Vellore Institute of Technology (VIT) is a private university located in&nbsp;Tamil Nadu, India. Founded in 1984, as Vellore Engineering College, the institution offers 20 undergraduate, 34 postgraduate, four integrated and four research programs. It has campuses in Vellore, Amravati, Bhopal and Chennai.

VIT is one of the top ranked private universities in India according to NIRF, THE and QS Rankings.&nbsp;Govt. of India has recognized&nbsp;VIT, Vellore as an&nbsp;Institution of Eminence. This has allowed VIT to take independent quality initiatives and move up in world ranking.

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VIT University

This article deals with estimation of spatially distributed thermal properties of two-dimensional heterogeneous media from the solution of inverse heat conduction problem. The experimental procedure involves sequential heating of sample at four discrete locations on one side and recording transient temperature on the other side non-intrusively. The inverse problem formulation is carried out as parameter estimation problem and the unknown parameters are estimated through minimization of sum of squared error between measured and simulated temperatures using Levenberg–Marquardt algorithm. The huge computational time required to calculate sensitivity matrix is reduced through parallel computation strategy. Numerical estimations are carried out with synthetic temperature and it is found that the resolution and accuracy of estimated spatially distributed thermal conductivity is in better agreement with the exact distribution when compared to volumetric heat capacity even at an error level of ± 0.1 K. Transient temperature response of the fabricated heterogeneous prototype is recorded using infrared radiation camera and the same is used for estimation of unknown parameters. The estimated thermal conductivity closely mimics the actual distribution. Therefore, this simple proposed method can be directly used in thermal tomography applications for identifying the shape and size of inclusions/inhomogeneities from the estimated thermal conductivity distribution alone. © 2019 Taylor & Francis Group, LLC.

Department of Thermal and Energy Engineering

School of Mechanical Engineering

Vellore Campus

World University root node

Heat Transfer Engineering

Estimation of Spatially Distributed Thermal Properties of Heterogeneous Media with Non-Intrusive Measurement

In the present article, a novel experimental methodology is proposed for the simultaneous estimation of unknown thermal conductivity (k) and specific heat capacity (cp) of engineering materials. The experimental method involves radiative heating of the test sample and measuring its temperature response at two different locations. Proper arrangements have been made to realize one-dimensional heat conduction within the test sample. The one-dimensional heat conduction equation with convection-radiation heat loss boundary condition is considered as the forward model as it best mimics the experimental heat transfer. The inverse problem is formulated as a parameter estimation problem, and solved using Levenberg-Marquardt algorithm. First, numerical estimations were carried out with synthetic temperature data. It was found that the time-dependent heat flux boundary condition is more suitable to estimate the properties of higher thermal conductivity materials. Then, real-time temperature measurements were carried out on Stainless Steel (SS), Mild Steel (MS), Brass (BS), Aluminium (Al), and Copper (Cu) test samples. The estimated k of SS, MS, BS, Al, and Cu in (W/(m K)) is 14.03, 54.63, 103.21, 221.53 and 379.89, respectively. And, the estimated cp of SS, MS, BS, Al, and Cu in (J/(kg K)) is 500.44, 460.84, 395.01, 939.58, and 398.43 respectively. The estimated thermal properties are also validated against experimentally measured values obtained using the Modified Transient Plane Source (MTPS) sensor. It was found that the estimated k and cp in case of SS has a deviation of 7% and 4%, respectively. © 2020 Elsevier Ltd

Thermal Science and Engineering Progress

Development of experimental methodology for estimation of thermo-physical properties of engineering materials using inverse method

In this article, an inverse analysis for simultaneous estimation of temperature dependent thermal conductivity (k(T)) and specific heat capacity (Cp(T)) of isotropic solids is presented. The unknown thermal properties are assumed a parametric variation with temperature and these parameters are then estimated from the solution of inverse problem. Pseudo-experimental temperature data are used to study the robustness of the present inverse parameter estimation solution strategy. Due to lack of sensitivity and existence of correlation among the unknown parameters, the solution to inverse problem is carried out with Levenberg–Marquardt, Genetic Algorithm (GA) and hybrid GA and it is found that hybrid GA is more suitable for this parameter estimation problem. The proposed inverse approach is also extended to real-time experiments involving heating of mild steel (MS) and stainless steel (SS304) samples with concentrated solar thermal energy source. The estimated constant k and Cp for MS are found to be 52.6 W/m-K and 507.24 J/kg-K respectively which are within 10% deviation from the literature data. Similarly, the estimated k and Cp of SS304 at 360 K are found to be 16.75 W/m-K and 512.7 J/kg-K with an absolute deviation of 6% and 4% respectively from literature data. © 2020 Elsevier Ltd

Inverse analysis for simultaneous estimation of temperature dependent thermal properties of isotropic materials

The knowledge of heat flux distribution on the receiver area is very important to improve the overall performance of the solar Concentrating Photovoltaic (CPV) system. In a CPV system, non-uniform flux distribution is one of the common issues. Non-uniform illumination of heat flux is mainly due to the limitations in the design of concentrator optics, slope error in the concentrator profile, tracking system error, misalignment of concentrator, and the efficiency of refractive lens/reflecting mirrors. The prediction of the heat flux distribution will play a vital role in the CPV system such as designing the receiver area, selection of the materials, thermal management and to estimate the power output. In this paper, an experimental work for in-situ prediction of heat flux distribution profile on a flat plate receiver is presented. Inverse heat transfer technique is adopted to predict the heat flux distribution. A Gaussian distribution is assumed to model the distribution of the heat flux. The forward problem is a 3-D steady state heat conduction equation subjected to convection and radiation heat loss boundary conditions. The forward problem is solved using Finite Element Method in Ansys APDL. The unknown parameters of the assumed heat flux distribution are then estimated by minimizing the sum of squared error between measured and simulated temperature distribution. A deterministic search technique, Levenberg-Marquardt algorithm is used to solve the inverse problem. The simulated temperature distribution with the predicted heat flux are in good agreement with the measured temperature with a maximum residue of ±5 °C. Also, the deviation between theoretical and predicted total solar energy is found to be <6%. © 2017 Elsevier Ltd

Solar Energy

In-situ prediction of focal flux distribution for concentrating photovoltaic (CPV) system using inverse heat transfer technique for effective design of receiver

This article presents a simple in-house laboratory experiment method for the simultaneous estimation of principal thermal conductivity and specific heat capacity of an orthotropic composite with non-intrusive temperature measurement. The principle of method involves in symmetrical heating of two identical samples with a planar heater sandwiched in-between them and measuring the temperature of non-heated surface non-intrusively using IR camera. The forward problem that mimics the heat conduction from heater to sample and then to ambient is a 3-D transient conduction equation which is solved using finite volume method whereas inverse problem is solved using Levenberg-Marquardt algorithm. At first numerical estimations are carried out with synthetic temperature data to decide upon the parameters to be identified/fixed as well as to find optimal experimental variables. Then, using measured temperature response of the non-heated surface, the thermal properties of unidirectional fiber reinforced carbon composite are estimated. Induced bias errors in the estimated parameters because of error in the fixed parameters are also approximately quantified. The estimated transverse thermal conductivity is found to be 0.72 W/m K whereas the in-plane conductivities parallel and perpendicular to fiber are 5.43 W/m K, 0.64 W/m K respectively. Also, the estimated specific heat capacity is found to be 1044 J/kg K. A maximum deviation of 10% from the absolute Guarded Hot Plate measurement is found in the estimated thermal conductivity parallel to fiber. © 2018 Elsevier Ltd

International Journal of Heat and Mass Transfer

Simultaneous estimation of thermal properties of orthotropic material with non-intrusive measurement

In this article, three different thermal properties such as thermal conductivity, heat transfer coefficient and emissivity are retrieved simultaneously using Bayesian inverse framework. Metropolis–Hasting Markov Chain Monte-Carlo (MH-MCMC) sampling is more commonly used in the literature to sample through posterior probability distribution function (PPDF) to find the expectations such as mean, standard deviation. However, when the posterior is multi-model/correlated, sometimes MH-MCMC struck with one mode and fails to sample through other modes which have significant probability. Nevertheless, efficient sampling techniques are being developed during the last decade to overcome this problem. Therefore, in the present work two population-based sampling techniques such as Parallel Tempering (PT) and Evolutionary Monte-Carlo (EMC) are used along with MH-MCMC to sample through correlated PPDF to retrieve the above three thermal properties. The estimation is carried out at three levels of measurement errors. The experimental data are obtained by adding normally distributed random noise with mean at zero and standard deviation ‘σexp’ to the exact solution of the forward problem. The results show that when the measurement error is zero, i.e when σexp = 0.01 , all three techniques perform well and estimates the parameter reasonably good. However, at σexp = 0.01 and 0.5, MCMC estimates the parameter poorly, whereas both PT and EMC performs equally and estimates the parameter within a maximum of 9% deviation from the exact value. © 2016 Informa UK Limited, trading as Taylor & Francis Group.

Inverse Problems in Science and Engineering

Inverse estimation of thermal properties using Bayesian inference and three different sampling techniques

One approach in statistical analysis that distinguishes between frequentist and Bayesian is the inclusion of available prior information about the data even before measuring/surveying the data. Many researchers argued that the inclusion of prior information resulted in a better model prediction/parameter estimation. Bayesian inference is repeatedly used in inverse problems to retrieve parameters due to the development of high efficient sampling algorithms such as Markov Chain Monte-Carlo (MCMC). Inverse problems are generally ill-posed in nature. Nevertheless, the inclusion of prior information reduces the ill-posedness of the problem to an extent. Any inverse problem relies on measured data by physical sensors, therefore induced random errors greatly affects the quality of estimation. When the uncertainty of the measured data is high, the inferences made from the resulting sampling distributions are nearly the same as the supplied prior information. The reason is that, probability of samples nearer to prior information is more at higher uncertainties of measurement and has more chance to get repeatedly accepted than the samples that are close to actual value. Therefore, in this work an effort is made to update the prior hyper parameters in each iterations of the MCMC algorithm based on the history of the likelihood function. The applicability of method is demonstrated by retrieving parameters from 1-D fin experiment. Three thermal properties such as thermal conductivity, heat transfer coefficient and emissivity are retrieved simultaneously. The estimation is carried out for both error and errorless temperature measurements and the results show that, the estimated parameters with the proposed method are in excellent agreement with the true parameter value and a maximum of 7% deviation occurs in estimating heat transfer coefficient at a measurement error of ±0.3K.

ECCOMAS Congress 2016 - Proceedings of the 7th European Congress on Computational Methods in Applied Sciences and Engineering

Updating prior parameters based on likelihood Function-Bayesian method for parameter estimation at high measurement uncertainty

In this work, inverse heat conduction problem (IHCP) involving the simultaneous estimation of principal thermal conductivities (kXX,kyy,kzz ) and specific heat capacity of orthotropic materials is solved by using surrogate forward model. Uniformly distributed random samples for each unknown parameter is generated from the prior knowledge about these parameters and Finite Volume Method (FVM) is employed to solve the forward problem for temperature distribution with space and time. A supervised machine learning technique- Gaussian Process Regression (GPR) is used to construct the surrogate forward model with the available temperature solution and randomly generated unknown parameter data. The statistical and machine learning toolbox available in MATLAB R2015b is used for this purpose. The robustness of the surrogate model constructed using GPR is examined by carrying out the parameter estimation for 100 new randomly generated test samples at a measurement error of ±0.3K. The temperature measurement is obtained by adding random noise with the mean at zero and known standard deviation (σ = 0.1) to the FVM solution of the forward problem. The test results show that Mean Percentage Deviation (MPD) of all test samples for all parameters is &lt; 10%. © Published under licence by IOP Publishing Ltd.