A Global Heat Compliance Measure Based Topology Optimization for the Transient Heat Conduction Problem

For topology optimization with transient loads, heat compliance varies with transient heat analysis. The peak value of the transient heat compliance should be minimized. Thus, this article proposes a global heat compliance measure to handle this kind of topology optimization for the transient heat conduction problem. The optimization model is then constructed by the global heat compliance measure. The finite-element, equivalent static loads, and continuum shape based sensitivity analyses are derived using the adjoint variable method. Through case studies, the effectiveness of the proposed global heat compliance measure for the transient heat conduction topology optimization is validated.     

THERMOELASTIC TOPOLOGY OPTIMIZATION FOR PROBLEMS WITH VARYING TEMPERATURE FIELDS

Elastic structures that exist in a thermal environment usually experience complex steady-state or transient heat conduction, whereby operational temperatures and stresses may change with time, heat sources, and thermal or kinematic boundary conditions. This article proposes an evolutionary optimization procedure for topology design involving thermoelasticity in which finite element heat analysis, finite element thermoelastic analysis, and subsequently design modification are iteratively carried out. To achieve as efficacious a material usage as possible, the relative efficiency of an element is defined in terms of its thermal stress level. In this article, design cases with uniform temperature fields, nonuniform temperature fields subjected to single or multiple heat load cases, and transient temperature fields are studied. The examples presented show the capabilities of the proposed procedure to solve various thermoelastic problems under varying temperature fields.     

Topology optimization of convection-dominated,steady-state heat transfer problems

The current push in the topology optimization community is to apply topology optimization to mechanics problems beyond typical structural design to other physical domains. Here, a framework for topology optimization of nonlinear steady-state heat transfer with conduction, convection, and radiation without explicitly accounting for fluid motion is evaluated. Convection-dominated diffusion problems are susceptible to numerical instabilities that, unless they are handled properly in the analysis, can severely affect the optimization. This numerical instability issue is the focus of this work, its origin is discussed in the context of density-design-variable-based topology optimization, and a method for avoiding such instabilities is described. Several design examples demonstrate the approach.     

Generating optimal heat conduction paths based on bionic growth simulation

This paper proposes a novel topology optimization method for designing the best-possible heat conduction paths. The design idea is originated from the natural observation that plant roots or leaf veins care by self-adaptive growth to minimize the flow resistance through the whole networks. Based on the analogy between fluid flow and heat flow problems, the natural growth rule is systematically transformed into a mathematical model and written as an algorithm, where the high conductivity material is treated as being alive and the topology optimization process is viewed as plant morphogenesis process. Specifically, a new treatment called ‘conductivity spreading approach (CSA)’ is proposed to transform nodal temperatures of cooling channels into those of the background mesh, by which cooling channels can be separated from the underlying grid so that they can branch and extend freely along any direction. The growth method is used to construct the heat conduction paths for a fundamental ‘volume-to-point’ problem. Unlike other methods, layout solution produced by the suggested method is favorable to practical problems because it provides clear information about the location, orientation and dimensions of each cooling channel. In addition, the growth method requires little of human involvement and is easily delegated to computers, offering great advantage of automated design for large-scale cooling channel layouts in heat conduction systems.     

Methodology for Estimation of Local Convective Heat Transfer Coefficient for Vapor Condensation

This paper aims to present an effective two-dimensional inverse heat conduction technique and an experimental design for accurately estimating the local convective heat transfer coefficient of vapor condensation over a conical surface, given temperature measurements at some interior locations. The functional form for the heat transfer coefficient is not known a priori. The method uses a sequential procedure together with Beck's function specification approach. Solution accuracy and the effects of experimental errors are examined using simulated temperature data. It is concluded that a good estimation of space-variable heat transfer coefficient can be made from the knowledge of transient temperature recordings using the proposed inverse heat conduction problem method. The method is also used in a series of numerical experiments to provide the optimum experimental design for condensation heat transfer investigation.     

Topology optimization for thermal conductors considering design-dependent effects,including heat conduction and convection

In structural designs considering thermal loading, in addition to heat conduction within the structure, the heat convection upon the structure’s surface can significantly influence optimal design configurations. In this paper, we focus on the influence of design-dependent effects upon heat convection and internal heat generation for optimal designs developed using a topology optimization scheme. The method for extracting the structural boundaries for heat convection loads is constructed using a Hat function, and heat convection shape dependencies are taken into account in the heat transfer coefficient using a surrogate model. Several numerical examples are presented to confirm the usefulness of the proposed method.     

Computational design of metadevices for heat flux manipulation considering the transient regime

The present work introduces the optimization-based approach for the design of metadevices to manipulate the heat flux in transient regime. It consists of solving a continuous, nonlinear, constrained, large-scale optimization problem where the objective function (to be minimized) is the error in accomplishing a given heat flux manipulation task along a transient heat conduction process. The response of the metadevice is modeled by using the finite element method, and its design is characterized by a set of parameters defining the material at all the finite elements in the device. These parameters are the design variables of the optimization problem, being chosen from an admissible design set in order to guarantee the feasibility of the optimal solution. As an example, this optimization-based approach is applied to the design of a heat flux shielding metadevice. Compared to a metadevice designed under the classical thermodynamics transformation approach and intuition, the current device performs the shielding task with considerably higher success. In order to highlight the versatility of the proposed optimization-based design method, this approach is also applied to the design of metadevices to satisfy multiple different simultaneous tasks, particularly shielding and cloaking.     

Evolutionary topology optimization for temperature reduction of heat conducting fields

This paper aims at developing an efficient finite element based computational procedure for the topology design of heat conducting fields. To evaluate the temperature change in a specific position, due to varying the conducting material distribution in other regions, a discrete temperature sensitivity is derived for an evolutionary topology optimization method. In the topology optimization of the conducting fields, the thermal conductivity of an individual finite element is considered as the design variable. By removing or degenerating the conductive material of the elements with the most negative sensitivity, the temperature objective at the control point can be most efficiently reduced. Illustrative examples are presented to demonstrate this proposed approach.     

Analytical solution for transient temperature and thermal stresses within convective multilayer disks with time-dependent internal heat generation,Part I: Methodology

This work deals with the exact solution for asymmetric transient problem of heat conduction and accordingly thermal stresses within multilayer hollow or solid disks which lose heat by convection to the surrounding ambient. The combination of the separation of variables method (SVM) and Duhamel's theorem is applied to the heat conduction problem which provides a versatile technique. The temperature distribution is obtained by the SVM which concerns the heat conduction problem with time-independent internal heat generation. Applying Duhamel's theorem on the previous solution, temperature distribution with time-dependent internal heat generation can be achieved. Accordingly, assuming plane stress condition, radial and tangential stresses are obtained which are incorporated into the equivalent tensile stress formulation to calculate von Mises stress. The comprehensive methodology described here can be useful addition for many new emerging fields in which both transient and steady-state temperature distributions and thermal stresses for composite disks are important.     

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.     

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.     

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.     

Solving the Temperature Distribution Field in Nonlinear Heat Conduction Problems Using the Hopfield Neural Network

This article employs the continuous-time analog Hopfield neural network (CHNN) to compute the temperature distribution in nonlinear heat conduction problems. The relationship between the CHNN synaptic connection weights and the governing equations of the nonlinear heat conduction problems is established and a corresponding network connectivity circuit design scheme proposed. The CHNN algorithm is used to solve the heat equation for conduction problems with a power-law nonlinearity. The results confirm that the proposed CHNN scheme provides an accurate means of solving the transient temperature distributions of nonlinear heat conduction problems on a real-time basis.     

Optimization of thermal energy storage in packed columns

We propose a method for optimizing the net economic income for thermal energy storage in a cylindrical column packed with solid spheres. The economic value of stored heat is maximized relative to equipment and operating costs for air-based solar energy storage systems packed with either rock or steel spheres. Variables optimized separately are bed length and diameter, air flow rate, spherical particle diameter and collection time. Simultaneous optimization of a subset of these variables is illustrated. The mathematical model for the transient temperature profile in the bed includes intraparticle heat conduction, axial dispersion and heat losses to the surroundings, as described in earlier papers.     

Heat transfer analysis of pile geothermal heat exchangers with spiral coils

This paper investigates the transient heat conduction around the buried spiral coils which could be applied in the ground-coupled heat pump systems with the pile foundation as a geothermal heat exchanger. A transient ring-coil heat source model is developed, and the explicit analytical solutions for the temperature response are derived by means of the Green’s function theory and the image method. The influences of the coil pitch and locations are evaluated and discussed according to the solutions. In addition, comparisons between the ring-coil and cylindrical source models give that the improved finite ring-coil source model can accurately describe the heat transfer process of the pile geothermal heat exchanger (PGHE). The analytical solutions may provide a desirable and better tool for the PGHE simulation/design.     

Transient heat fluxes measurement analysis from platinum based thin film gauges in open and closed cavities

Platinum thin film gauges (PTFGs) measure heat fluxes in the applications involving very short duration of the heating environment. Heat transfer measurement is the frequently used technique for measuring the surface heat flux using thin film gauges. The present investigation has been focused on the design and manufacturing methods for heat transfer gauge, their stability, and dynamic calibrations in certain situations where the heat load suddenly build up. PTFGs measure heat fluxes in heating environments applications during the very duration. The measurement for heat transfer is a technique used often with thin film gauges to measure the surface heat flux. The convection devices are regarded as the best measuring units in short-term transient temperature measurement applications and are usually used when the heat transfer mode is dominant means gas turbine engines, high speed aircraft, etc. In addition to that, there are many difficulties incurred for convection based measurement practically and few interdisciplinary research fields. A convective heat load is provided with a hot air gun to get the temperature signal. By using thin film gauge through present investigations, it is very ambitious to explore the possibility of short term conduction based transient measurements with pure conduction heat transfer mode. A simple experimental set up is used to supply the thin film gauges with heat flux, which is manually manufactured with platinum as a sensing material and quartz as a substrate material. The body's nose tip to high speed flow is expected to be the maximum heat transfer at the stagnation point. The stagnation point probes are fabricated for PTFGs, and baking material is quartz. The recorded temperature histories are compared with the experimentally recorded temperature signals from the gauges through the finite element method. The heat flux forecast was configured by using the one dimension thermal conduction equation convolution integral and by comparison with the heat input loads. This study reveals the ability of PTFGs to be used for a short period.     

Monitoring of transient 3D temperature distribution and thermal stress in pressure elements based on the wall temperature measurement

Abstract

Two methods for monitoring the thermal stresses in pressure components of thermal power plants are presented. In the first method, the transient temperature distribution in the pressure component is determined by measuring the transient wall temperature at several points located on the outer insulated surface of the component. The transient temperature distribution in the pressure component, including the temperature of the inner surface is determined from the solution of the inverse heat conduction problem (IHCP). In the first method, there is no need to know the temperature of the fluid and the heat transfer coefficient. In the second method, thermal stresses in a pressure component with a complicated shape are computed using the finite element method (FEM) based on experimentally estimated fluid temperature and known heat transfer coefficient. A new thermometer with good dynamic properties has been developed and applied in practice, providing a much more accurate measurement of the temperature of the flowing fluid in comparison with standard thermometers. The heat transfer coefficient on the inner surface of a pressure element can be determined from the empirical relationships available in the literature. A numerical-experimental method of determination of the transient heat transfer coefficient based on the solution of the 3D-inverse heat conduction problem has also been proposed. The heat transfer coefficient on the internal surface of a pressure element is determined based on an experimentally determined local transient temperature distribution on the external surface of the element or the basis of wall temperature measurement at six points located near the internal surface if fluid temperature changes are fast. Examples of determining thermal and pressure stresses in the thick-walled horizontal superheater header and the horizontal header of the steam cooler in a power boiler with the use of real measurement data are presented.     

A radial integration boundary element method for solving transient heat conduction problems with heat sources and variable thermal conductivity

A new radial integration boundary element method (RIBEM) for solving transient heat conduction problems with heat sources and variable thermal conductivity is presented in this article. The Green’s function for the Laplace equation is served as the fundamental solution to derive the boundary-domain integral equation. The transient terms are first discretized before applying the weighted residual technique that is different from the previous RIBEM for solving a transient heat conduction problem. Due to the strategy for dealing with the transient terms, temperature, rather than transient terms, is approximated by the radial basis function; this leads to similar mathematical formulations as those in RIBEM for steady heat conduction problems. Therefore, the present method is very easy to code and be implemented, and the strategy enables the assembling process of system equations to be very simple. Another advantage of the new RIBEM is that only 1D boundary line integrals are involved in both 2D and 3D problems. To the best of the authors’ knowledge, it is the first time to completely transform domain integrals to boundary line integrals for a 3D problem. Several 2D and 3D numerical examples are provided to show the effectiveness, accuracy, and potential of the present RIBEM.     

Total heat transfer coefficients for canned foods during sterilization

An analytical mathematical model for determining the total heat transfer coefficient of a cylindrically shaped canned food subjected to sterilization was developed. There is a need to determine these coefficients in a simple and accurate form for process heat transfer analysis and energy optimization. In the mathematical modelling, a new technique for heat sterilization conduction problem was used by considering the boundary condition of the third kind in transient heat conduction. The temperature data at the centres of the cylindrically shaped cans were obtained in the experimental investigation at the medium temperatures of 115 and 121°C and were used to determine the total heat transfer coefficients of the individual canned products. The total heat transfer coefficient for an individual canned product increased with increasing medium temperature. The results of this study shows that the present analytical model is a simple tool for determining the total heat transfer coefficients for the individual canned products.