Thermal-electrical Analogy Research Articles

Fractal analysis of effective thermal conductivity for three-phase (unsaturated) porous media

A fractal analysis of effective thermal conductivity for unsaturated fractal porous media is presented based on the thermal-electrical analogy and statistical self-similarity of porous media. Here, we derive a dimensionless expression of effective thermal conductivity without any empirical constant. The effects of the parameters of fractal porous media on the dimensionless effective thermal conductivity are discussed. From this study, it is shown that, when the thermal conductivity of solid phase and wet phase are greater than that of the gas phase (viz., ks∕kg>1, kw∕kg>1), the dimensionless effective thermal conductivity of unsaturated fractal porous media decreases with decreasing degree of saturation (Sw) and increasing fractal dimension for pore area (Df), fractal dimension for tortuosity (Dt), and porosity (ϕ); when the thermal conductivities of solid phase and wet phase are lower than that of the gas phase (viz., ks∕kg<1, kw∕kg<1), the trends were just opposite. Our model was validated by comparing the model prediction with existing experimental data. Excellent agreement was found except for the cases at very low level of saturation.

Modeling of Transverse Direction Thermal Conductivity in Micro-nano Fiber-reinforced Composites

Analytical modeling for heat transfer behavior of micro-nano fiber-reinforced composites to determine the dimensionless effective thermal conductivity in the transverse direction has been performed. A hexagonal unit cell was developed that contained matrix, filler and interface (barrier) as the components. Thermal-electrical analogy method was used in the model. Models were developed with and without barrier effect. Filler ratios were taken to be between 10 and 30 %. Effects of barrier thickness and filler volume fraction on the dimensionless effective transverse thermal conductivity have been analyzed. The Rule of Mixtures and analytical modeling results have been compared. The model showed that increasing the volume fraction of the filler inside the matrix increased the total effective thermal conductivity values. When the barrier thickness increased, the dimensionless effective thermal conductivity value increased.

Thermal modeling and heat management of supercapacitor modules for vehicle applications

Temperature has a huge influence on supercapacitor cells and modules ageing. Consequently, thermal management is a key issue concerning lifetime and performance of supercapacitor modules. This paper presents thermal modeling and heat management of supercapacitor modules for vehicle applications. The thermal model developed is based on thermal-electric analogy and allows the determination of supercapacitor temperature. Relying on this model, heat management in supercapacitor modules was studied for vehicle applications. Thus, the modules were submitted to real life driving cycles and the evolution of temperatures of supercapacitors was estimated according to electrical demands. The simulation results show that the hotspot is located in the middle of supercapacitors module and that a forced airflow cooling system is necessary.

Analysis of thermal conductivity in tree-like branched networks

Asymmetric tree-like branched networks are explored by geometric algorithms. Based on the network, an analysis of the thermal conductivity is presented. The relationship between effective thermal conductivity and geometric structures is obtained by using the thermal-electrical analogy technique. In all studied cases, a clear behaviour is observed, where angle (δ, θ) among parent branching extended lines, branches and parameter of the geometric structures have stronger effects on the effective thermal conductivity. When the angle δ is fixed, the optical diameter ratio β* is dependent on angle θ. Moreover, γ and m are not related to β*. The longer the branch is, the smaller the effective thermal conductivity will be. It is also found that when the angle θ < δ/2, the higher the iteration m is, the lower the thermal conductivity will be and it tends to zero, otherwise, it is bigger than zero. When the diameter ratio β1 < 0.707 and angle δ is bigger, the optimal k of the perfect ratio increases with the increase of the angle δ; when β1 > 0.707, the optimal k decreases. In addition, the effective thermal conductivity is always less than that of single channel material. The present results also show that the effective thermal conductivity of the asymmetric tree-like branched networks does not obey Murray's law.

Power transformer top‐oil temperature model based on thermal–electric analogy theory

AbstractThis paper presents a thermal–electric analogous thermal model of an oil‐immersed power transformer. The model is established to calculate the top‐oil temperature in the form of simple equivalent circuit based on the fundamental heat transfer theory. The presented model takes into account application of the lumped capacitance, nonlinear thermal resistances, and oil viscosity, whereas Levenberg–Marquardt Method is used as a search method to determine the thermal model parameters. For the OFAN and OFAF power transformers, a lot of experimental data and curves show the proposed model in this paper can yield better results than IEEE thermal model and be used widely in the power transformer fault prediction field. Copyright © 2007 John Wiley &amp; Sons, Ltd.

Dynamic Thermal Modeling of Power Transformers: Further Development—Part II

This paper presents new temperature calculation methods based on heat-transfer theory, the application of the lumped capacitance method, the thermal-electrical analogy, and a new definition of nonlinear thermal resistances at different locations within a power transformer. The methods presented in this paper take into account oil viscosity changes and loss variation with temperature. The changes in transformer time constants due to changes in the oil viscosity are also accounted for in the thermal models. The models are validated using experimental results, which have been obtained from a series of thermal tests performed on a range of power transformers. The results are also compared with the IEEE-Loading guide (1995) Annex G method

Cylindrical Orthotropic Thermal Conductivity of Spiral Woven Composites. Part II: A Mathematical Model for their Effective Transverse Thermal Conductivity

This is the second in a series of papers on the cylindrical orthotropic thermal conductivity of spiral woven composites. Based on the thermal-electrical analogy, a mathematical model for determining the effective transverse thermal conductivity of spiral woven fabric composites has been developed in terms of geometric parameters and constituent thermal properties. It is shown by a comparison with publishing results that the present model is capable of predicting the effective transverse thermal conductivity of spiral woven composites.

Prediction of Thermal Conductivities of Fibre Reinforced Composites using a Thermal-Electrical Analogy

An approach for predicting the effective thermal conductivities of fibre reinforced composites has been developed, based on a thermal-electrical analogy. In the voxelization method, the unit cell of the laminate composites is divided into a number of volume elements, and the material properties considering the local variations of fibre orientation have been given to each element. By constructing a series-parallel thermal resistance network, the thermal conductivities of a fibre reinforced composite in both in-plane and out-of-plane directions have been predicted. The reported thermal conductivities of a graphite/epoxy composite of a balanced plain weave laminate were used for the comparison with the predicted values of the model, and good agreement was found.

Model for thermal conductivities in spun yarn carbon fabric composites

A study on the thermal conductivities of spun yarn-type carbon/phenolic (spun C/P) composites using a thermal-electrical analogy method is presented. This method is based on the similarity between the partial differential equation that governs the thermal potential and electrical potential distribution. The unit cell of a laminate composite is divided into several conduction elements. By constructing an equivalent thermal resistance network in series, and in parallel based on analogy, we were able to predict the thermal conductivity of the composite. The prediction values obtained from the model are compared with known thermal conductivities on a carbon/epoxy composite with an eight-harness satin (8HS) texture. It is shown that the model provides a good estimate of the thermal conductivity of the spun yarn fabric-reinforced composite. With the use of this model, the thermal conductivity of the spun C/P composites with 8HS was validated experimentally. Good agreement was found between the present approach and the experimental results. POLYM. COMPOS., 26:791–798, 2005. © 2005 Society of Plastics Engineers

A simplified transformer thermal model based on thermal-electric analogy

This paper presents a further simplified thermal-electric analogous thermal model of an oil-immersed power transformer. The method is rooted on the principles of heat exchange and electric circuit laws. A set of differential equations is derived to calculate both the transient-state temperatures and the stationary-state equilibria in the main parts of a transformer. For the problem of thermal parameters identification, a genetic algorithm is employed to search global solutions for thermal parameters with onsite measurements. The validation of the simplified model and calculations of hot-spot temperatures are discussed in detail.

Evolutionary algorithms for compact thermal modelling of microsystems: application to a micro-pyrotechnic actuator

In this work, we approach the problem of extracting a dynamic multiport thermal compact model from thermal impedance transients of microsystems using genetic algorithms. The model takes the form of a unique RC network, using a thermal-electrical analogy. The model topology is codified in a binary chromosoma and nonlinear least squares is used for sizing their components. The compact model topology evolution is genetically controlled to obtain the RC network that minimizes the reconstruction error of the thermal impedance transients. As an example, the proposed methodology is applied to an innovative silicon microthruster and compared with random search and sequential forward selection.

Fractal geometry model for effective thermal conductivity of three-phase porous media

An approximate model, a fractal geometry model, for the effective thermal conductivity of three-phase/unsaturated porous media is proposed based on the thermal-electrical analogy technique and on statistical self-similarity of porous media. The proposed thermal conductivity model is expressed as a function of porosity (related to stage n of Sierpı́nski carpet), ratio of areas, ratio of component thermal conductivities, and saturation. The recursive algorithm for the thermal conductivity by the proposed model is presented and found to be quite simple. The model predictions are compared with the existing measurements. Good agreement is found between the present model predictions and the existing experimental data. This verifies the validity of the proposed model.

Study on Optimization of Transverse Thermal Conductivities of Unidirectional Composites

Abstract Two models, E-S and R-S unit cell models, are presented based on the thermal-electrical analogy technique. The analytical expressions for transverse thermal conductivities of unidirectional composites are derived. The dimensionless effective transverse thermal conductivities ke+ are expressed as a function of the ratio (β) of thermal conductivities of filler to matrix, filler volume fraction vf and the geometry ratio ρ=a/b of the filler. The optimization of transverse thermal conductivities of unidirectional composites is then analyzed under different filler volume fractions vf, thermal conductivity ratios β and different geometric architectures. The present analysis allows for a fairly precise evaluation of configuration performance and comparisons of different arrangements. The results show that if a composite is designed for insulation material, we should choose ρ&amp;lt;1, and if a composite is designed for heat dissipating purpose, we should choose ρ&amp;gt;1.

A self-similarity model for effective thermal conductivity of porous media

A new model, the self-similarity model, for effective thermal conductivity of porous media is proposed based on the thermal–electrical analogy technique and on statistical self-similarity of porous media. The proposed thermal conductivity model is expressed as a function of porosity (related to stage n of Sierpinski carpet), ratio of areas, ratio of component thermal conductivities, and contact resistance. A recursive algorithm for the thermal conductivity is obtained using the proposed model and is found to be quite simple. The predictions of the model are compared with those of other models and with existing measurements and good agreement was found. This proves that the proposed model is a valid one.

Thermal simulation of semiconductor ICs: general and practical approach

Three-dimensional models of the heat exchange process in semiconductor ICs have been developed. The models were used for the simulation of the thermal resistance of plastic IC packages. The method presented makes it possible to use a combination of the thermal-electrical analogy technique and a 3D analytical approach to simulating the heat removal process in semiconductor IC packages. The utilization of this method is illustrated by an example of the thermal resistance simulation in an IC package.

Thermal-Electrical Analogy. Cooling a Can of Beer.

Thermal-Electrical Analogy. Cooling a Can of Beer.

Closed-form solutions of the in-plane effective thermal conductivities of woven-fabric composites

A micromechanics model is developed to predict the in-plane effective thermal conductivities of plain-weave fabric composites based on a thermal-electrical analogy. Closed-form solutions of the effective thermal conductivities in the warp and fill directions are presented. In order to affirm the applicability of these solutions, the in-plane effective thermal conductivities of S-glass, E-glass, graphite, and Kevlar-49 plainweave fabric-reinforced epoxy composites are predicted. Excellent agreement is found between the present predictions and published analytical, numerical, and experimental results.

A thermal-electrical analogy model of heat exchanges in a solar greenhouse

A dynamic simulation model, based upon the thermal-electrical analogy, has been developed to simulate the free thermal behavior of a solar greenhouse. The simple linearized model treats greenhouse air and ground temperatures as lumped parameters. It requires only six input parameters, which were measured on site or obtained from a regional weather-station. Model development focused on radiative transfers through the glazing (i.e. solar input) and within the greenhouse (i.e. re-emitted infrared) and on heat losses by infiltration which were determined experimentally. The model was validated by comparisons with the actual thermal behavior of SERSOL, a solar greenhouse built by students on the campus of the University of Montreal. Data were recorded in SERSOL during 10 days over a 3-month winter period. Several key parameters were adjusted by curve fitting of the results obtained in specially designed experiments. Results obtained over a broad spectrum of weather conditions show good agreement between simulated and actual behavior. The main default of the model appears to be a time shift, which could not be satisfactorily corrected.

Very Low-Drift Complimentary Semiconductor Network dc Amplifiers

This paper describes a new approach to the fabrication of a variety of monolithic direct coupled amplifiers with typical equivalent differential input drifts of 0.1 to 0.2 /spl mu/v//spl deg/C. These amplifiers exhibit a significant improvement in temperature stability over current state-of-the-art IC amplifiers, and complete with chopper stabilized units in many respects. In these amplifiers, a monolithic silicon wafer is maintained at a near constant temperature by means of an electrically separate temperature-control circuit diffused within the same substrate. A thermal-electrical analogy is used to predict temperature gradients on the surface of the silicon bar. Performance of several amplfier circuit configurations is discussed.

A systematic method of deriving new semiconducting compounds by structural analogy : B. R. Pamplin. J. Phys. Chem. Solids25, 675 (1964)

The paper presents a review of publications devoted to the use of thermal-electric analogy in the analyses of solar collectors’ performance, with special focus on the shortcomings of the proposed models of the equivalent thermal network (ETN). Additionally, the study describes the principles of construction of the ETN, especially for large-scale solar thermal circuits. The process of heating the working medium flowing through the collector battery was also shown. The ETN model was presented both analytically (nodal potential method) and with the use of the Simulink package (MATLAB), which made it possible to investigate the effect of operating conditions on the parameters of the solar collector.