Simulation Of Heat Transfer Problems Research Articles

Transient heat transfer and solidification modelling in direct-chill casting using a generalized finite differences method

The goal of this work is to achieve a novel solution of the transient heat transfer problem in the start-up phase of directchill casting processes using a Generalized Finite Differences Method. This formulation is applied in order to solve the heat transfer equation in strong form under a Lagrangian description. The boundary conditions incorporation is done in a simple and natural way. The meshfree nature of this approach allows to capture the motion and phase boundaries evolution without using remeshing approaches. The simplicity, efficiency and suitability of this numerical formulation is demonstrated by comparison of the obtained numerical results with the results already published by other researchers. This shows that our approach is promising for the numerical simulation of heat transfer problems during the start-up phase of direct-chill casting processes.

An a posteriori error estimate for the generalized finite element method for transient heat diffusion problems

SummaryWe propose the study of a posteriori error estimates for time‐dependent generalized finite element simulations of heat transfer problems. A residual estimate is shown to provide reliable and practically useful upper bounds for the numerical errors, independent of the heuristically chosen enrichment functions. Two sets of numerical experiments are presented. First, the error estimate is shown to capture the decrease in the error as the number of enrichment functions is increased or the time discretization refined. Second, the estimate is used to predict the behaviour of the error where no exact solution is available. It also reflects the errors incurred in the poorly conditioned systems typically encountered in generalized finite element methods. Finally, we study local error indicators in individual time steps and elements of the mesh. This creates a basis towards the adaptive selection and refinement of the enrichment functions. Copyright © 2016 John Wiley & Sons, Ltd.

Immersed boundary method for the simulation of heat transfer and fluid flow based on vorticity–velocity formulation

ABSTRACTThe present paper, based on the vorticity–velocity formulation of the Navier–Stokes equations, proposes an immersed boundary method for the simulation of heat transfer problems within a geometrically complex domain. The desired boundary conditions are imposed by the direct modification of the initial conditions of vorticity transport and energy equations using smooth interpolations. The time advancement of both transport equations is performed by the explicit fourth-order Runge–Kutta method. One of the main objectives of this paper is to present global smooth interpolations to evaluate the local Nusselt number. The forced convection of moving and fixed circular cylinders, natural convection problem in complex geometries, and the mixed convection between two concentric cylinders—at various Reynolds numbers—are studied.

МОДЕЛЮВАННЯ ЗАДАЧІ КОНВЕКТИВНОГО ТЕПЛООБМІНУ В ХОЛОДИЛЬНІЙ ШАФІ РЕФРИЖЕРАТОРНОГО КОНТЕЙНЕРА

Materials of the study are directed on the solving the problem of air velocity calculating in a confined volume of refrigerating chamber of 20 foot refrigerated container with forced air convection from Carrier Transicold producer firm and on this basis –of convective heat transfer. Problem simulation has been performed in a two-dimensional coordinate system using COMSOL Multiphysics, Femlab 3.0, Fluid Dynamics - Incompressible Navier-Stokes - Convection and Conduction software. As an object of research differential equations of air movement impulse and transfer of energy with it were applied. As a subject of research was selected thermal physical phenomena inside and around the net volume of empty and loaded refrigerated container at air movement. Significant impact of the air movement on the temperature distribution inside the refrigerating container chamber has been established.The obtained results allow to get closer to the theoretical evaluation of the refrigerating machine efficiency in an ordered mode during changes of thermophysical parameters of cargo volume and the environment during perishable products transportation. Tested method is useful for application by scientists and post-graduate students engaged in theoretical simulation of heat transfer problems in the field of refrigeration engineering.

Mathematical solutions and numerical models employed for the investigations of PCMs׳ phase transformations

Abstract Latent heat thermal energy storage (LHTES) has recently attracted increasing interest related to the thermal applications, and has been studied by researchers using theoretical and numerical approaches. The heat transfer mechanisms during the charging and discharging periods of the phase change materials (PCMs) and two basic problems for phase transformations have been discussed in this paper. 1D, 2D and 3D popular mathematical solutions based on the heat transfer mechanisms of conduction and/or convection have been analyzed. Then, various numerical models for encapsulated PCMs in terms of macro-encapsulated PCM and micro-encapsulated PCM were investigated. The numerical simulation of heat transfer problems in phase change processes is complicated and the achieved results are approximate according to a number of conditions. The accuracy of numerical solution depends on the assumptions that are made by the authors. Therefore this review will enable the researchers to have an overall view of the mathematical and numerical methods used for PCM׳s phase transformations. It offers the researcher a guideline of selecting the appropriate theoretical solutions according to their researches׳ purposes.

Research and Numerical Simulation of Heat Transfer Problems in the Industrial Production

This article focuses on heat conduction problems in the process of steel industry. Modeling the direct problems of heat transfer, establish heat conduction and thermal radiation model. Model discretization method are used, discussion process from one dimension to two. We give the difference schemes, and the numerical example. Through the results we compare differences between one and two dimensional models, and the impact to the results of the two heat transfer mode.

Numerical Simulation of Solidification by SPH in Sand Cast Process

In this paper, Smoothed Particle Hydrodynamics (SPH) was used for the prediction of heat conduction problems in sand cast process. The implementation of solidification modeling in a curved casting based on SPH has been described. The treatment of latent heat was introduced in SPH conduction problem by temperature compensation method, which demonstrated the role of latent heat has a great influence on the heat distribution in the casting. The temperature distribution calculated by SPH provided a great agreement with those computed through numerical software MSC.Marc, which validated the efficiency and precision of SPH simulation of heat transfer problems in sand cast process.

Numerical Simulation of Heat Transfer Problem in Hot and Cold Rolling Process

An efficient numerical model had been developed to model the thermal behaviour of the rolling process. An Eulerian formulation was employed to minimize the number of grid points required. The model is capable to calculate the temperature distribution, the heat penetration depth, the convection heat transfer coefficient of cooling, the flow of metal through the roll gap, and the heat generation by plastic deformation and friction. The roll is assumed to rotate at constant speed, and the temperature variations are assumed to be cyclically steady state and localized with a very thin layer near the surface. The Conventional Finite Difference (CFDM) based on cylindrical coordinates was used to model the roll, and a Generalized Finite Difference Method (GFDM) with non-orthogonal mesh was employed in the deformed strip region and the roll-strip interface area. An upwind differencing scheme was selected to overcome the numerical instability resulting from the high velocity ( high Peclet number ) involved in the rolling process. The equations of the strip and roll are then coupled together and solved simultaneously. Both cold and hot rolling heat transfer behaviours, velocity distribution, and heat generation by deformation and friction under typical rolling conditions were presented to demonstrate the feasibility and capability of the developed numerical model. It has been found that, while the strip is under deformation, the bulk temperature inside the strip increases continuously; this is largely controlled by the deformation energy. On the other hand, the strip surface temperature changes much more drastically and it is mainly controlled by the friction heat and the roll temperature. The roll acts like a heat sink, because the coolant heavily cools it. Thus, as soon as the strip hits the roll its surface temperature drops. Since considerable friction and deformation heat are created along the interface and transferred from the neighboring sub-layer, the surface temperature picks up rapidly. Finally, the results of the temperature distribution for both cold and hot rolling and the heat generation by deformation and friction obtained from the present study were compared with previous published work to verify the validity of the numerical solution. Good acceptable agreements were obtained.

A stabilized finite element method for incompressible flow and heat transfer: A natural derivation based on the use of local time-steps

In a recent paper the author introduced a stabilized finite element method suitable for the solution of incompressible viscous flows. In this work the method is extended to deal with problems involving coupled flow and heat transfer. Minimization of momentum and energy squared residuals are employed to obtain a stabilized finite element formulation suitable for the simulation of heat transfer problems in free, mixed and forced convection. Numerical solutions of some representative examples demonstrate the application of the proposed stabilized formulation.

Advanced numerical simulation of heat transfer problems

AbstractThis paper describes two kinds of practical numerical techniques for heat transfer problems. One is a parallel large eddy simulation technique with heat transfer using tetrahedral finite elements and the other is the Voxel method using a uniform grid combined with the discrete element method for liquid–solid two‐phase flow problems. These two approaches are taken to be the candidates for the practical use of large‐scale heat transfer analysis for various kinds of problems. The former can reduce the overall computing time in performing a large‐scale heat transfer analysis through the combined use of an automatic mesh generation software, and the latter is very useful and efficient to analyse a complicated heat transfer phenomena such as a liquid–solid two‐phase flow in a fluidized bed. Numerical examples for both approaches show fairly good agreement with experimental results and these two methods are demonstrated to be powerful tools for analysing large‐scale and complicated heat transfer problems. Copyright © 2004 John Wiley & Sons, Ltd.

A non-steady-state probe measurement method to determine heat conductivity, heat capacity as well as moisture in solids and bulk materials

It is important to know the heat conductivity coefficent for an effective use of energy, for quality control of many products or numerical simulation of heat transfer problems. Measurement of heat conductivity should be realized with high reliability and accuracy, in a short time and with low expenditure both in the laboratory and in situ at the production process, to be able to influence the current process. A non-stationary probe and measurement method developed at Dresden University (Institute of Thermodynamics and Human Engineering) allows the determination of heat conductivity, heat capacity as well as water content of solid and bulk materials. Comparative measurements on standard materials and expert opinions of various institutions confirm the high accuracy and the reliability of the non-steady-state probe measurement device also in so called “problematic” materials.