Modeling Of Heat Transfer Processes Research Articles

Experimental study and mathematical modelling of heat transfer processes in heat accumulating media

Experimental results on reversing non-stationary heat transfer are presented for filtration of an air flow through an immobile heat accumulating medium consisting of lead (D = 2.0, 3.5, and 4.5 mm) and glass (D = 3.2 mm) balls. The studied device imitated the cyclic modes of heat regeneration in the ventilation system for domestic and office rooms. Dependency between the time of flow switching and Re number was measured. The mathematical model describing heat transfer between a gas flow and an immobile layer of balls was developed. Good correspondence between the experimental data and calculation results is observed for high Reynolds numbers. For low Re numbers the effect of heat losses is considerable, and experimental time of flow switching is shorter than the calculation one.

Integrating Finite Element Based Heat Transfer Analysis with Multivariate Optimization for Efficient Weld Pool Modeling

Measurement of weld thermal cycle and peak temperature is a difficult task in fusion welding due to high peak temperature and rapid thermal cycle. Numerical modeling of heat transfer process in fusion welding provides a useful tool for the prediction of the weld pool shape and thermal cycles. However, the reliability of the predictions greatly depends on the accuracy of the input parameters provided to such models. In the case of laser beam welding, the absorptivity represents an important variable that defines the actual heat input for a given power while the value of absorptivity rarely known a-priori with confidence. The present work provides a novel framework where the unknown value of the absorptivity is obtained using an inverse approach by integrating finite element based heat transfer simulation and multivariate optimization procedure. The heat transfer simulation predicts the weld pool dimensions for known welding conditions and assigned values of absorptivity. The optimization algorithm tracks the error in the prediction, its sensitivity with small change in absorptivity, and finally yields the optimum value of absorptivity iteratively. Eight known welding conditions and corresponding weld pool measurements were utilized in this work. It is experienced that the optimum value of absorptivity remains nearly same irrespective of the number of known measurements used for the optimization process thereby indicating the robustness of the inverse approach.

Hierarchic modeling of heat transfer processes in heat exchangers

An alternate approach based on hierarchic modeling is proposed to simulate fluid and heat flow in heat exchangers. On the first level, the direct simulations have been performed for the geometry that is similar to a segment of the examined heat sink. Based on the obtained results, the Reynolds number dependencies of the scaling factors f and StPr 2/3 have been established. On the second level, the integral model of the whole heat sink has been built using the volume averaging technique (VAT). The averaging of the transport equations leads to a closure problem. The direct model Reynolds number dependencies f and StPr 2/3 have been used to calculate the local values of the drag coefficient C ^ d and the heat transfer coefficient ϑ ^ , which are needed in the integral model. The example calculations have been performed for 14 different pressure drops Δ p ¯ across the aluminum heat sink. The whole-section drag coefficient C ¯ d and Nusselt number Nu ¯ have been calculated and compared with the experimental data [M. Rizzi, M. Canino, K. Hu, S. Jones, V. Travkin, I. Catton, Experimental investigation of pin fin heat sink effectiveness, in: Proc. of the 35th National Heat Transfer Conference Anaheim, California, 2001]. A good agreement between the modeling results and the experiment data has been reached with same discrepancies in the transitional regime. The constructed computational algorithm offers possibilities for geometry improvements and optimization, to achieve higher thermal effectiveness.

Grid approximation of a singularly perturbed boundary value problem modelling heat transfer in the case of flow over a flat plate with suction of the boundary layer

In the present paper we consider a boundary value problem on the semiaxis (0,∞) for a singularly perturbed parabolic equation with the two perturbation parameters ε 1 and ε 2 multiplying, respectively, the second and first derivatives with respect to the space variable. Depending on the relation between the parameters, the differential equation can be either of reaction–diffusion type or of convection–diffusion type. Correspondingly, the boundary layer can be either parabolic or regular. For this problem we consider the case when the boundary layer can be controlled by continuous suction of the fluid out of the boundary layer (model problems of this type appear in the mathematical modelling of heat transfer processes for flow past a flat plate). Errors in the approximations generated by standard numerical methods can be unsatisfactorily large for small values of the parameter ε 1. We construct a monotone finite difference scheme on piecewise uniform meshes which generates numerical solutions converging ε-uniformly with order O(N −1 ln N+N 0 −1) , where N 0 is the number of nodes in the time mesh and N is the number of meshpoints on a unit interval of the semiaxis in x. Although the solution of problem has a singularity only for ε 1→0, the character of the boundary layer depends essentially on the vector-valued parameter ε=( ε 1, ε 2). This prevents us from constructing an ε-uniformly convergent scheme having a transition parameter which is independent of the parameter ε 2.

Analysis of thermal processes in solidifying casting using the combined variant of the BEM

In the paper the numerical model of heat transfer processes proceeding in the heterogeneous system casting-mould-core is presented. The problem is treated as a 2D boundary-initial task. Non-steady temperature field is found on the basis of the boundary element method. In particular, the variant called the BEM using discretization in time is applied [Curran et al., Appl. Math. Modelling 4 (1980) 398; W. Sichert, Berechnung von Instationaren thermishen Problemen mittels der Rangelementmethode (1989)]. The method is adapted for non-homogeneous system, at the same time the solidification process is taken into account by the approach called the one domain method [V.R. Voller, Comput. Modelling Free Moving Problems, 1991, p. 3], while the numerical model of this phenomena bases on the temperature field correction method [E. Majchrzak, B. Mochnacki, Comput. Assisted Mech. Eng. Sci. 3 (4) (1996) 327; E. Majchrzak, B. Mochnacki, Eng. Anal. Boundary Elements 16 (1995) 99]. In the final part of the paper the computations of complex casting solidification are shown.

Mathematical simulation of heat transfer process in skin cover at burn injury.

The results of an investigation regarding the correlation between contact thermal burns and temperature profile in skin cover of bioobject are given in this work. Simple temperature criterion of burns appearance is determined on the basis of modeling of heat transfer process. The physical model of skin and critical temperature criterion are suggested for estimation of heat protecting properties of material for clothes.

Modeling of heat transfer processes at catalytic materials in shock tube

The heat transfer properties of catalytic materials at high temperatures has been studied using a method based on the numerical analysis of the thermal viscous boundary layer near the shock-tube end. Major analysis has been carried out in terms of one-dimensional nonsteady flow models. Finally, a very valuable information regarding the characteristics of the thermal boundary layer near the tube and the parameters of catalytic wall materials has been derived from the observed dependence of heat flux and pressure at the shock-tube end as well as reflected shock wave velocity upon time. 12 refs.

Numerical modeling of heat-transfer processes in the investigation of the state of thermal stress of tribotechnical systems

On the basis of an analysis of the electrothermomechanical processes occurring in rapid sliding of solids, the article suggests a mathematical model for investigating the thermal state of structural elements with a view to the physical peculiarities of their interaction. A combined numerical and analytical approach is used. The analytical method is used for a quantitative estimate of the dissipation of electromagnetic and mechanical energies into thermal energy, the numerical method is used for calculating the field characteristics of the thermal processes. A numerical analysis is made of the slider-type pair (Cu-Sn) with a straight guide with constant sliding speed of the moving element v = 7000 m/sec.

Modelling of heat transfer processes in low-pressure CVD reactors

Assuming a parabolic rate profile, the temperature field in a reactor for low-pressure chemical vapour deposition is investigated by a numerical solution of the differential equation of convection heat transfer. It is found that the length of the tube in which the gas is heated, is a function of the gas flow rate and its thermophysical characteristics. For a number of gas components this length changes in the range of 10–14 cm from the beginning of the temperature plateau of the reactor. The analysis carried out by means of the model shows a good agreement between the predicted and experimentally fixed distances for positioning the wafer holder.

Quasidynamic modeling of heat-transfer processes

An analytic method is developed for describing heat-transfer dynamics, making effective use of the quasi-dynamic features of the processes. The results are given specific form for heat exchangers of two-flow, one-flow, and immersion type.

A mathematical model of heat transfer processes in hardening high vacuum furnaces

The present work illustrates the scheme adopted as well as its consequent calculation process to stimulate the behaviour of samples of different steels (AISI 316, X210 Cr 13 KU, 88 MnV 8 KU) during a complete thermal cycle carried out in high vacuum furnaces. The results which were obtained by numerical simulation are compared with the corresponding experimental data.

Numerical modelling of heat transfer processes with supplementary data

AbstractMathematical models of heat transfer processes are usually studied using formulation that is unique in the mathematical sense. For example, in solving initial‐boundary value problems in conduction heat transfer, the mathematical model consists of the governing equation and initial and boundary conditions. An extension of such an approach by introducing the supplementary information (or data) concerning the process has been proposed here as a method for verifying the accuracy of the model equations. This means that the mathematical model consists of more equations than unknowns which leads in consequence to a finite set of probable solutions. A criterion for choosing the most probable solution has been proposed. Special attention has been paid to numerical formulation. Computational methods have been derived using the Lagrange multipliers. Theoretical considerations have been illustrated by computing the temperature distribution inside a laboratory combustion chamber.

Equivalence of one- and two-phase models for heat transfer processes in packed beds: one dimensional theory

From a two-phase model for an adiabatic packed bed through which a gas is flowing, a one-phase model is derived without assuming that the solid and gas temperatures are equal. By means of the derivation, a relationship between the axial effective thermal conductivity in the one-phase model and the heat transfer coefficient in the two-phase model is obtained. The validity of this relationship is confirmed using the experimental results of other authors. These results can also be applied to fixed bed chemical reactors if the reaction takes place in or on the surface of the catalyst. Essential to the derivation is the assumption that the thermal capacity of the gas phase can be neglected. For a fluid where this assumption is not valid, a separate derivation, whose assumptions are more restrictive, is presented in the appendix.

Kinetic model of heat transfer processes in a fluidized bed

In the present paper equations are obtained for determining the temperature field in a fluidized layer. The heat and mass transfer processes in a fluidized bed depend significantly on the motion of the solid particles which form the bed. In any small volume of a fluidized bed with nonuniform thermal conditions there are particles with different average temperatures. Therefore it is natural to resort to the statistical representation of such a system, developed previously in [1, 2], for the study of the heat transfer processes. The expression obtained here for the heat conductivity coefficient of the bed is in good qualitative agreement with the experimental data.