The paper proposes a heat-flux based topology optimization approach to design self-supported enclosed voids for additive manufacturing. The enclosed overhangs that require supports in additive manufacturing are removed from the optimized design by constraining the maximum temperature of a pseudo heat conduction problem. In the pseudo problem, heat flux is applied on the non-self-supported open and enclosed surfaces. Since the density-based topology optimization involves no explicit boundary representation, we impose such surface slope dependent heat flux through a domain integral of a Heaviside projected density gradient. In addition, the solid materials and the void materials in the pseudo problem are assumed to be thermally insulating and conductive, respectively. As such, heat flux on the open surfaces can be successfully conducted to external heat sink through the void (or conductive) materials. However, heat flux on the non-self-supported enclosed surfaces is isolated by the solid (or insulating) materials and thus leads to locally high temperature. Hence, by limiting the maximum temperature of the pseudo problem, self-supported enclosed voids can be achieved, and the slope of the open surfaces would not be affected. Numerical examples are presented to demonstrate the validity and effectiveness of the proposed approach in the design of self-supported enclosed voids.

This paper examines an inverse problem which arises in thermal imaging. We investigate the problem of detecting and imaging corrosion in a material sample by applying a heat flux and measuring the induced temperature on the sample’s exterior boundary. The goal is to identify the profile of some inaccessible portion of the boundary. We study the case in which one has data at every point on the boundary of the region, as well as the case in which only finitely many measurements are available. An inversion procedure is developed and used to study the stability of the inverse problem for various experimental configurations.

In this contribution we propose new numerical methods for solving inverse heat conduction problems. The methods are constructed by considering the desired heat flux at the boundary as piecewise constant (in time) and then deriving an explicit expression for the solution of the equation for a stationary point of the minimizing functional. In a very special case the well-known Beck method is obtained. For the time being, numerical tests could not be included in this contribution but will be presented in a forthcoming paper.

The computed effects of an eccentric rotor on the mass and heat ingress through a gas turbine wheelspace rim seal have been studied using a 3-D Navier-Stokes computer code with a recent three-scale k-∈ turbulence model and orthogonal body-fitted coordinates. All compressibility and thermal/momentum interaction effects were included, as actual engine temperatures, pressures, Reynolds numbers, etc were used. The combined effects of an eccentric coolant inlet seal, in conjunction with an eccentric rim seal, were compared with the case of an eccentirc rim seal alone. It was found that heat and mass ingress into the cavity through the rim seal are not affected by the coolant/purge inlet seal eccentricity, whereas they are strongly affected by the eccentricity of the rim seal. The total heat flux through the rim seal, due to mass ingress thermal transport and turbulent heat diffusion, was examined in order to better understand this wheelspace cavity heating mechanism. It was found that the turbulent heat diffusion flux is a significant percentage of the total heat flux at small rotor eccentricity, whereas it is entirely negligible at large eccentricity.

In todays mechanical design, static and dynamic numerical models are widely used, and thermal models are needed to make robust design. Thermal models, based on the thermal network method, are now available. Several hypotheses are made as physical phenomena are complex and experimental validation is necessary. A thermal model of gearbox has been already presented and compared to few experimental results that had allowed global validation of the model. Now, the experimental validation is concerned with thermal transient and steady state behavior of gearbox versus transmitted power and lubrication conditions in order to finely validate the model. The test gearbox is compound of 3 spur gears supported by 6 spherical roller bearings, a housing and a lubrication circuit cooled by an oil-air exchanger. The maximum transmitted power is 500 kW. Gears, bearings, housing, shafts, and the lubrication circuit have been equipped with thermocouples, flux-meters and flow-meters. Heat flux were measured on the internal and external side walls of the housing. Oil flowing on a side wall has been measured. Experiments were run under several transmitted powers and oil flows at meshing. Thermal map at steady state and transient temperature rises of technological elements are obtained for each test. Finally, transient temperature rises and steady state from numerical and experimental results are compared. The comparison shows a good agreement, and the importance of taking into account oil flowing on the inside walls of the housing is brought to the fore. The difficulty of evaluating the oil flowing on the internal walls of a housing is discussed and illustrated with numerical results.

The paper presents a formulation for support optimization to maximize heat dissipation in additive manufacturing. To simulate heat transfer from the part to the supports, a boundary-dependent heat flux is applied on the part/support interface. Since the density-based topology optimization does not involve explicit boundary, the heat flux is implicitly imposed through a domain integration of a Heaviside projected density gradient. As such, this formulation also supports simultaneous optimization of support and parts in additive manufacturing. Self-supporting supports are obtained by controlling the anisotropic thermal conductivity of the supports. Three different objective functions related to heat dissipation efficiency are investigated. Numerical examples are presented to demonstrate the validity and efficiency of the proposed approach.

This paper develops an experimental platform and performs a parametric study of an air-based battery thermal management system (BTMS) for electric vehicles. A flexible experimental platform with ten battery cells is built up to investigate how key BTMS design parameters affect the battery thermal performance. Three design parameters are studied in this paper, including the mass flow rate of cooling air, the heat flux from the battery cells to the cooling air, and the passage spacing size. To evaluate the thermal performance of the battery system, two metrics (i.e., the maximum temperature rise and the maximum temperature Uniformity) are used. A design of experiments (here 30 groups) are conducted to analyze how the three key design parameters affect the thermal performance of the BTMS. A computational fluid dynamics (CFD) of the BTMS is also performed to compare and help explain the experimental results. Both the experimental and CFD simulation results shows that: (i) decreasing the mass flow rate may deteriorate the thermal performance of the battery module; (ii) increasing the heat flux and enlarging the passage spacing size also deteriorate the battery thermal performance.

Plastic gears bring some interesting advantages compared to metal gears. However, they also have some drawbacks, many of them related to the dependency of their mechanical properties with the temperature. Among other reasons, the friction between the gear teeth causes a heat flux that heats the gears and produces temperature variations within the gear geometries. These temperature variations have effects on the mechanical response of the gears, that must be taken into account when designing plastic gear drives. In this work, two different finite element models have been proposed to perform heating contact analysis, that is a coupled thermal-stress analysis that takes into account the heating produced by friction and the non-linear properties of the material. As a result of these models, the temperature field of the gears can be determined at any running time, as well as other interesting results, such as the transmission error function or the instantaneous power loss.

Despite significant efforts examining the suitability of the proper form of the heat transfer partial differential equation (PDE) as a function of the time scale of interest (e.g. seconds, picoseconds, femtoseconds, etc.), very little work has been done to investigate the millisecond-microsecond regime. This paper examines the differences between the parabolic and one of the hyber-bolic forms of the heat conduction PDE that govern the thermal energy conservation on these intermediate timescales. Emphasis is given to the types of problems where relatively fast heat flux deposition is realized. Specifically, the classical parabolic form is contrasted against the lesser known Cattaneo-Vernotte hyperbolic form. A comparative study of the behavior of these forms over various pulsed conditions are applied at the center of a rectangular plate. Further emphasis is given to the variability of the solutions subject to constant or temperature-dependent thermal properties. Additionally, two materials, Al-6061 and refractory Nb1Zr, with widely varying thermal properties, were investigated.

This paper proposes a design development process to analyze and optimize the design of a brake rotor for a Formula Student Electric Vehicle so as to minimize its weight and reduce thermal stress by keeping the rotor within its operating temperature during the entire braking duration. In today’s world where lesser energy consumption is essential, regenerative braking plays an important role, and is also a factor in weight reduction of brake discs. Regenerative braking is an effective method to maximize brake disc’s life, minimize pad wear and extend working range of electric vehicles. The proposed technique consists of using a tire model and building mathematical models in a MATLAB environment to find transient vehicle speed, which in turn provides wheel loads, frictional torque, braking power and heat flux to the brake disc as a function of time. The heat flux to brake disc increases its temperature and is dissipated mainly through convection, which is also a time-dependent parameter based on air velocity. The entire transient heat transfer model, which also depends on the geometry, material of the brake rotor and mechanical boundary conditions is setup in ANSYS FLUENT and ANSYS Transient Structural and simulation results are presented. Stress fields for floating rotor and fixed rotor are compared since fastening techniques also play a crucial role. Disc brakes are used in almost all ground vehicles and thus, the given design process is vital as the work presented can be extended and modified as per requirements to incorporate the needs of the specific situations one needs to work upon.

Optimization-based solutions to inverse problems involve the coupling of an analysis model, such as a finite element model, with a numerical optimization method. The goal is to determine a set of parameters that minimize an objective function that is determined by solving the analysis model. In this paper, we present an approach that dramatically reduces the computational cost for solving this inverse problems in this way by replacing the original full order finite element model (FOM) with a reduced order model (ROM) that is both accurate and quick to compute. The reduced order model is constructed with basis functions generated using proper orthogonal decomposition of set of solutions from the FOM. A discrete Galerkin method is used to project the differential equation on the basis functions. This approach allows us to transform the linear full order finite element model into an equivalent discrete ROM with far fewer unknowns. The method is applied to a parameter estimation problem in heat transfer. Specifically, we determine the parameters governing the magnitude and distribution of an unknown surface heat flux moving at a constant velocity across the surface of a solid bar of material. A finite element model was implemented in the commercial package COMSOL and a corresponding ROM was constructed. The ROM was coupled with an optimization algorithm to determine the parameter values that minimized the distance between the computed surface temperatures and the target surface temperature. The target surface temperature was generated using simulated measurements produced from the full order finite element model. Several optimization methods were used. The results show the approach can recover the parameters with high accuracy with twenty seven FOM runs.

The direct measurement of temperatures and heat fluxes may be difficult or impossible on boundaries that are obstructed, such as internal cavities, or exposed to harsh environmental conditions that would destroy the thermal sensors. In such circumstances, one may inversely determine the temperature and heat fluxes on these unknown boundaries by using over-specified conditions on boundaries where such information can be readily collected. This assumes the geometry and material properties of the domain are known. Algorithms for solving these problems, such those based on finite difference, finite element, and boundary element, are well known for the case where measured boundary conditions are not a function of time. In this work, I demonstrate an inverse finite element method that effectively solves this inverse heat conduction problem using over-specified temperatures and heat fluxes that are time varying. The material properties may highly heterogeneous and non-linear. A boundary regularization method in space and time is used to stabilize the method for cases involving errors in temperature and heat flux measurements. Several three dimensional examples are given using simulated measurements with and without measurement errors, to demonstrate the accuracy of the method.

Sequential Monte Carlo (SMC) or Particle Filter Methods, which have been originally introduced in the beginning of the 50’s, became very popular in the last few years in the statistical and engineering communities. Such methods have been widely used to deal with sequential Bayesian inference problems in fields like economics, signal processing, and robotics, among others. SMC Methods are an approximation of sequences of probability distributions of interest, using a large set of random samples, named particles. These particles are propagated along time with a simple Sampling Importance distribution. Two advantages of this method are: they do not require the restrictive hypotheses of the Kalman filter, and can be applied to nonlinear models with non-Gaussian errors. This papers uses a SMC filter, namely the ASIR (Auxiliary Sampling Importance Resampling Filter) to estimate a heat flux in the wall of a square cavity undergoing a natural convection. Measurements, which contain errors, taken at the boundaries of the cavity are used in the estimation process. The mathematical model, as well as the initial condition, are supposed to have some error, which are taken into account in the probabilistic evolution model used for the filter.

In the continuous casting process of steel, the control of the mould heat removal is a key parameter, since it directly affects the shell growth and the stresses and strains that are produced in the mould. An inverse heat conduction model was developed to calculate mould heat transfer from temperature measurements, recorded using thermocouples buried inside the copper mould wall. The mould is water-cooled to solidify the hot metal directly in contact with it. The direct stationary conduction problem was solved both on a 2D and a 3D domain; the 2D geometry concerns only a longitudinal section of the mould, while in the 3D domain a whole face is considered. The inverse problem was solved using a Conjugate Gradient algorithm, a Genetic Algorithm and the Nelder-Mear SIMPLEX algorithm. For the 3D geometry, the heat flux profile calculated at the axis of the face is close to that obtained from the 2D model, although the former is slightly lower. For both geometries, there is a good agreement between numerical and experimental temperatures. Moreover, the 3D model provides a better estimate of the outlet water temperature.

Transient thermal stresses develop in pipes during start-up and shut-down. In previous papers the present authors [1–4] proposed an inverse method for determining the optimum thermal inlet liquid temperature history which reduced the maximum transient thermal stress in pipes. The papers considered multiphysics including heat conduction, heat transfer, and elastic deformation. The inverse method used the relationship between inner surface temperature history, transient temperature distribution and transient thermal stresses. The coefficient of heat transfer plays an important role in the evaluation of thermal stress. In this study an inverse method was developed for estimating heat flux and temperature-dependence of the coefficient of heat transfer from the history of the outer surface temperature and the liquid temperature. The method used the relationship between the outer surface temperature and the inner surface temperature. For the regularization of solution the function expansion method was applied in expressing the history of flux on the inner surface. Numerical simulations demonstrated the usefulness of the proposed inverse analysis method. By examining the effect of measurement errors of temperature on the estimation, the robustness of the method was shown.

A common approach to the validation of simulation models focuses on validation throughout the entire design space. In a more recent methodology, we proposed to validate designs as they are generated during a simulation-based optimization process, relying on validating the simulation model through calibration in a sequence of local domains. In that work, the size of the local domains was held fixed and not linked to uncertainty, and the confidence in designs was quantified using Bayesian hypothesis testing. In this article, we present an improved methodology where the size and shape of the local domain at each stage of a sequential design optimization process, are determined from a parametric bootstrap methodology involving maximum likelihood estimators of unknown model parameters. Validation through calibration is carried out in the local domain at each stage. The sequential process continues until the local domain does not change from stage to stage during the design optimization process, ensuring convergence to an optimal design. The proposed methodology is illustrated with the design of a thermal insulator using one-dimensional, linear heat conduction in a solid slab with heat flux boundary conditions.

The paper presents the results of modeling the heat transfer process in heterogeneous media with the assumption that part of the heat flux is dispersed in the air around the beam. The heat transfer process in solid material (beam) can be described by integer order partial differential equation. However, in heterogeneous media it can be described by sub- or hyperdiffusion equation which results in fractional order partial differential equation. Taking into consideration that the part of the heat flux is dispersed into the neighbouring environment we additionally modify the main relation between heat flux and the temperature, and we obtain in this case the heat transfer equation in the new form. This leads to the transfer function which describes the dependency between the heat flux at the beginning of the beam and the temperature at the given distance. The article also presents the experimental results of modeling real plant in the frequency domain basing on the obtained transfer function.

We report a novel active heat sink (AHS) that allows high-density electronic components to operate at a stable temperature over a broad range of ambient conditions. AHS receives heat at high flux and transfers it at reduced flux to environment, coolant fluid (e.g., air or engine coolant), heat pipe, or structures. Temperature of the heat load can be controlled electronically. Target applications for AHS include thermal management of high-power inverters for hybrid electric vehicles. Depending on the configuration, AHS can handle a heat load of several hundred watts at a heat flux over 1,000 W/cm 2 with a thermal resistance as low as 0.1 °C/W. AHS physics, engineering design for inverter applications, performance simulations, and initial test data are presented.

This paper presents a global fractional approach from system identification to path planning; these results will be applied to a typical fractional application: a thermal diffusion in an aluminium rod. The objective is to follow a desired path using fractional linear flatness. However, models of true systems are not always known. Through a black box identification using a fractional model, the temperature versus the heat flux of an aluminium rod is modeled. The coosrivcf algorithm enables to optimize as well the parameter coefficients and the commensurate order. The fractional flat output generates the input command so that the system follows that desired path.

A Least Squares Finite Element Method (LSFEM) formulation for the detection of unknown boundary conditions in steady heat conduction is presented. The method is capable of determining temperatures and heat fluxes in locations where such quantities are unknown provided such quantities are sufficiently overspecified in other locations. In several finite element and boundary element inverse implementations, the resulting system of equations becomes become rectangular if the number of overspecified conditions exceeds the number of unknown conditions. In the case of the finite element method, these rectangular matrices are sparse and can be difficult to solve efficiently. Often we must resort to the use of direct factorizations that require large amounts of core memory for realistic geometries. This difficulty has prevented the solution of large-scale inverse problems that require fine meshes to resolve complex 3-D geometries and material interfaces. In addition, the Galerkin finite element method (GFEM) does not provide the same level of accuracy for both temperature and heat flux. In this paper, an alternative finite element approach based on LSFEM will be shown. The LSFEM formulation always results in a symmetric positivedefinite matrix that can be readily treated with standard sparse matrix solvers. In this approach, the differential equation is cast in first-order form so equal order basis functions can be used for both temperature and heat flux. Enforcement of the overspecified boundary conditions is straightforward in the proposed formulation. The methods allows for direct treatment of complex geometries composed of heterogeneous materials.