Simultaneous estimation of spatially distributed thermal conductivity,heat capacity and surface heat transfer coefficient in thermal tomography

In thermal tomography, the thermal properties of a target are estimated as spatially distributed parameters based on non-invasive measurements of surface temperatures. In the measurement setup, the target is sequentially heated at different source locations and the induced temperature evolutions are measured at several measurement locations on the surface. In [V. Kolehmainen, J. Kaipio, H. Orlande, Reconstruction of thermal conductivity and heat capacity using a tomographic approach, Int. J. Heat Mass Transfer 50 (25–26) (2007) 5150–5160], it was demonstrated with simulations that simultaneous estimation of spatially distributed thermal conductivity and volumetric heat capacity from transient boundary data is feasible when the boundary heat flux from the target to the surrounding medium is known all over the target boundary. In this article, we extend the computational methods towards the more practical setup of imaging targets, where the boundary heat flux from the target to the surrounding medium is not known. We model the surface heat transfer coefficient as a spatially distributed parameter on the target boundary and estimate it simultaneously with the spatially distributed thermal conductivity and volumetric heat capacity using the statistical (Bayesian) inversion framework. The feasibility of the approach is evaluated with simulations.     

Simultaneous measurement of thermal properties by thermal probe using stochastic approximation method

A novel thermal probe method is proposed for the simultaneous measurement of the thermal properties by the Monte Carlo stochastic approximation method. In this method, thermal capacity of probe and thermal contact resistance between probe and sample are considered. An experimental system is set up with the method to validate the measurement accuracy of the method. The thermal properties of several liquid samples as well as solid samples are measured. The results show that: (1) the thermal conductivity and the volumetric heat capacity can be measured with an error of less than 1.2% and 3% respectively, therefore, the measurement accuracy by the method is much higher than the conventional method and (2) the thermal contact resistance has a great effect on thermal conductivity for solid sample, while little influence on thermal conductivity for liquid sample and volumetric heat capacity.     

Estimation of soil and grout thermal properties through a TSPEP (two-step parameter estimation procedure) applied to TRT (thermal response test) data

In this paper, a versatile TSPEP (two-step parameter estimation procedure) based on a three-dimensional numerical model of a geothermal system is presented. The procedure is applied to both simulated and experimental TRT (thermal response test) data in order to restore the grout and soil thermal conductivities and volumetric heat capacities. The TSPEP is essentially a two-step process. The first step uses the parameter estimation procedure, in the early transient regime to restore the grout thermal conductivity and volumetric heat capacity. The values from the first step are used as the input values in the second step, in which the parameter estimation procedure is applied to the late transient regime to restore the soil thermal conductivity and volumetric heat capacity. Further iterations of these two steps can be used to improve the accuracy of the procedure and are discussed in this paper. The time separation used between the estimation of the soil properties and the estimation of the grout properties partially uncouples the two problems and makes the estimation of these four parameters feasible. A criterion to select the time separation is discussed and validated in this paper.     

A practical method for computing the thermal properties of a Ground Heat Exchanger

The aim of this paper is to show a practical way of estimating the thermal ground properties, namely the ground thermal conductivity, and in particular the thermal diffusivity and the volumetric heat capacity in a reliable manner, for sizing Ground Heat Exchangers (GHEs). A well-known thermal model, proposed by Blackwell in 1954, is applied and is validated both in the heating mode and in the cooling mode, using a GHE as a probe. The value of the thermal conductivity can be easily determined by the model but the procedure also requires knowledge of the ground specific heat capacity and density, which are normally deduced from the (non-accurate) geological data of the site.In addition to the above, the thermal model is also solved analytically –based on the actual parameters used in the experiment–leading to the computation of the ground thermal diffusivity, the volumetric heat capacity and the thermal resistance of the GHE. The possible errors and drawbacks of the whole method are then discussed and finally a complete set of guidelines is provided to the field Engineer for estimating the ground thermal properties from a single test, rendering the use of the geological data of the side unnecessary.     

Bayesian Estimation of Temperature-Dependent Thermophysical Properties and Transient Boundary Heat Flux

In this article, we apply a Bayesian approach for the simultaneous identification of volumetric heat capacity, thermal conductivity, and boundary heat flux, in a one-dimensional nonlinear heat conduction problem. The Markov chain Monte Carlo sampling approach, implemented in the form of the Metropolis–Hastings algorithm, was used for the solution of the inverse problem. Simulated temperature measurements were used in the inverse analysis in order to examine the accuracy and stability of the overall approach. Independent measurement data were used to construct the prior model for the coefficients to be estimated. The approach is also applied to experiments involving the heating of a reference material with an oxyacetylene torch.     

Two-dimensional thermal analysis of liquid hydrogen tank insulation

Liquid hydrogen (LH₂) storage has the advantage of high volumetric energy density, while boil-off losses constitute a major disadvantage. To minimize the losses, complicated insulation techniques are necessary. In general, Multi Layer Insulation (MLI) and a Vapor-Cooled Shield (VCS) are used together in LH₂ tanks. In the design of an LH₂ tank with VCS, the main goal is to find the optimum location for the VCS in order to minimize heat leakage. In this study, a 2D thermal model is developed by considering the temperature dependencies of the thermal conductivity and heat capacity of hydrogen gas. The developed model is used to analyze the effects of model considerations on heat leakage predictions. Furthermore, heat leakage in insulation of LH₂ tanks with single and double VCS is analyzed for an automobile application, and the optimum locations of the VCS for minimization of heat leakage are determined for both cases.     

High heat flux point source sensitivity and localization analysis for an ultrasonic sensor array

State estimation procedures using the extended Kalman filter are investigated for a transient heat transfer problem in which a high heat flux point source is applied on one side of a thin plate and ultrasonic pulse time of flight is measured between spatially separated transducers on the opposite side of the plate. This work is an integral part of an effort to develop a system capable of locating the boundary layer transition region on a hypersonic vehicle aeroshell. Results from thermal conduction experiments involving one-way ultrasonic pulse time of flight measurements are presented. Uncertainties in the experiments and sensitivity to heating source location are discussed. One key finding is that sensitivity to heating source location is greater in the direction normal to the ultrasonic pulse propagation path. Scaled sensitivities to boundary conditions and thermal conductivity are presented and analyzed for all possible source locations using a square sensor grid. While sensitivity to the primary heat flux was determined to be the highest, sensitivity to the other parameters is either on the same order of magnitude or one order of magnitude less. Two different measurement models are compared for heating source localization: (1) directly using the one-way ultrasonic pulse time of flight as the measurement vector and (2) indirectly obtaining distance from the one-way ultrasonic pulse time of flight and then using these obtained distances as the measurement vector in the extended Kalman filter. Heating source localization results and convergence behavior are compared for the two measurement models. Two areas of sensitivity analyses are presented: (1) heat source location relative to sensor array position, and (2) sensor noise. The direct measurement model produced the best results when considering accuracy of converged solution, ability to converge to the correct solution given different initial guesses, and smoothness of convergence behavior.     

Prediction of soil thermal conductivity based on penetration resistance and water content or air-filled porosity

Accurate data of thermal conductivity are required in many agricultural, meteorological and engineering applications. New regression equations for predicting thermal conductivity based on easily measured quantities such as penetration resistance and water content or air-filled porosity are presented. The thermal conductivities from the equations are compared with those from a statistical-physical model of a good estimation capability. The measurements of the quantities were done on silt loam in a sloping vineyard (Italy) at various times and locations to get a wide range of measured values. It is shown that the performance of the equations relating the thermal conductivity with penetration resistance and air-filled porosity is greater (R² = 0.94) than with penetration resistance and volumetric water content (R² = 0.77). Therefore, the equations based on measured penetration resistance and air-filled porosity are recommended for predicting the thermal conductivity of the soil. Adding sand content and transformation of strength values to root squares somewhat improved the predictions. To minimize the effects of spatial variability of the measured quantities on the thermal conductivity and to reduce measurement time and soil disturbance, systems for combined measurements of penetration resistance and water content at the same place need to be used in further studies.     

Engineering improvement of NaAlH4 system

The significant engineering challenges associated with developing lower-pressure, materials-based, hydrogen storage systems for hydrogen fuel cell light-duty vehicles are being addressed by focusing on the role that powder consolidation can play. NaAlH₄ with 4 mol % TiCl₃ was selected as the model material. We focused on the changes in the physical (density and thermal conductivity) and mechanical properties (biaxial flexure strength) and on how these impacted the volumetric capacity of the hydrogen storage system. Both the thermal conductivity and the density of the ball milled material improved with applied pressure in a uniaxial press over the range of 14 MPa–281 MPa. The thermal conductivity reached a value of (1.64 ± 0.02) W/m/K, which was a factor seven higher than that of the unconsolidated powder. The volume of the material was reduced by 42% at the highest applied pressure. A method was developed for determining the strength of NaAlH₄ pellets before and after hydrogen absorption and desorption cycles. It is based on a biaxial flexure test that was originally designed for determining the strength of green ceramic materials. The tests showed that the pellets were strong with biaxial flexure strength of 1.4 kpsi which was unaltered over three studied hydrogen absorption/desorption cycles. The increased materials density did not affect the hydrogen absorption and desorption kinetics, which is important in order to benefit from the improved volumetric capacity. The new material properties of the compacted NaAlH₄ were used in finite element modeling of a hydrogen storage system that targeted a fast refueling time. The results clearly show an improvement of the volumetric capacity of the system by powder consolidation but the gravimetric capacity remains below target, as expected. A system level study of a light-duty vehicle with such a hydrogen storage system is required in order to determine whether the amount of hydrogen stored in the pore volume of the sodium alanate will still be enough to enable one cold start from room temperature to its operating temperature (120–140 °C) or that a buffer volume needs to be installed. While it is recognized that a sodium alanate based hydrogen storage system has its limitations, it has been demonstrated that powder consolidation can address some of those limitations by improving the thermal conductivity and volumetric capacity.     

Determination of the thermal transport properties of ammonia borane and its thermolysis product (polyiminoborane) using the transient plane source technique

Reliable thermal property data are necessary to improve the fidelity of chemical hydride thermal decomposition models. The thermal diffusivity and conductivity of ammonia borane (NH₃BH₃) and its partial thermolysis product (polyiminoborane) were measured at various packing densities using a transient plane source technique under ambient conditions. The particle size of the ammonia borane powder was between 200 and 600 μm, while the particle size of the polyiminoborane powder was between 10 and 30 μm. The thermal diffusivity and conductivity of the ammonia borane increased from 0.17 to 0.24 mm²/s and 0.19 to 0.44 W/m K (±10%), respectively, when its packing density was increased from 0.37 to 0.58 g/cm³. The increase in thermal conductivity is due to the increase in contact area between particles and the increase in the thermal diffusivity is related to an increase in density and volumetric heat capacity caused by compaction. The thermal conductivity of the polyiminoborane powder was approximately three times lower, likely due to its higher porosity. The thermal diffusivity and conductivity of this product changed from 0.21 to 0.12 mm²/s and 0.068 to 0.23 W/m K (±10%), respectively, when its packing density was increased from 0.13 to 0.96 g/cm³.     

Controlled degradation of highly compacted sodium alanate pellets

Compaction of sodium alanate doped with 3 mol% titanium chloride (TiCl₃) into rigid cylindrical pellets improves thermal conductivity, density and volumetric hydrogen capacity of a traditionally poorly conductive material. However, hydrogen cycling of alanate pellets results in significant expansion which counteracts the advantages of compaction. Restricting the area in which pellets can expand into minimizes these losses with no adverse effect to cycling capacity. Confined pellets had a 50% less decrease in density over 30 cycles, 5 times greater thermal conductivity within 10 cycles and maintain structural integrity through 50 cycles compared to free pellets. In addition, pellets within mechanical confinement fused into a rigid stack within the first few hydrogen cycles thereby reducing surface contact resistance between pellets by 3.5 times. Improved thermal conductivity and heat transfer through a pellet bed of materials such as complex metal hydrides, is a key aspect for on-board storage applications.     

An analysis of the characteristics of the thermal boundary layer in power law fluid

This paper presents a theoretical analysis of the heat transfer for the boundary layer flow on a continuous moving surface in power law fluid. The expressions of the thermal boundary layer thickness with the different heat conductivity coefficients are obtained according to the theory of the dimensional analysis of fluid dynamics and heat transfer. And the numerical results of CFD agree well with the proposed expressions. The estimate formulas can be successfully applied to giving the thermal boundary layer thickness.     

Prediction of thermal conductivity of ethylene glycol–water solutions by using artificial neural networks

The objective of this study is to develop an artificial neural network (ANN) model to predict the thermal conductivity of ethylene glycol–water solutions based on experimentally measured variables. The thermal conductivity of solutions at different concentrations and various temperatures was measured using the cylindrical cell method that physical properties of the solution are being determined fills the annular space between two concentric cylinders. During the experiment, heat flows in the radial direction outwards through the test liquid filled in the annual gap to cooling water. In the steady state, conduction inside the cell was described by the Fourier equation in cylindrical coordinates, with boundary conditions corresponding to heat transfer between the solution and cooling water. The performance of ANN was evaluated by a regression analysis between the predicted and the experimental values. The ANN predictions yield R² in the range of 0.9999 and MAPE in the range of 0.7984% for the test data set. The regression analysis indicated that the ANN model can successfully be used for the prediction of the thermal conductivity of ethylene glycol–water solutions with a high degree of accuracy.     

Effect of electroplating on the thermal conductance of fin–tube interface

This paper presents the experimental results of thermal contact conductance, heat transfer and interfacial temperature drop of finned tube heat exchanger test specimens. The results were based on the measured temperatures at several locations on the test specimen so that the thermal contact conductance could be directly determined. Each test specimen was assembled by mechanically expanding seven tubes into a single fin. The geometry of the specimens was based on a commonly used model of heat exchangers. The specimens included one bare tube (non-coated) specimen and four electroplated tube specimens. The plating metals were zinc, tin, silver and gold. The thickness of the plating in each case was 5 μm.Experiments have been conducted in both vacuum and nitrogen. Maximum enhancement was obtained when the tube was coated with tin. This indicates that, although the thermal conductivity is important, the softness of the plating material also plays an important role in enhancing the thermal conductance of the interface. The presence of an interstitial gas such as nitrogen is beneficial for the heat transfer and the thermal contact conductance. It is also noted that the interfacial temperature drop alone does not fully reflect the efficiency of the heat exchanger.     

Study on the efficiency of effective thermal conductivities on melting characteristics of latent heat storage capsules

Improvement of the thermal conductivity of a phase change materials (PCM) is one effective technique to reduce phase change time in latent heat storage technology. Thermal conductivity is improved by saturating porous metals with phase change materials. The influence of effective thermal conductivity on melting time is studied by analyzing melting characteristics of a heat storage circular capsule in which porous metal saturated with PCM is inserted. Numerical and approximate analyses were made under conditions where there are uniform or non-uniform heat transfer coefficients around the cylindrical surface. Four PCMs (H₂O, octadecane, Li₂CO₃, NaCl) and three metals (copper, aluminum and carbon steel) were selected as specific materials. Porosities of the metals were restricted to be larger than 0.9 in order to keep high capacity of latent heat storage. Results show that considerable reduction in melting time was obtained, especially for low conductivity PCMs and for high heat transfer coefficient. Melting time obtained by approximate analysis agrees well with numerical analysis. A trial estimation of optimum porosity is made balancing the desirable conditions of high latent heat capacity and reduction of melting time. Optimum porosity decreases with increase in heat transfer coefficient.     

Determining boundary heat flux profiles in an enclosure containing solid conducting block

A numerical implementation of estimating boundary heat fluxes in enclosures is proposed in the present work. Particularly, the flow field is dynamically coupled with the heat convection in the fluid and the heat conduction in the solid domain. An iterative conjugate gradient method is applied such that the gradient of the cost function is introduced when the appropriate sensitivity and adjoint problems are defined. In this approach, no a priori information is needed about the unknown function to be determined. Numerical solutions are obtained for the case of a square enclosure centrally-inserted with a solid block and subjected to an unknown heat flux on one side and to known conditions on the remaining sides. Fluid and heat transports are visualized by the streamlines and heatlines respectively, which are evidently affected by the thermal Rayleigh number, solid body size and thermal conductivity of solid phase, and the functional form of the imposed heat flux. The accuracy of the heat flux profile estimations is shown to depend strongly on the thermal Rayleigh number, body size and relative thermal conductivity of the solid material. Effects of functional form of the unknowns, sensors number and position, and measurement errors on the accuracy of estimation are also investigated. The present work is significant for the flow control simultaneously involving the heat conduction and convection.     

Improved PV/T solar collectors with heat extraction by forced or natural air circulation

The photovoltaic (PV) cells suffer efficiency drop as their operating temperature increases especially under high insolation levels and cooling is beneficial. Air-cooling, either by forced or natural flow, presents a non-expensive and simple method of PV cooling and the solar preheated air could be utilized in built, industrial and agricultural sectors. However, systems with heat extraction by air circulation are limited in their thermal performance due to the low density, the small volumetric heat capacity and the small thermal conductivity of air and measures for heat transfer augmentation is necessary. This paper presents the use of a suspended thin flat metallic sheet at the middle or fins at the back wall of an air duct as heat transfer augmentations in an air-cooled photovoltaic/thermal (PV/T) solar collector to improve its overall performance. The steady-state thermal efficiencies of the modified systems are compared with those of typical PV/T air system. Daily temperature profiles of the outlet air, the PV rear surface and channel back wall are presented confirming the contribution of the modifications in increasing system electrical and thermal outputs. These techniques are anticipated to contribute towards wider applications of PV systems due to the increased overall efficiency.     

Estimation of parameters in multi-mode heat transfer problems using Bayesian inference – Effect of noise and a priori

Parameter estimation problems and heat source/flux reconstruction problems are some of the most frequently encountered inverse heat transfer problems. These problems find their application in many areas of science and engineering. The primary focus of this paper is on the heat transfer parameter estimation for a two-dimensional unsteady heat conduction problem with (a) convection boundary condition and (b) convection and radiation boundary condition. The paper demonstrates the effect of a priori model on the performance of the algorithm at different noise levels in the measured data. The inverse problem is solved using three different a priori models namely normal, log normal and uniform. The posterior PDF is sampled using the Metropolis–Hastings sampling algorithm. Both single-parameter estimation and multi-parameter estimation problems are addressed and the effects of corresponding a priori models are studied. It was found that the mean and maximum a posteriori estimates for thermal conductivity and the convection heat transfer coefficient were insensitive to the a priori model at all the considered noise levels for the single-parameter estimation problem. At high noise levels in the two-parameter estimation problem, the estimates for thermal conductivity and convection coefficient were sensitive to the a priori model. It was also found that the standard deviation of the samples was correlated to the error in estimation in the single-parameter estimation case. In three parameter estimation case, alternate solutions to the same problem were retrieved due to a strong correlation between the convection coefficient and the emissivity. However, a more informative a priori model could address this issue.     

Thermal management of electronic components with thermal adaptation composite material

Thermal adaptation composite material is a kind of composite material with required thermal conductivity or coefficient of thermal expansion through the selection and design of its components. A kind of thermal adaptation composite material that has excellent thermal conductivity and heat storage capacity is prepared by absorbing paraffin into expanded graphite. An electronic cooling experimental system based on the thermal adaptation composite material is built. The temperature variations of the simulative chip are respectively measured in this system and the traditional cooling system to investigate the effect of the thermal adaptation composite material on electronic cooling. At the same time, the impacts of composite material dosage and combining active cooling manner on the performance of electronic cooling are also studied. The experimental results show that the apparent heat transfer coefficients of the electronic cooling experimental system are 1.25–1.30 times higher than those of the traditional cooling system. It also can be found that the dosage of composite material has positive impact on the performance of electronic cooling. By combining active cooling manner, it can compensate the deficiency of cooling capacity in phase change thermal control.     

A review of nanofluid preparation,stability, and thermo‐physical properties

This paper represents a comprehensive review on the preparation and stability of nanofluid, the convective heat transfer coefficient and different thermo‐physical properties such as thermal conductivity, specific heat capacity, viscosity, and so on. Here, for each thermo‐physical property, measurement methods, enhancement mechanisms, and criticisms of different studies are also presented. However, based on the available literature, it is concluded that a nanofluid has, in general, better thermo‐physical properties even at a very low particle concentration (typically 1% or less) than conventional heat transfer fluids. The only drawback is high viscosity which leads to a higher pressure drop. At a very low particle concentration, this drawback can be minimized. Three tables are provided for three thermo‐physical properties namely thermal conductivity, specific heat capacity, and viscosity, which can be used as a ready reference for calculating the nanofluid properties.