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This paper aims to propose a characteristic stabilized finite element method for non-stationary conduction-convection problems.

To avoid difficulty caused by the trilinear term, the authors use the characteristic method to deal with the time derivative term and the advection term. The space discretization adopts the low-order triples (i.e. P₁-P₁-P₁ and P₁-P₀-P₁ triples). As low-order triples do not satisfy inf-sup condition, the authors use the stability technique to overcome this flaw.

The stability and the convergence analysis shows that the method is stable and has optimal-order error estimates.

Numerical experiments confirm the theoretical analysis and illustrate that the authors’ method is highly effective and reliable, and consumes less CPU time.

The purpose of this paper is to propose a new method to solve the incompressible natural convection problem with variable density. The main novel ideas of this work are to overcome the stability issue due to the nonlinear inertial term and the hyperbolic term for conventional finite element methods and to deal with high Rayleigh number for the natural convection problem.

The paper introduces a novel characteristic variational multiscale (C-VMS) finite element method which combines advantages of both the characteristic and variational multiscale methods within a variational framework for solving the incompressible natural convection problem with variable density. The authors chose the conforming finite element pair (P₂, P₂, P₁, P₂) to approximate the density, velocity, pressure and temperature field.

The paper gives the stability analysis of the C-VMS method. Extensive two-dimensional/three-dimensional numerical tests demonstrated that the C-VMS method not only can deal with the incompressible natural convection problem with variable density but also with high Rayleigh number very well.

Extensive 2D/3D numerical tests demonstrated that the C-VMS method not only can deal with the incompressible natural convection problem with variable density but also with high Rayleigh number very well.

This paper aims to propose two parallel two-step finite element algorithms based on fully overlapping domain decomposition for solving the 2D/3D time-dependent natural convection problem.

The first-order implicit Euler formula and second-order Crank–Nicolson formula are used to time discretization respectively. Each processor of the algorithms computes a stabilized solution in its own global composite mesh in parallel. These algorithms compute a nonlinear system for the velocity, pressure and temperature based on a lower-order element pair (P₁b-P₁-P₁) and solve a linear approximation based on a higher-order element pair (P₂-P₁-P₂) on the same mesh, which shows that the new algorithms have the same convergence rate as the two-step finite element methods. What is more, the stability analysis of the proposed algorithms is derived. Finally, numerical experiments are presented to demonstrate the efficacy and accuracy of the proposed algorithms.

Finally, numerical experiments are presented to demonstrate the efficacy and accuracy of the proposed algorithms.

The novel parallel two-step algorithms for incompressible natural convection problem are proposed. The rigorous analysis of the stability is given for the proposed parallel two-step algorithms. Extensive 2D/3D numerical tests demonstrate that the parallel two-step algorithms can deal with the incompressible natural convection problem for high Rayleigh number well.

The purpose of this paper is to examine numerically the three natural convection of air induced by temperature difference between a cold outer cubic enclosure and a hot inner cylinder. Simulations have been carried out for Rayleigh numbers ranging from 103 to 107 and titled angle of the enclosure from 0° to 90°. The developed mathematical model is governed by the coupled equations of continuity, momentum and energy, and is solved by finite volume method. The effects of cylinder inclination and Rayleigh number on fluid flow and heat transfer are presented. The distribution of isocontours of temperature and isosurfaces of velocity eventually reaches a steady state in the range of Rayleigh numbers between 103 and 107 for titled inclination of 90°; however, for the remaining inclinations, Rayleigh number must be in the range 103-106 to avoid unsteady state, which is manifested by the division of the area containing the maximum local heat transfer rate into three parts for a Rayleigh number equal to 107 and an inclination of 90°. We mention that instability study is not included in the present paper, which is solely devoted to three-dimensional calculations. Results also indicate that optimal average heat transfer rate is obtained for both high Rayleigh number of 106 and high inclination of 90° for the two cases of the inner cylinder and cubical enclosure.

The manuscript deals with prediction of the three-dimensional natural convection phenomena in a cubical cavity induced by an isothermal cylinder at the center with different inclinations by simulating the flow using highly numerical methods such as finite volume method.

It is found that the local Nusselt number through active walls for titled inclination set at 90°, the symmetry of the flow is conserved and the area containing the maximum heat transfer is divided into three smaller areas situated near the upper portion of the wall, taking the maximum value. That may be due to the preparation of local occurrence of instabilities and bifurcation phenomena that appear for Ra > 107, which is not included in the present paper to save journal space. It was found also that an optimal heat transfer appears when the cylinder orientation becomes vertical (a = 90°). For this inclination, buoyancy forces act upward, corresponding to an aiding situation. In addition, heat transfer rate is increasing with Rayleigh numbers, so correlations of average Nusselt through the cubical cavity and the cylinder are established as function of two parameters (Ra, a). Comparisons of the numerical results with those obtained from all correlations show good agreements.

To the author’s knowledge, studies have thus far adressed three-dimensional cuboids enclosures induced by an inner shape which the location is changed. However, no study has examined three-dimensional natural convection between the inner isothermal cylinder and outer cooled cubical enclosure when the outer enclosure is tilted.

This paper aims to study numerically the simulation of convective–radiative heat transfer under an effect of variable thermally generating source in a rotating square chamber. The performed analysis deals with a development of passive cooling system for the electronic devices.

The domain of interest of size H rotating at a fixed angular velocity has heat-conducting solid walls with a constant cooling temperature for the outer boundaries of the vertical walls and with thermal insulation for the outer borders of the horizontal walls. The chamber has a heater on the bottom wall with a time-dependent volumetric heat generation. The internal surfaces of the walls and the energy element are both grey diffusive emitters and reflectors. The fluid is transparent to radiation. Computational model has been written using non-dimensional parameters and worked out by the finite difference technique. The effect of the angular velocity, volumetric heat generation frequency and surface emissivity has been studied and described in detail.

The results show that growth of the surface emissivity leads to a diminution of the mean heater temperature, while a weak rotation can improve the energy transport for low volumetric thermal generation frequency.

An efficient computational approach has been used to work out this problem. The originality of this work is to analyze complex (conductive–convective–radiative) energy transport in a rotating system with a local element of time-dependent volumetric heat generation. To the best of the authors’ knowledge, an interaction of major heat transfer mechanisms in a rotating system with a heat-generating element is scrutinized for the first time. The results would benefit scientists and engineers to become familiar with the analysis of complex heat transfer in rotating enclosures with internal heat-generating units, and the way to predict the heat transfer rate in advanced technical systems, in industrial sectors including transportation, power generation, chemical sectors and electronics.

In this paper we consider several aspects related to the application of the pseudo‐concentration techniques to the simulation of mould filling processes. We discuss, in particular, the smoothing of the front when finite elements with interior nodes are employed and the evacuation of air through the introduction of temporary free wall nodes. The basic numerical techniques to solve the incompressible Navier—Stokes equations are also briefly described. The main features of the numerical model are the use of div‐stable velocity—pressure interpolations with discontinuous pressures, the elimination of the pressure via an iterative penalty formulation, the use of the SUPG approach to deal with convection‐dominated problems and the temporal integration using the generalized trapezoidal rule. At the end of the paper we present some numerical results obtained for a two‐dimensional test problem showing the ability of the method to capture complicated flow patterns.

A new heat transfer simulation capability is described. Non‐traditional features of this capability include: a seamless link to CAD‐CAM for rapid problem specification/description, integrated automatic grid generator tools for rapid mesh generation, nonlinear and/or varying material properties, source‐terms and boundary conditions, a one‐element type approach for simplicity and efficiency, automatic self‐adaptive mesh refinement and coarsening with accurate error estimation, heavy reliance on iterative solvers, and on‐line display on workstations for immediate visualization and user feedback. These innovations are documented on several examples that demonstrate the usefulness of the developed capability.

The purpose of this paper is to determine the time-dependent heat transfer coefficient during FC-72 flow boiling in a 1.7-mm-deep vertical and asymmetrically heated minichannel.

The temperature of the minichannel heated wall was recorded continuously with the use of thermocouples. The heat transfer coefficients for the subcooled and saturated boiling regions at the heated wall–fluid contact surface were calculated from the Robin boundary condition. Both the wall and fluid temperatures were obtained from the solution of the inverse nonstationary problems in two adjacent domains: the heated wall and flowing fluid. The FEM with Trefftz-type basis functions was applied to solve the inverse problem.

The obtained time-dependent heat transfer coefficient in subcooled boiling achieved rather low values, whereas in saturated boiling, the coefficient was the highest at the channel inlet. The boiling curves were plotted to illustrate the results.

The results of experiments are the best source of information for the design of minichannel cooling systems used for thermoregulation of components and heat exchangers. High-tech minichannel heat exchangers are applied in various industrial applications as microelectronics devices, gas turbines, internal combustion engines, nuclear reactors, X-ray sources and organic rankine cycle (ORC) modules.

In the study, the Trefftz functions for the nonstationary Fourier–Kirchhoff equation with the factor describing void fraction were determined and then used to construct the time-dependent basis functions in FEM.

To provide an analysis of transient heat conduction, which is solved using different iterative solvers for graduate and postgraduate students (researchers) which can help them develop their own research.

Three‐dimensional transient heat conduction in homogeneous materials using different time‐stepping methods such as finite difference (Θ explicit, implicit and Crank‐Nicolson) and finite element (weighted residual and least squared) methods. Iterative solvers used in the paper are conjugate gradient (CG), preconditioned gradient, least square CG, conjugate gradient squared (CGS), preconditioned CGS, bi‐conjugate gradient (BCG), preconditioned BCG, bi‐conjugate gradient stabilized (BCGSTAB), reconditioned BCGSTAB and Gaussian elimination with incomplete Cholesky factorization.

Provides information on which time‐stepping method is the most accurate, which solver is the fastest to solve a symmetric and positive system of linear matrix equations of all those considered.

Fortran 90 code given as an abstract can be very useful for graduate and postgraduate students to develop their own code.

This paper offers practical help to an individual starting his/her research in the finite element technique and numerical methods.

The paper aims to propose a parallel algorithm in order to increase speed and efficiency of an analysis of transient thermal field in layered DC cables.

Initial-boundary problem of thermal field was discretized by means of implicit finite difference method in cylindrical coordinates. A two-stage time decomposition method was applied to introduce parallel computations. An assumed duration of the transient state was decomposed. The system of algebraic equations was being solved with the use of a conjugate gradient method (with diagonal preconditioning) in all time intervals simultaneously.

A method for solving (with the use of parallel computing system) the transient heat conduction equation in a DC cable consisting of arbitrary number of material layers was given. The dependence of the convective heat transfer coefficient on the location on the perimeter of the cable and on its surface temperature (which introduced non-linearity in the boundary condition) was taken into account. The influence of the determined field on the efficiency of the heat source was also taken into consideration in the model.

The main limitation is induced by cylindrical and coaxial structure of the consecutive layers of the system. Thermal field is generated by direct current flow only. The length of the fragment of the cable under consideration should be much greater than its diameter.

The time-spatial distribution of thermal field in the cross-section of the cable can be used for analysis of its reliability and for determination of important characteristics and parameters of the system.

A parallel algorithm of solving initial-boundary parabolic problem was proposed as a result of synthesis of three methods (finite difference, time decomposition and conjugate gradient). An algorithm of minimization of disturbances of the solution introduced at the division points was given. Equations approximating real distribution of heat transfer coefficient from the surface of the cable were proposed.