Heat transfer study on solid and porous convective fins with temperature-dependent heat generation using efficient analytical method

A simple and highly accurate semi-analytical method, called the differential transformation method(DTM), was used for solving the nonlinear temperature distribution equation in solid and porous longitudinal fin with temperature dependent internal heat generation. The problem was solved for two main cases. In the first case, heat generation was assumed variable by fin temperature for a solid fin and in second heat generation varied with temperature for a porous fin. Results are presented for the temperature distribution for a range of values of parameters appearing in the mathematical formulation(e.g. N, εG, and G). Results reveal that DTM is very effective and convenient. Also, it is found that this method can achieve more suitable results in comparison to numerical methods.

Radiation heat transfer model for complex superalloy turbine blade in directional solidification process based on finite element method

For the sake of a more accurate shell boundary and calculation of radiation heat transfer in the Directional Solidification(DS) process, a radiation heat transfer model based on the Finite Element Method(FEM)is developed in this study. Key technologies, such as distinguishing boundaries automatically, local matrix and lumped heat capacity matrix, are also stated. In order to analyze the effect of withdrawing rate on DS process,the solidification processes of a complex superalloy turbine blade in the High Rate Solidification(HRS) process with different withdrawing rates are simulated; and by comparing the simulation results, it is found that the most suitable withdrawing rate is determined to be 5.0 mm·min^(-1). Finally, the accuracy and reliability of the radiation heat transfer model are verified, because of the accordance of simulation results with practical process.

Streamline upwind finite element method for conjugate heat transfer problems

This paper presents a combined finite element method for solving conjugate heat transfer problems where heat conduction in a solid is coupled with heat convection in viscous fluid flow. The streamline upwind finite element method is used for the analysis of thermal viscous flow in the fluid region, whereas the analysis of heat conduction in solid region is performed by the Galerkin method. The method uses the three-node triangular element with equal-order interpolation functions for all the variables of the velocity components, the pressure and the temperature. The main advantage of the proposed method is to consistently couple heat transfer along the fluid-solid interface. Three test cases, i.e. conjugate Couette flow problem in parallel plate channel, counter-flow in heat exchanger, and conjugate natural convection in a square cavity with a conducting wall, are selected to evaluate the efficiency of the present method.

Regularization Method to the Parameter Identification of Interfacial Heat Transfer Coefficient and Properties during Casting Solidification

The accurate material physical properties, initial and boundary conditions are indispensable to the numerical simulation in the casting process, and they are related to the simulation accuracy directly. The inverse heat conduction method can be used to identify the mentioned above parameters based on the temperature measurement data. This paper presented a new inverse method according to Tikhonov regularization theory. A regularization functional was established and the regularization parameter was deduced, the Newton-Raphson iteration method was used to solve the equations. One detailed case was solved to identify the thermal conductivity and specific heat of sand mold and interfacial heat transfer coefficient (IHTC) at the meantime. This indicates that the regularization method is very efficient in decreasing the sensitivity to the temperature measurement data, overcoming the ill-posedness of the inverse heat conduction problem (IHCP) and improving the stability and accuracy of the results. As a general inverse method, it can be used to identify not only the material physical properties but also the initial and boundary conditions' parameters.

Nodeless variable finite element method for heat transfer analysis by means of flux-based formulation and mesh adaptation

Based on flux-based formulation, a nodeless variable element method is developed to analyze two-dimensional steady-state and transient heat transfer problems. The nodeless variable element employs quadratic interpolation functions to provide higher solution accuracy without necessity to actually generate additional nodes. The flux-based formulation is applied to reduce the complexity in deriving the finite element equations as compared to the conventional finite element method, The solution accuracy is further improved by implementing an adaptive meshing technique to generaie finite element mesh that can adapt and move along corresponding to the solution behavior. The technique generates small elements in the regions of steep solution gradients to provide accurate solution, and meanwhile it generates larger elements in the other regions where the solution gradients are slight to reduce the computational time and the computer memory. The effectiveness of the combined procedure is demonstrated by heat transfer problems that have exact solutions. These problems tire： （a） a steady-state heat conduction analysis in a square plate subjected to a highly localized surface heating, and （b） a transient heat conduction analysis in a long plate subjected to moving heat source.

ANALYSIS OF THE HEAT TRANSFER IN FIN ASSEMBLIES BY THE BOUNDARY ELEMENT METHOD

The special formulation that allows an accurate and efficient solution to the heat transfer problems within fin assemblies with very large aspect ratios has been developed in this paper Numerically,it consists of the boundary element method in the wall region and the analytical solution in the fin region This modified BEM makes tractable a large class of heat transfer problems in the long and thin domains which are frequently encountered in practice.

Zonal method solution of radiative heat transfer in a one-dimensional long roller-hearth furnace in CSP

A radiative heat transfer mathematical model for a one-dimensional long furnace was set up in a through-type roller-hearth furnace （TTRHF） in compact strip production （CSP）. To accurately predict the heat exchange in the furnace, modeling of the complex gas energy-balance equation in volume zones was considered, and the heat transfer model of heating slabs and wall lines was coupled with the radiative heat transfer model to identify the surface zonal temperature. With numerical simulation, the temperature fields of gas, slabs, and wall lines in the furnace under one typical working condition were carefully accounted and analyzed. The fundamental theory for analyzing the thermal process in TI＇RI-IF was provided.

Study of heat transfer by using DEM–CFD method in a randomly packed pebble-bed reactor

The pebble-bed reactor is one of the most promising designs for the nuclear energy industry. In this paper,a discrete element method-computational fluid dynamics(DEM-CFD) approach that includes thermal conduction, radiation, and natural convection mechanisms was proposed to simulate the thermal-fluid phenomena after the failure of forced circulation cooling system in a pebble-bed core. The whole large-scale packed bed was created using the DEM technique, and the calculated radial porosity of the bed was validated with empirical correlations reported by researchers. To reduce computational costs, a segment of the bed was extracted, which served as a good representative of the large-scale packed bed for CFD calculation. The temperature distributions simulated with two different fluids in this DEM-CFD approach were in good agreement with SANA experimental data. The influence of the natural convection mechanism on heat transfer must be taken into account for coolants with strong convective capacity. The proposed DEM-CFD methodology offers a computationally efficient and widely applied method for understanding the heat transfer process in a pebble-bed core. The method can also be easily extended to assess the passive safety features of newly designed fluoride-salt-cooled pebble-bed reactors.

An GPU accelerated finite difference method for heat transfer simulation

The heat transfer mathematic models are widely used in iron and steel industry area. Many computational models that represent this physical process is based on finite difference methods. The simulation of these phenomena demands a high computa- tional cost. In this paper we employ GPU for the development of algorithm for a two-dimensional heat transfer problem with f＇mite difference methods. The performance evaluation has been made and the comparison between CPU and GPU were discussed. The experimental result shows that GPU can solve this problem more efficiently when we need to divide calculation material into a large number of meshes.

Differential Quadrature Method for Steady Flow of an Incompressible Second-Order Viscoelastic Fluid and Heat Transfer Model

The two-dimensional steady flow of an incompressible second-order viscoelastic fluid between two parallel plates was studied in terms of vorticity, the stream function and temperature equations. The governing equations were expanded with respect to a snmll parameter to get the zeroth- and first-order approximate equations. By using the differenl2al quadrature method with only a few grid points, the high-accurate numerical results were obtained.

Modeling of Coupled Heat and Mass Transfer in a Trapezoidal Porous Bed on a Grid

We investigate heat and mass transfer in an isosceles trapezoidal cavity, filled with charcoal considered as a granular porous medium. The Darcy-Brinkman-Forchheimer flow model is coupled to the energy and mass equations with the assumption of non-thermal equilibrium. These equations are discretized by the finite volume method with an offset mesh and then solved by the line-by-line method of Thomas. The coupling between pressure and velocity is obtained by Semi-Implicit Method for Pressure Linked Equations. (SIMPLE) algorithm. The results show that the temperature in the cavity increases when the inclination angle of the sides walls decreases. The 15° inclination is selected as being able to offer better thermal performance in the cookstove combustion chamber.

ANALYSIS OF THE THERMOPHYSICAL PARAMETERS OF MOIST WOOD PARTICLE MATERIAL IN A COUPLED HEAT AND MASS TRANSFER PROCESS OF FREEZING BY USING FINITE ELEMENT METHOD

The coupled heat and moisture transfer in a freezing process of wood particle material was mathematically modeled in the paper. The models were interactively solved by using the numerical method(the finite element method and the finite difference method). By matching the theoretical calculation to an experiment, the nonlinear problem was analyzed and the variable thermophysical parameters concerned was evaluated. The analysis procedure and the evaluation of the parameters were presented in detail. The result of the study showed that by using the method as described in the paper, it was possible to determine the variable (with respect to temperature, moisture content and freezing state) thermophysical parameters which were unknown or difficult to measure as long as the governing equations for a considered process were available. The method can significantly reduces the experiment efforts for determining thermophysical parameters which arc very complicated to measure. The determined variable of the effective heat conductivity of wood particle material was given in the paper. The error of the numerical calculation was also estimated by the comparison with a matched experiment.

Simulation of heat transfer in steel billets during continuous casting

This work is focused on the development of computational algorithms to create a simulator for solving the heat transfer during the continuous casting process of steel. The temperatures and the solid shell thickness profiles were calculated and displayed on the screen for a billet through a defined continuous casting plant （CCP）. The algorithms developed to calculate billet temperatures, involve the solutions of the corresponding equations for the heat removal conditions such as radiation, forced convection, and conduction according to the billet posi- tion through the CCP. This is done by a simultaneous comparison with the kinematics model previously developed. A finite difference method known as Cmnk-Nicholson is applied to solve the two-dimensional computational array （2D model）. Enthalpy （HIJ） and temperature （TIL） in every node are updated at each step time. The routines to display the results have been developed using a graphical user interface （GUI） in the programming language C＋＋. Finally, the results obtained are compared with those of industrial trials for the surface temperature of three steel casters with different plant configurations in different casting conditions.

Mixed convection heat transfer in horizontal channel filled with nanofluids

The laminar fully developed nanofluid flow and heat transfer in a horizonal channel are investigated. Highly accurate solutions for the temperature and nanopavticle concentration distributions are obtained. The effects of the Brownian motion parameter Nb, the thermophoresis parameter Nt, and the Lewis number Le on the temperature and nanoparticle concentration distributions are discussed. The current analysis shows that the nanoparticles can improve the heat transfer characteristics significantly for this flow problem.

Determination of interfacial heat transfer coefficient and its application in high pressure die casting process

In this paper,the research progress of the interfacial heat transfer in high pressure die casting(HPDC)is reviewed.Results including determination of the interfacial heat transfer coefficient(IHTC),influence of casting thickness,process parameters and casting alloys on the IHTC are summarized and discussed.A thermal boundary condition model was developed based on the two correlations:(a)IHTC and casting solid fraction and(b)IHTC peak value and initial die surface temperature.The boundary model was then applied during the determination of the temperature field in HPDC and excellent agreement was found.

Effects of slip, viscous dissipation and Joule heating on the MHD flow and heat transfer of a second grade fluid past a radially stretching sheet

The flow and heat transfer of an electrically conducting non-Newtonian second grade fluid due to a radially stretching surface with partial slip is considered. The partial slip is controlled by a dimensionless slip factor, which varies between zero （total adhesion） and infinity （full slip）. Suitable similarity transformations are used to reduce the resulting highly nonlinear partial differential equations into ordinary differential equations. The issue of paucity of boundary conditions is addressed and an effective numerical scheme is adopted to solve the obtained differential equations even without augmenting any extra boundary conditions. The important findings in this communication are the combined effects of the partial slip, magnetic interaction parameter and the second grade fluid parameter on the velocity and temperature fields. It is interesting to find that the slip increases the momentum and thermal boundary layer thickness. As the slip increases in magnitude, permitting more fluid to slip past the sheet, the skin friction coefficient decreases in magnitude and approaches zero for higher values of the slip parameter, i.e., the fluid behaves as though it were inviscid. The presence of a magnetic field has also substantial effects on velocity and temperature fields.

Non-uniform heat transfer behavior during shell solidification in a wide and thick slab continuous casting mold

By employing a two-dimensional transient thermo-mechanical coupled finite element model for simulating shell heat transfer behaviors within a slab continuous casting mold, we predicted the evolution of shell deformation and the thermal behaviors, including the mold flux film dynamical distribution, the air gap formation, as well as the shell temperature field and the growth of carbon steel solidification, in a 2120 mm × 266 mm slab continuous casting mold. The results show that the shell server deformation occurs in the off-corners in the middle and lower parts of the mold and thus causes the thick mold flux film and air gap to distribute primarily in the regions of 0–140 mm and 0–124 mm and 0–18 mm and 0–10 mm, respectively, from the corners of the wide and narrow faces of the shell under typical casting conditions. As a result, the hot spots, which result from the thick mold flux film filling the shell/mold gap, form in the regions of 20–100 mm from the corners of the wide and narrow faces of the shell and tend to expand as the shell moves downward.

Numerical calculation of thermal field and heat transfer coefficient for 160 kA aluminum reduction cell

The principle of thermal flux being constant in heat flow tube and the principle of heat balance were applied to analyze and calculate the steady state thermal field and the electrolyte ledge heat transfer coefficient of aluminum reduction cell by finite element method. The calculated results show that the melt ledge heat transfer coefficient in the 160kA prebaked anode aluminum reduction cell of Guizhou Aluminum Smelter is higher than that of other cells of the same current. It is also found that the electrolyte and metal flow much faster, which may be the results of poor bus bar arrangements. Meanwhile, the calculated results of melt ledge heat transfer coefficient by heat flow tube method are almost in full agreement with the former works. This verifies the applicability of this method.

Heat Transfer Between a Missile's Combustion Chamber and the Warhead

Under higher temperatures the charge within a warhead will be subjected to physical and chemical changes, which will influence the security of the warhead launching process. In this paper the problem is studied adopting finite difference method for the case of a rocket powered missile. Temperature distribution tables are given through quadrature experiments, and the results fit the actual measured values very well. The results also show that to ensure the launching security of rocket powered missiles having warhead charge critical temperature close to about 60?℃, the designer can select appropriate heat insulation structural parameters.

A new hybrid method—combined heat flux method with Monte-Carlo method to analyze thermal radiation

A new hybrid method, Monte-Carlo-Heat-Flux （MCHF） method, was presented to analyze the radiative heat transfer of participating medium in a three-dimensional rectangular enclosure using combined the Monte-Carlo method with the heat flux method. Its accuracy and reliability was proved by comparing the computational results with exact results from classical ＂Zone Method＂.