Assumption Of Constant Material Properties Research Articles

Numerical analysis of thermoelectric power generation coupled with temperature-dependent material properties

Thermoelectric generator (TEG) with improved performance is a promising technology in power supply and energy harvesting. Existing studies primarily adopt constant material properties to investigate TEG performance. However, thermoelectric (TE) material properties are subjected to considerable variations with temperature. Thus, reasonable doubts have risen concerning the influence level of temperature-dependent material properties on TEG performance. To solve this problem, an efficient and a comprehensive one-dimensional numerical model is developed to fully consider the third-order polynomial temperature-dependent thermal conductivity, Seebeck coefficient, and electrical resistivity. Control volume and finite difference algorithms are compared, and experiments are conducted to verify the developed numerical model. The temperature distribution along the TE leg obviously differs from the parabolic shape, which is a classic temperature distribution under the assumption of constant material properties. Insights find that the local change rate of thermal conductivity and Thomson effect are the essential reasons for the abovementioned phenomenon. It has been found that Thomson heat is released in the part of the leg near the cold-end, whereas it is absorbed in the remaining parts of the leg near the hot-end. The electric power on the basis of constant material properties is confirmed to be accurate enough by the developed numerical model, but the parabolic shape of the TE efficiency can be only obtained when temperature-dependent material properties are considered. Furthermore, it is wise to improve the TE efficiency by structural optimization. The present work provides an efficient and a comprehensive one-dimensional numerical model to include temperature-dependent material properties. New insights into the temperature and heat flux distribution, Thomson influence, and structural optimization potential are also presented for the in-depth understanding of the TE conversion process.

Topology optimization of thermo‐elastic structures with temperature‐dependent material properties under large temperature gradient

AbstractIn this work, high temperature and large temperature gradient are addressed for the first time in the topology optimization of thermo‐elastic structures. The conventional assumption of constant material properties (CMPs) is broken through with the full consideration of temperature‐dependent material properties (TDMPs) including thermal conductivity, elastic tensor, and coefficient of thermal expansion. Nonlinear heat conduction is thus implemented to give varying temperature fields in thermoelasticity. The maximum displacement of the specified region is taken as the objective function in the formulation of the optimization problem. The Kreisselmeier‐Steinhauser (KS) function is employed to approximate the regional maximum displacement/temperature. Corresponding sensitivity analyses, which are carried out using the adjoint method, theoretically reveal how TDMPs affect the thermo‐elastic optimization problem. Typical numerical examples are investigated to validate the proposed approach. The results show that the use of TDMPs produces optimized structures of high fidelity with displacements precisely predicted and temperature constraints rigorously satisfied under large temperature gradient, while thermo‐elastic analysis and optimization with CMPs lead to undesirable designs with significant inaccuracy.

A General Expression for the Welding Tendon Force

Abstract This study presents a novel expression for the tendon force associated with residual stresses produced during welding of large, thin sections. A general engineering equation is presented as the combination of a closed-form expression, based on idealized treatment, and correction factors to account for the effects of temperature-dependent thermal and mechanical material properties. The closed-form expression corresponds to the assumption of constant material properties. A rigorous mathematical treatment is utilized to derive explicit, exact expressions for the temperature-dependent correction factors without the need for empirical correlations. The temperature-dependent behavior of materials is captured accurately using four dimensionless groups. The analysis was validated through numerical simulations with common structural grades of low-carbon steel, stainless steel, aluminum, and titanium. The idealized treatment resulted in predictions with a mean difference of 18%, which was reduced to 7% by incorporating the correction factors. The remaining error is a systematic overestimate, which can be attributed to compliance effects of the finite plate used in the simulations, and is the focus of ongoing research. The utility of applying the novel tendon force equation to problems in fabrication procedure design is demonstrated with an example predicting distortion during manufacturing of hollow structural sections.

Topology optimization of nonlinear heat conduction problems involving large temperature gradient

In this work, we develop a topology optimization method for steady-state nonlinear heat conduction problems involving large temperature gradient to minimize the maximum structural temperature. Temperature-dependent material properties (TDMPs) are taken into account to break the widely-used assumption of constant material properties (CMPs) in conventional topology optimization. The Kreisselmeier–Steinhauser function is adopted as an aggregated measure of the maximum temperature over a specific region and the adjoint method is used to derive the sensitivity expressions. To effectively solve the well-known unsymmetric adjoint problem caused by material nonlinearity, an engineering-oriented stationary iterative method (ESIM) is constructed to transform the unsymmetric adjoint problem into a symmetric one with a series of right-hand sides that can be efficiently solved with mature linear system solvers. Both 2D and 3D numerical examples are provided to illustrate the validity and utility of the proposed method, including the accuracy and convergence of the ESIM. The results show that the assumption of CMPs can result in significant inaccuracy in the analysis and design of heat conduction systems working under large temperature gradient. On the contrary, by considering TDMPs and employing the proposed method, reasonable designs are achieved and thermal performance is greatly improved.

Characteristics analysis and parametric study of a thermoelectric generator by considering variable material properties and heat losses

The output power and conversion efficiency of the thermoelectric generator (TEG) are closely related to not only the materials properties but also the geometric structure. This paper developed a multi-physics, steady-state, and three-dimensional numerical TEG model to investigate the TEG performance, and then the model is compared with the classical thermal resistance model. Bismuth-telluride are used as p- and n-type materials. The comparison reveals that the assumption of constant material properties leads to underestimated inner electrical resistance, and overestimated thermal conductance and Seebeck coefficient, so that the thermal resistance model predicts unrealistically high performance than the present model. The results also indicate that when heat losses exist between the TEG and the ambient, although the output power is slightly elevated, the conversion efficiency is significantly reduced, hence, improvement of the heat insulation effect is critically important for high-temperature TEGs. Furthermore, the TEG geometry also affects its performance significantly: usage of thin ceramic plates increases the junction temperature difference, and hence enhances the TEG performance; there are two optimal leg lengths which correspond to the maximum output power and the maximum conversion efficiency, respectively; when heat losses are not ignorable, a large semiconductor cross-sectional area remarkably reduces the ratio of the heat liberated to the ambient to the heat absorbed from the high-temperature heat source, and hence improves the conversion efficiency.

Prediction of varying thermal resistivity of organic insulation materials

Temperature, humidity and aging have significant influence on the thermal performance of insulation materials. The assumption of constant material properties frequently leads to the wrong results for simulating heat transfer through insulation materials. Therefore, the impact of hygrothermal conditions and aging on the long-term behavior of insulation materials should be investigated. The objective of this work is to evaluate the influence of coupled hygrothermal conditions and aging on the thermal resistivity of organic foamy materials. A model of aging conversion coefficient for two organic foamy materials is proposed. The thermal resistivity ratio (TRR) is calculated using the coupled heat and moisture transfer model which introduces effective thermal conductivity for expanded polystyrene and extruded polystyrene. The comparison of predicted values with experimental data shows a good agreement. This paper provides an estimation approach to the aging conversion coefficient that affects the thermal conductivity of the organic foamy materials.

Multi-fidelity optimization of laminated conical shells for buckling

Optimum laminate configuration for minimum weight of filament-wound laminated conical shells is investigated subject to a buckling load constraint. In the case of a composite laminated conical shell, due to the manufacturing process, the thickness and the ply orientation are functions of the shell coordinates, which ultimately results in coordinate dependence of the stiffness matrices (A,B,D). These effects influence both the buckling load and the weight of the structure and complicate the optimization problem considerably. High computational cost is involved in calculating the buckling load by means of a high-fidelity analysis, e.g. using the computer code STAGS-A. In order to simplify the optimization procedure, a low-fidelity model based on the assumption of constant material properties throughout the shell is adopted, and buckling loads are calculated by means of a low-fidelity analysis, e.g. using the computer code BOCS. This work proposes combining the high-fidelity analysis model (based on exact material properties) with the low-fidelity model (based on nominal material properties) by using correction response surfaces, which approximate the discrepancy between buckling loads determined from different fidelity analyses. The results indicate that the proposed multi-fidelity approaches using correction response surfaces can be used to improve the computational efficiency of structural optimization problems.

Residual Stresses in Injection Molded Thermoplastics

Residual stresses in molded thermoplastics are caused by heterogeneous cooling and by different pressures frozen in at different time of the cycle. This usually leads to a core in tension, surface regions in compression, and sometime thin extreme surface layers in tension again. In a first part, the mechanisms of residual stresses formation are presented. In a second part, a technique to measure residual stresses, based on the measurement of the bending moments necessary to lay-flat a specimen after removal of a thin layer, is applied to unfilled and fiber reinforced materials with success. The technique, unlike the curvature measurement based method, eliminates the necessity of the assumption of constant material properties. Finally, we show the dependence of the solid polymer viscoelastic data on the thermomechanical history of the test specimen, and the consequences on the computed residual stresses, which are compared to the measurements.

Variability analysis of timber bridge responses

Large variations in timber moduli of elasticity cause large variations in the loads accepted by various girders (stringers) of a timber bridge. These variations cannot be accounted for by deterministic analyses based on the assumption of constant material properties. In this paper the problem of variation of loads accepted by timber stringer is studied through Monte Carlo simulations. Two separate mathematical models are used for representing timber bridges; one model assumes that transverse load distribution is due only to the transverse shear stiffness of the bridge, and the other that it is due to the transverse bending stiffness. Each model, however, is a special case of the more general and accurate bridge model, known as the semicontinuum model. It has been shown that both models yield similar conclusions regarding the variability of load acceptance by the girders. It is found that the coefficient of variation of loads accepted by those girders which resist appreciable amounts of the applied loads is always less than the coefficient of variation of the timber modulus of elasticity, and that the amount of variation depends upon the transverse position of the loads and the load distribution characteristics of the bridge. A simple expression is given by which the upper bound value of a distribution coefficient, corresponding to a desired confidence limit, can be estimated.

Ultrafiltration of macromolecular solutions and cross-flow microfiltration of colloidal suspensions. A contribution to permeate flux calculations

Ultrafiltration and cross-flow microfiltration are pressure-driven membrane processes which exhibit concentration polarisation in front of the membrane or gel layer, respectively. In ultrafiltration the concentration polarization is essentially determined by diffusion in the boundary layer. With the usual assumption of constant material properties, the film theory predicts fluxes quite accurately in the case of ultrafiltration of low molecular weight solutions. The calculated fluxes are, however, significantly lower than the observed figures in case of ultrafiltration of macromolecular solutions. It will be shown that with concentration-dependent material properties, especially a variable density (!) and a variable diffusion coefficient, the film theory can predict fluxes of ultrafiltration of macromolecular solutions very accurately. Such a theory fails, however, in case of cross-flow filtration of colloidal suspensions. Even with the assumption of a variable density in the boundary layer, the calculated fluxes are too low by a factor of about 10. For cross-flow microfiltration of colloidal suspensions, a model is presented considering basically the membrane-parallel drag forces acting on a particle in the vicinity of the membrane and a “friction” force as a consequence of the lateral drag forces. The model has been tested with different module systems and with different colloidal suspensions.