Equivalent Thermophysical Properties Research Articles

Early freezing dynamics of an aqueous foam.

Phase-change is an essential and unavoidable process to obtain solid foam. We study experimentally the solidification dynamics of a model aqueous foam in contact with a cold substrate. The substrate temperature, the foam bubble radius and the liquid fraction are changed. We show that the freezing dynamics always starts by following a self-similar square root of time diffusive dynamics. These early dynamics are then predicted as a function of the control parameters using a 1D diffusion model and by treating our foam as a homogeneous fluid with equivalent thermophysical properties. In particular, we build a new expression for the foam conductivity. Finally, experimental and theoretical results are compared and interpreted. This study paves the way towards the understanding of the complex foam freezing dynamics at longer times, when the freezing is then coupled to water migration in the foam.

A coupled model of composite synthesis in combustion regime

The work proposes a model for synthesising a ‘metallic matrix–reinforcing inclusions’ composite in a simplified reaction scheme. A suggested mathematical model takes into account the interdependence of thermal, chemical and mechanical phenomena. The problem includes kinetic equations for determining the composition of the synthesis products. The reactions are initiated by a thermal impulse from a surface. It was established that after some mathematical transformations and partial analytical solution, the model includes equivalent parameters of the reactions and equivalent thermophysical properties that depend on the mechanical modules. The model allowed us to study two variants of composite synthesis: in the quasi-stationary mode for a sample whose dimensions exceed the size of the heating and reaction zones, and in the unsteady mode for a finite-sized sample. It is shown that the consideration of the coupling of thermal, chemical and mechanical processes changes all the characteristics of conversion propagation and the values of stresses and strains in the reaction zone. The stresses in the reaction zone and in the products are affected by the parameters characterising the reaction itself. It is shown that there is a range of parameters at which a stable combustion wave is not formed.

On the equivalent thermo-physical properties for modeling building walls with unknown stratigraphy

It is known that energy efficiency passes through the renovation of the built heritage. However, the technical data may be unknown, thus applying not always suitable assumptions. Documents may have been lost and uncertainties may occur. In this context, the description of multilayer walls through equivalent models could solve the information lack issues.In this study, an experimental campaign is conducted on two test rooms, and the measured data are used to generate equivalent homogeneous walls through an inverse approach. The comparison between the original and equivalent walls is performed, finding the equivalent thermo-physical properties able to best reproduce the thermal behaviors of the original walls and calculating the model efficiency index (EF). Finally, a building simulation code is used to perform a comparison on annual energy demands.The main results allow to obtain EF indexes higher than 0.93 in almost all the analyzed scenarios. The main issue is related to the experimental equivalent thermal conductivity, the determination of which is correlated to suitable measurement conditions. Considering the energy simulations, the comparison between the equivalent models and the original ones allows to obtain a range of percentage difference of ±10 % for both energy demands and peak loads.

Combinatorial structural-analytical models for the prediction of the mechanical behaviour of isotropic porous pure metals

This work provides insight on the prediction of the mechanical behaviour of isotropic porous pure metals using empirical and structural-analytical models and proposes two new combinatorial structural-analytical models for the estimation of the mechanical properties. Porous metals such as foams are advanced engineering materials and therefore the prediction of their properties for their optimisation is beneficial. Nevertheless, the estimation of their mechanical behaviour generally relies on semi-empirical models, which are limited to specific materials (i.e. type of metal + type of internal structure + individual property) and for which empirical constants need to be determined. Among the available structural-analytical models, which were developed to estimate mathematically equivalent thermophysical properties, the Symmetric and Interconnected Skeleton Structural (SISS) model gives the best prediction over a broad range of volume fraction of pores (i.e. 0.4–1.0) but always significantly overestimates the elongation to failure. This study presents the derivation of new combinatorial structural-analytical models that are able to rapidly and accurately predict the Young modulus plus ultimate tensile strength and the elongation to failure, respectively, across the entire range of volume fraction of pores. These models have physical bases, are not time- and computing-intensive (thus rapid and low cost), and have reasonable accuracy for materials whose microstructure is uncertain.

Creep-fatigue strength design of plate-fin heat exchanger by a homogeneous method

Creep-fatigue life prediction is essential to plate-fin heat exchangers (PFHE) work at high temperatures and pressures in addition to thermal cycles. As the core of PFHE, the plate-fin structure is a complex pore structure and it is pretty difficult to carry out the stress analysis by conventional finite element method. Thus in this paper, a homogeneous method is proposed to do the strength design for plate-fin structure. This method treats the pore structure as an equivalent solid structure, and the key is to calculate the equivalent material properties and the equivalent stress. The equivalent mechanical properties have been obtained in our previous work [1], and in this paper the equivalent thermophysical properties including thermal conductivity, coefficient of thermal expansion, specific heat and density have been derived. This equivalent method is also verified by the three-dimensional finite element method. Besides, creep and fatigue tests of plate-fin structure are applied to calculate the stress and strain magnification factors. Basing on the equivalent material properties, a full scale stress analysis of PFHE by the equivalent finite element model has been carried out successfully to calculate the equivalent stress. After that, we multiply the equivalent stress-strain by the stress and strain magnification factors to calculate the local stress and strain. Then the creep and fatigue damages are predicted according to design curves of base metal. The result of equivalent model agrees well with that of the classical model, which concludes that this homogeneous method is effective to predict the macroscopic performance of plate-fin structure.

Description of multilayer walls by means of equivalent homogeneous models

The accurate characterization of building envelopes represents the first step to realize a model of built structures, upon which is possible to work for the design of appropriate retrofit measures. External building walls, indeed, are one of the most significant paths of heat transfer between outer and inner environment and, as such, their control is crucial to go in the direction of energy saving. Simple models that capture the essential thermal characteristics of building walls, which are usually layered structures, would be desirable. A homogeneous wall that can be equivalent, under appropriate circumstances, to a given multilayer structure would provide an example of such a simple model. Homogeneous walls that are completely equivalent to generic multilayer walls are in general not achievable. However, we show in this work that this is possible in particular cases, i.e. if one focuses only on temperature or on heat flux behavior. It is shown that, in such situations, both an exact and an approximate solution for equivalent thermophysical properties can be devised. The evaluation of the level of approximation introduced is presented. In addition, the significance and the implications of the introduced equivalent models is discussed both regarding their exact and their approximate formulations.

Low mass fraction impregnation with graphene oxide (GO) enhances thermo-physical properties of paraffin for heat storage applications

Whereas previous researchers analyzed the thermal behavior of paraffin waxes impregnated with graphene oxide nanoparticles (P-GONP) at high mass fraction (>1%), this paper analyzes behavior and stability at only 0.3% mass fraction. GONP was prepared by Hummer’s method. The morphology was studied using scanning electron microscope (SEM), transmission electron microscope (TEM), X-Ray diffraction (XRD) and Fourier Transformation-Infrared (FT-IR) Spectrometer and the thermal properties were measured using laser flash analyser (LFA), differential scanning calorimetry (DSC), thermo-gravimetric analysis (TGA) and thermal cycling. LFA showed a 101.2% and 94.5% increase in the thermal conductivity of P-GONP compared to pure paraffin (P) in solid and liquid state respectively. Melting and solidifying temperatures and latent heat were found to be 63.5, 59°C & 102kJ/kg and 57.5, 56°C & 64.7kJ/kg for P and P-GONP respectively. Thermal cycling over 4000 cycles showed that P-GONP was 27% more stable than P. The latent heat was 64.7kJ/kg, a 36.5% deterioration compared to virgin paraffin. Compared against higher mass fraction impregnation, lower mass fraction P-GONP was found to have almost equivalent thermo-physical properties (namely thermal conductivity, melting and solidifying characteristics, thermo-chemical stability and reliability) while providing considerable cost saving.

2D Conduction Simulation of a PCM Storage Coupled with a Heat Pump in a Ventilation System

Efforts to simulate heat transfer in a PCM (Phase Change Material) storage device are generally led by considerations of Biot number and material thickness, of 2D versus 1D representation, and of possible hysteresis effects arising from the characterisation of the PCM using differential scanning calorimetry (DSC). In this paper we present a numerical treatment of heat conduction in a paraffin-based storage brick, based on experimental data for a full scale, heat storage component studied under laboratory conditions. The PCM was modelled adopting equivalent thermophysical properties during the phase change. An equivalent heat capacity and thermal conductivity were provided for an appropriate description of energy release and storage in the process of solidification and melting. The geometry of the metal container induces 2D effects that are generally neglected in numerical modelling. The thickness of the plates (about 2 cm) is sufficiently large to require the modelling of conduction in the PCM, but can also induce convection that has been neglected in this study. Experimental results are presented and compared for both a 1D and 2D model of the PCM device. It was concluded that a 2D representation is essential for configurations; like the case study and geometry we had; with a large difference in thermal conductivity between PCM and metal casing. Two curves of equivalent heat capacity (measured via DSC) were introduced for heating and cooling phases. Comparisons to experimental results indicated significant errors in the models during melting and solidification of the PCM, which could be reduced by instead adopting the mean of the two heat capacity curves. The rate of temperature change during the experiments and for the DSC characterisation was analysed and found to explain well the observations. In particular, as novelty, two peaks of equivalent heat capacity have been observed with DSC when the rate is very low instead of only one peak using current rate: and that explains the real behaviour in the experiments.

Multi-objective optimization of a building envelope for thermal performance using genetic algorithms and artificial neural network

The objective of this paper is to present a method to optimize the equivalent thermophysical properties of the external walls (thermal conductivity kwall and volumetric specific heat (ρc)wall) of a dwelling in order to improve its thermal efficiency. Classical optimization involves several dynamic yearly thermal simulations, which are commonly quite time consuming. To reduce the computational requirements, we have adopted a methodology that couples an artificial neural network and the genetic algorithm NSGA-II. This optimization technique has been applied to a dwelling for two French climates, Nancy (continental) and Nice (Mediterranean). We have chosen to characterize the energy performance of the dwelling with two criteria, which are the optimization targets: the annual energy consumption QTOT and the summer comfort degree Isum. First, using a design of experiments, we have quantified and analyzed the impact of the variables kwall and (ρc)wall on the objectives QTOT and Isum, depending on the climate. Then, the optimal Pareto fronts obtained from the optimization are presented and analyzed. The optimal solutions are compared to those from mono-objective optimization by using an aggregative method and a constraint problem in GenOpt. The comparison clearly shows the importance of performing multi-objective optimization.

A moving boundary problem in a food material undergoing volume change – Simulation of bread baking

This paper presents a mathematical model for describing processes involving simultaneous heat and mass transfer with phase transition in foods undergoing volume change, i.e. shrinkage and/or expansion. We focused on processes where the phase transition occurs in a moving front, such as thawing, freezing, drying, frying and baking. The model is based on a moving boundary problem formulation with equivalent thermophysical properties. The transport problem is solved by using the finite element method and the Arbitrary Lagrangian–Eulerian method is used to describe the motion of the boundary. The formulation is assessed by simulating the bread baking process and comparing numerical results with experimental data. Simulated temperature and water content profiles are in good agreement with experimental data obtained from bread baking tests. The model well describes the stated general problem and it is expected to be useful for other food processes involving similar phenomena.

Bread baking as a moving boundary problem. Part 2: Model validation and numerical simulation

A simultaneous heat and mass transfer model proposed to describe the bread baking process is validated. The mathematical model is based on a moving boundary problem formulation with equivalent thermophysical properties and includes the moving evaporation front, the evaporation–condensation mechanism and the development of the crust observed during bread baking. The problem is solved over an irregular three-dimensional geometry using the finite element method. Variation in temperature and water content of bread during baking is predicted with high accuracy by the model. Parameter estimation procedure and sensitivity analysis are performed for some thermophysical properties. The proposed formulation and analysis can be applied for other bakery products as well as for similar food engineering applications.

Bread baking as a moving boundary problem. Part 1: Mathematical modelling

A mathematical model for the bread baking process is developed in this work. Experimental data (temperature, water content, weight loss, crust thickness) obtained during baking is used to well understand the simultaneous heat and mass transfer occurring during the process. The evaporation–condensation mechanism is responsible for the rapid heating of the porous matrix and takes place either in a closed (dough) or open (crumb) structure. The existence of a moving evaporation front inside bread, which is a determining step of baking, is incorporated in a model applying a moving boundary formulation with equivalent thermophysical properties. The approach proposed here can be extended to other similar processes such as baking of other products (e.g. biscuit, cake), high-temperature drying, cooking and roasting.

Homogenization of the fluid flow and heat transfer in transpiration cooled multi-layer plates

To predict the aerothermal behavior of transpiration cooled plates, a multi-scale approach based on the homogenization method of periodic material structures is developed. This method allows one to calculate effective equivalent thermophysical properties either for each layer or for the multi-layer of superalloy, bondcoat and TBC. A general formulation is developed here for the fluid flow through a porous media which is able to deduce as equivalent macroscopic behavior either a Darcy law with a constant permeability or a more general Fochheimer law with a permeability function of the mean velocity. Effective Darcy permeabilities are calculated by solving special Stokes flow problems on a unit cell. Finally, effective conductivities and permeabilities are determined for different configurations of cylindrical and shaped transpiration cooling channels.

Homogenization of the thermal properties of transpiration cooled multi-layer plates

To predict the aerothermal behaviour of transpiration cooled plates, a multi-scale approach based on the homogenization method of periodic material structures is presented. This method allows to calculate effective equivalent thermophysical properties either for each layer or for the multi-layer of superalloy, bondcoat and thermal barrier coating. Its variational formulation and finite element discretization are then presented. From the 3-D conjugate flow and heat transfer analysis, the stationary state is extracted and transferred to the micro-scale unit cell discretized by finite elements. The effect of the different cooling designs on the effective orthotropic conductivities are then discussed. Finally, the influence of the FE discretization and the position of unit cell on these effective thermal properties is investigated.

3-D CONJUGATE ANALYSIS OF COOLED COATED PLATES AND HOMOGENIZATION OF THEIR THERMAL PROPERTIES

To predict the aerothermal behavior of a transpiration cooled plate, a multiscale approach based on the homogenization method of periodic material structures is presented here. This method allows calculation of effective equivalent thermophysical properties either for each layer or for the multilayer of superalloy, bondcoat, and thermal barrier coating (TBC). From the 3-D conjugate flow and heat transfer analysis, the stationary state is extracted and transferred to the microscale unit cell discretized by finite elements. The analysis proves for different cooling configurations a significant decrease in the amount of cooling fluid to obtain a desired superalloy temperature. Beyond, the hole outlet shaping leads to a reduction of the thermal gradients on the multilayer. The effect of the different cooling designs on the effective conductivities are discussed then. Finally, the influence of the selection of the unit cell position on these effective thermal properties is investigated.

Equivalent thermophysical properties and surface heat transfer coefficient of fruit layers in trays during cooling

Experimental engineering data and predictive equations are established for the equivalent thermophysical properties (thermal conductivity, thermal diffusivity, specific heat capacity and density) and surface heat transfer coefficient of bulk layers of fruits (strawberries, raspberries, apricots, peaches, grapes and apples) in trays. Both packed layers and uncovered trays are considered as a system of fruits and air. In the first case the influence of air inclusions and free convection in closed space is taken into account, while in the second – special attention is devoted to the effect of air infiltration between the fruits placed in trays and pallets. The regression equations derived give the relationship between the considered equivalent values and the velocity of longitudinal air flow between the trays. The results are appropriate to be used for mathematical modelling and engineering calculations in real industrial heat transfer scenarios.