Modelling earth-to-air heat exchanger behaviour with the convolutive response factors method

This paper shows a new numerical model of earth-to-air heat exchanger. The system is discretized into “n” sections perpendicular to the exchanger pipe. In each section, the problem of conduction is solved using response factors method in order to reduce computational time. Each response factor is calculated using a finite elements program that solves 2D conduction problems. The particularity of this problem is that the time-constants are very high, making it impossible to use conventional properties of response factors to reduce the number of calculations. We will set out a new approach to solve this particular problem. Heat flux entering the pipe is then expressed as a function of the temperature of the air crossing the pipe and the external solicitations. A heat balance is then applied for each layer to find the resulting outlet air temperature. The model is then compared to an analytical model and a 3D model based on the dynamic finite volume approach. Finally an example of coupling between an earth-to-air heat exchanger and a low-consumption building is presented.     

Inverse boundary design of square enclosures with natural convection

An optimization technique is applied to design of heat transfer systems in which the natural convection is important. The inverse methodology is employed to estimate the unknown strengths of heaters on the heater surface of a square cavity with free convection from the knowledge of the desired temperature and heat flux distributions over a given design surface. The direct and the sensitivity problems are solved by finite volume method. The conjugate gradient method is used for minimization of an objective function, which is expressed by the sum of square residuals between estimated and desired heat fluxes over the design surface. The performance and accuracy of the present method for solving inverse convection heat transfer problems is evaluated by comparing the results with a benchmark problem and a numerical experiment.     

Two-Dimensional Inverse Heat Transfer Analysis of Functionally Graded Materials in Estimating Time-Dependent Surface Heat Flux

Two-dimensional transient inverse heat conduction problem (IHCP) of functionally graded materials (FGMs) is studied herein. A combination of the finite element (FE) and differential quadrature (DQ) methods as a simple, accurate, and efficient numerical method for FGMs transient heat transfer analysis is employed for solving the direct problem. In order to estimate the unknown boundary heat flux in solving the inverse problem, conjugate gradient method (CGM) in conjunction with adjoint problem is used. The results obtained show good accuracy for the estimation of boundary heat fluxes. The effects of measurement errors on the inverse solutions are also discussed.     

Application of optimization techniques and the enthalpy method to solve a 3D-inverse problem during a TIG welding process

Tungsten inert Gas (TIG) welding takes place in an atmosphere of inert gas and uses a tungsten electrode. In this process heat input identification is a complex task and represents an important role in the optimization of the welding process. The technique used to estimate the heat flux is based on solution of an inverse three-dimensional transient heat conduction model with moving heat sources. The thermal fields at any region of the plate or at any instant are determined from the estimation of the heat rate delivered to the workpiece. The direct problem is solved by an implicit finite difference method. The system of linear algebraic equations is solved by Successive Over Relaxation method (SOR) and the inverse problem is solved using the Golden Section technique. The golden section technique minimizes an error square function based on the difference of theoretical and experimental temperature. The temperature measurements are obtained using thermocouples at accessible regions of the workpiece surface while the theoretical temperatures are calculated from the 3D transient thermal model.     

Inverse Transient Heat Conduction Problems of a Multilayered Functionally Graded Cylinder

Inverse transient heat conduction problems of a multilayered functionally graded (FG) cylinder are presented. The approach is based on measurement of temperature on the outer surface of the cylinder to estimate the heat flux and convection heat transfer coefficient on its inner surface. The non-Fourier heat transfer equation is employed to accurately formulate the problem. The conjugate gradient method (CGM) is used for the optimization procedure and the incremental differential quadrature method (DQM) is applied to solve the direct, sensitivity, and adjoint problems. The accuracy of the presented approach is examined by simulating the exact and noisy data through different examples. Good accuracy of the obtained results validates the presented approach.     

Inverse Boundary Design Problems in Enclosures With Non-Gray Media

In this work, the inverse analysis is applied to radiative heat transfer boundary design problems with non-gray media. The objective of the inverse problem is to find the power of the heaters on the heater surface that produces the desired output, that is, temperature and heat flux distribution over the design surface. The inverse problem is formulated as an optimization problem for minimization of an objective function, which is defined by the sum of the squared difference between estimated and desired heat flux distributions over the design surface. The non-gray optimization problem is solved using the conjugate gradient method, which is a gradient-based optimization method. The spectral line weighted-sum-of-gray-gases model (SLW) is used to account for non-gray gas radiation properties. The radiative transfer equation is solved by the discrete ordinates method combined with two models for simulation of non-gray media. Enclosures with diffuse and gray walls are considered. Radiation is assumed the dominant mode of heat transfer. Example problems including homogeneous/nonhomogeneous, isothermal/nonisothermal media are considered. The results obtained using the SLW model and the gray model are compared.     

Temperature-Constrained Topology Optimization of Transient Heat Conduction Problems

A regional temperature measure model is constructed to obtain a small number of temperature constraints for local transient temperature control. The temperature sensitivity is derived using the adjoint variable method. The multiple temperature criteria and three-phase topology optimization are further investigated for transient heat conduction design. The material layout design of transient heat conduction is replaced by a static optimization problem, which is subsequently solved by the method of moving asymptotes. Finally, several numerical examples are provided to demonstrate the feasibility and validity of the proposed topology optimization for transient heat conduction problems.     

Heat flux estimation of a plasma rocket helicon source by solution of the inverse heat conduction problem

A solution of the inverse heat conduction problem (IHCP) by the steepest descent method is carried out in order to determine the waste heat flux from a helicon plasma discharge using transient surface temperature measurements obtained from infrared thermography. The infrared camera data is calibrated against thermocouple data and mapped to real locations on the observed surface. The magnitude and distribution of the heat flux to the gas containment tube in the helicon is investigated as the applied power, gas flow rate, magnetic field distribution and neutral gas are varied.     

有限体积法在电站锅炉炉膛辐射换热计算中的应用

辐射换热是大型锅炉炉膛内的主要换热形式,准确的计算炉膛内的辐射换热量对大型锅炉设计和优化有重要意义。本文将有限体积法推广用于求解和分析大型电站锅炉炉膛内的辐射换热。给出了有限体积法对辐射传递方程进行离散和求解的基本过程。评估了有限体积法求解大型电站锅炉炉膛辐射换热的可靠性。将有限体积法用于分析某电厂600MW锅炉炉膛内的辐射换热,结果表明有限体积法可以有效的求解大型电站锅炉炉膛内的复杂辐射换热过程。     

APPLICATION OF THE NETWORK METHOD TO HEAT CONDUCTION PROCESSES WITH POLYNOMIAL AND POTENTIAL-EXPONENTIALLY VARYING THERMAL PROPERTIES

Nonlinear transient heat conduction in a finite slab with potential-exponential temperature-dependent specific heat and thermal conductivity is investigated numerically by using the network method. A general network model for this process is proposed, whatever the exponent of the temperature-dependent functions may be, including initial and boundary conditions. With this network model and using the electrical circuit simulation program PSPICE, time-dependent temperature and heat flux profiles at any location can be obtained. This approach allows us to solve this conduction problem by a general, efficient, and relatively simple method. To show the accuracy of the network method, a comparison is made of the present results and those obtained by other methods for a particular case.     

Utilisation de modèles d'identification non entiers pour la résolution de problèmes inverses en conduction

Heat flux estimation through inverted non-integer identification models. A model of non-integer order that reproduced the transient thermal behaviour of a system is identified. This model is expressed as a linear relationship between the fractionnal derivates of the temperature at a point of the medium and those of the solicitation applied on the system. Using recursive form of the derivates lead to identify the unknows of the model applying the linear least square method from experimental data. The application concerned a semi-infinite medium submited to a single heat flux on its surface. Among the applications of this approach, the identified model is used in an inverse technique to estimate the heat flux applied on the medium.     

The Robust Optimization for Large-Scale Space Structures Subjected to Thermal Loadings

Large-scale space structures may experience unexpected thermal-elastic deformation due to thermal loadings in space. This thermal response could be minimized by using optimization method in design phase and the uncertainty of material properties should also be considered to ensure the reliable performance of the produced structure. For this purpose, the robust optimization is applied to this kind of structures in this paper. Firstly, a perturbation based stochastic finite element program is developed, which is tailored for the problem of thermal-elastic deformation of thin-walled structures subjected to incident thermal flux and energy emission through radiation. Based on this program, a robust design scheme is formulated as a two-objective optimization problem, in which all required sensitivities are calculated analytically. Then, the Pareto front of this problem is effectively determined by using the adaptive weighted sum method. Finally, numerical examples are presented to illustrate the validity and capability of this proposed method.     

Identification of boundary heat fluxes in a falling film experiment using high resolution temperature measurements

In this paper, we consider a three-dimensional inverse heat conduction problem (IHCP) in a falling film experiment. The wavy film is heated electrically by a thin constantan foil and the temperature on the back side of this foil is measured by high resolution infrared (IR) thermography. The transient heat flux at the inaccessible film side of the foil is determined from the IR data and the electrical heating power. The IHCP is formulated as a mathematical optimization problem, which is solved with the conjugate gradient method. In each step of the iterative process two direct transient heat conduction problems must be solved. We apply a one step θ-method and piecewise linear finite elements on a tetrahedral grid for the time and space discretization, respectively. The resulting large sparse system of equations is solved with a preconditioned Krylov subspace method. We give results of simulated experiments, which illustrate the performance and tuning of the solution method, and finally present the estimation results from temperature measurements obtained during falling film experiments.     

TRANSIENT THERMOELASTIC ANALYSIS OF DISK BRAKE USING THE FAST FOURIER TRANSFORM AND FINITE ELEMENT METHOD

This article introduces a finite element method that combines the fast Fourier transform technique and a conventional finite element method as a computational technique for investigating a thermomechanical problem. The conventional finite element formulation is very inefficient in the analysis of a three-dimensional disk brake model of a rotating axisymmetric disk subjected to a nonaxisymmetric transient heat flux condition due to frictional contact with asymmetric pads fixed in space. Because the proposed technique reduces the three-dimensional disk brake mathematics to two dimensions, is an extreme time saver, and costs less, we can solve the transient thermoelastic problem and the thermoelastic instability. As a result of the study we present some analyses on temperature distributions and displacement distributions in a disk brake system at a low speed and on the hot spots at a high speed above critical speed.     

Estimation of the time-dependent heat flux using the temperature distribution at a point by conjugate gradient method

In this paper, the conjugate gradient method coupled with adjoint problem is used in order to solve the inverse heat conduction problem and estimation of the time-dependent heat flux using the temperature distribution at a point. Also, the effects of noisy data and position of measured temperature on final solution are studied. The numerical solution of the governing equations is obtained by employing a finite-difference technique. For solving this problem the general coordinate method is used. We solve the inverse heat conduction problem of estimating the transient heat flux, applied on part of the boundary of an irregular region. The irregular region in the physical domain (r,z) is transformed into a rectangle in the computational domain (ξ,η). The present formulation is general and can be applied to the solution of boundary inverse heat conduction problems over any region that can be mapped into a rectangle. The obtained results for few selected examples show the good accuracy of the presented method. Also the solutions have good stability even if the input data includes noise and that the results are nearly independent of sensor position.     

Reconstruction of local heat fluxes in pool boiling experiments along the entire boiling curve from high resolution transient temperature measurements

In this paper, we consider a transient inverse heat conduction problem (IHCP) defined on an irregular three-dimensional (3D) domain in pool boiling experiments. Heat input to a circular copper heater of 35 mm diameter and 7 mm thickness is provided by a resistance heating foil pressed to the bottom of the heater. The heat flux at the inaccessible boiling side is estimated from a number of temperature readings in the heater volume. These temperatures are measured by some high-resolution microthermocouples, which are mounted 3.6 μm below the surface in the test heater. The IHCP is formulated as a mathematical optimization problem and solved by the conjugate gradient (CG) method. The arising partial differential equations (PDEs) are solved using the software package DROPS. A simulation case study is used to validate the performance of the solution approach. Finally, we apply the solution approach to the IHCP in pool boiling experiments. The procedure enables the reconstruction of local instantaneous heat flux distribution on the heater surface at different locations along the boiling curve.     

Topology optimization of heat and mass transfer problems in two fluids—one solid domains

Abstract

Among various topology optimization methods used in fluid flow problems, density approach has gained more interest compared to other techniques as level set approach, topological derivative technique, and phase field method. The key part of density approach is the penalized interpolation function, which forces progressively porous cells made of fluid and solid simultaneously to belong discretely to fluid or solid sub-domains. However this type of problem was only solved in mono-fluid domains, in which the method accounts for the distribution of a single fluid and a single solid. The actual work aims to extend topology optimization in fluid flow problems to bi-fluid domain. A new interpolation function was developed for this purpose. Furthermore a penalization function was integrated in the multiobjective function, which ensure that each fluid takes its own path in the device, while maintaining a minimal required solid thickness between the channels of different fluids. The results showed the capacity of the proposed method to deal with multiple fluid phases in minimizing the pressure drop while maximizing heat exchange between different flows. The main conclusion is the potential of density approach to be applied on optimization of heat exchangers.     

Heat and mass transfer influence on potential variation in a PEMFC membrane

Water transport in the membrane of a PEM fuel cell is provided essentially by a convective force, resulting from a pressure gradient, an osmotic force, due to a concentration gradient and an electric force caused by the protons migration from the anode to the cathode. Through these three types of force the two-dimensional behavior of electric potential has been studied in this paper. The adopted model in this work is based on the assumption of single phase and multi-species flow, supposed two-dimensional and transient in a porous medium. The species conservation equation is coupled with the energy equation through the diffusion coefficient of water and the heat convective flux. The set of governing equations in the form of convection–diffusion problem has been solved numerically using the finite volume method. The obtained results show the transient two-dimensional effect of heat and mass transfer on the voltage variation within the membrane.     

Robust experiment design for the estimation of thermophysical parameters using stochastic algorithms

This numerical study deals with the design of experiments. It aims at optimizing thermocouple positions in order to reduce uncertainties in the estimation of thermophysical properties when an inverse method is applied. The 2D system under investigation is a squared sample of orthotropic material submitted to a constant heat flux on left and bottom edges. The temperature response is given by three sensors. The unknown parameters are the volumetric thermal capacity and the conductivities in the two principal directions. The experiment design is based on an original optimality criterion. Two stochastic algorithms are used to find its minimum and their efficiency is compared to a pure random search algorithm. To deal with the fact that the experiment design depends on the unknowns, a robust optimization approach is proposed.     

Multi-objective genetic optimization of the heat transfer from longitudinal wavy fins

In the present work, we investigate the optimization of the heat transfer from wavy fins cooled by a laminar flow under conditions of forced convection and from a multi-objective point of view. The problem is addressed by means of a finite element method which allows to compute the velocity and the temperature distributions in a finned conduit cross section under conditions of imposed heat flux. Thereafter, the fin profile is optimized by means of multi-objective genetic algorithm which aims to find geometries that maximize the heat transfer and, at the same time, minimize the hydraulic resistance. The geometry of the fins is parameterized by means of a polynomial function and several order are investigated and compared.