with abrupt transitions among the various sub-regions interfaces are then defined and incorporated into this single domain representation for the governing convection-diffusion equations. The application here considered for analysis is a multi-stream micro-heat exchanger designed for waste heat recovery and built on a PMMA substrate to allow for flow visualization.

The methodology here advanced is carefully validated against experimental results from non-intrusive techniques, namely, infrared thermography measurements of the substrate external surface temperatures and fluid temperature measurements obtained through Laser Induced Fluorescence. A very good agreement among the proposed hybrid methodology predictions, a finite elements solution from the COMSOL code, and the experimental findings has been achieved. The proposed methodology has been demonstrated to be quite flexible, robust, and accurate.

The hybrid nature of the approach, providing analytical expressions in all but one independent variable, and requiring numerical treatment at most in one single independent variable, makes it particularly well suited for computationally intensive tasks such as in optimization, inverse problem analysis, and simulation under uncertainty.