Faculty Publications
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Item MCMC and approximation error model for the simultaneous estimation of heat flux and heat transfer coefficient using heat transfer experiments(Begell House Inc., 2018) Gnanasekaran, N.; Kumar, M.K.; Balaji, C.This work deals with the simultaneous estimation of the heat flux and the heat transfer coefficient from a mild steel fin losing heat to the ambient by natural convection. Steady state heat transfer experiments are performed on a mild steel fin of dimension 150x250x6 (all dimensions are in mm) placed on to an aluminum base plate of dimension 150x250x8 (all dimensions are in mm). The experimental set up is placed inside a large enclosure to avoid natural disturbances. Nine calibrated K-type thermocouples are used to measure the temperatures of the fin and the base plate. The forward solution of a three dimensional conjugate heat transfer fin model is solved using commercially available ANSYS software in order to obtain the temperature distribution of the fin. An inverse problem is proposed for the estimation of unknown parameters within the Bayesian framework of statistics. Furthermore, a model reduction in the form of Approximation Error Model (AEM) is considered for the inverse conjugate natural convection heat transfer problem. Such an approach not only mitigates the complexity of the inverse problem but also compensates the model reduction with all necessary statistical parameters. Additionally, the sample space within the Bayesian framework is explored with the help of Markov Chain Monte Carlo Method (MCMC) along with the Metropolis-Hastings algorithm. The results of the inverse estimation using Approximation Error Model based on the experimental temperature prove to be a promising alternative in inverse conjugate heat transfer problems. © 2018 International Heat Transfer Conference. All rights reserved.Item Computation of error model for the inverse bioheat transfer problem(Dalian University of Technology, 2018) Gnanasekaran, N.; Vishweshwara, P.S.An inverse estimation of size and location of tumor is proposed in this paper using Bayesian framework. The forward model comprises of the Pennes equation and solved using commercial software. The forward solution of the problem is validated against the available literature and the results are found to be promising. Estimation of the size and location of the tumor is attempted based on Bayesian framework along with the Markov chain Monte Carlo method. This paper also demonstrates 2D and 3D modelling of the cancerous tissue and exploits the advantage of 2D model in the computation of MCMC method. An Approximation Error Model (AEM) is proposed in order to statistically account the model error during the estimation of the unknown parameters. The results of the AEM provide a new trend in the parametric study of cancerous tissue. © 2018 by the authors of the abstracts.Item Inverse approach for estimating boundary properties in a transient fin problem(Springer, 2018) Gnanasekaran, N.; Balaji, S.A solution methodology is proposed for an inverse estimation of boundary conditions from the knowledge of transient temperature data. A forward model based on prevalent time-dependent heat conduction fin equation is solved using a fully implicit finite volume method. First, the inverse model is formulated and accomplished for time-invariant heat flux at the fin base, and later extended to transient heat flux, base temperature and average heat transfer coefficient. Secondly, the Nusselt number is then replaced with Rayleigh number in the forward model to realistically estimate the base temperature, which varies with respect to time, based on in-house transient fin heat transfer experiments. This scenario further corroborates the validation of the proposed inverse approach. The experimental set-up consists of a mild steel 250×150×6mm3 fin mounted centrally on an aluminium base 250×150×8mm3 plate. The base is attached to an electrical heater and insulated with glass-wool to prevent heat loss to surroundings. Five calibrated K-type thermocouples are used to measure temperature along the fin. The functional form of the unknown parameters is not known beforehand; sensitivity studies are performed to determine suitability of the estimation and location of sensors for the inverse approach. Conjugate gradient method with adjoint equation is chosen as the inverse technique and the study is performed as a numerical optimization; subsequently, the estimates show satisfactory results. © 2018, Indian Academy of Sciences.Item A combined ANN-GA and experimental based technique for the estimation of the unknown heat flux for a conjugate heat transfer problem(Springer Verlag service@springer.de, 2018) Kumar, M.K.; Vishweshwara, P.S.; Gnanasekaran, N.; Balaji, C.The major objectives in the design of thermal systems are obtaining the information about thermophysical, transport and boundary properties. The main purpose of this paper is to estimate the unknown heat flux at the surface of a solid body. A constant area mild steel fin is considered and the base is subjected to constant heat flux. During heating, natural convection heat transfer occurs from the fin to ambient. The direct solution, which is the forward problem, is developed as a conjugate heat transfer problem from the fin and the steady state temperature distribution is recorded for any assumed heat flux. In order to model the natural convection heat transfer from the fin, an extended domain is created near the fin geometry and air is specified as a fluid medium and Navier Stokes equation is solved by incorporating the Boussinesq approximation. The computational time involved in executing the forward model is then reduced by developing a neural network (NN) between heat flux values and temperatures based on back propagation algorithm. The conjugate heat transfer NN model is now coupled with Genetic algorithm (GA) for the solution of the inverse problem. Initially, GA is applied to the pure surrogate data, the results are then used as input to the Levenberg- Marquardt method and such hybridization is proven to result in accurate estimation of the unknown heat flux. The hybrid method is then applied for the experimental temperature to estimate the unknown heat flux. A satisfactory agreement between the estimated and actual heat flux is achieved by incorporating the hybrid method. © 2018, Springer-Verlag GmbH Germany, part of Springer Nature.Item Evaluation of artificial neural network in data reduction for a natural convection conjugate heat transfer problem in an inverse approach: experiments combined with CFD solutions(Springer, 2020) Kumar, M.K.H.; Vishweshwara, P.S.; Gnanasekaran, N.In this work, natural convection fin experiments are performed with mild steel as the fin and an aluminium plate as base. The dimension of the mild steel fin is 250 mm × 150 mm × 6 mm and the aluminium base plate is 250 mm × 150 mm × 8 mm. A heater is provided on one side of the aluminium base plate and the mild steel fin emerges on the other side of the plate. The heater provides required heat flux to the fin base; several steady-state natural convection experiments are performed for different heat fluxes and corresponding temperature distributions are recorded using thermocouples at different locations of the fin. In addition, a numerical model is developed that contains the dimensions of the fin set-up along with extended domain to capture the information of the fluid. Air is treated as a working fluid that enters the extended domain and absorbs heat from the heated fin. The temperature and the velocity of the fluid in the extended domain are obtained by solving the Navier–Stokes equation. The numerical model is now treated as a forward model that provides the temperature distribution of the fin for a given heat flux. An inverse problem is proposed to determine the heat flux that leads to the temperature distributions during experiments. The temperature distributions of the experiments and forward model are compared to identify the unknown heat flux. In order to reduce computational cost of the inverse problem the forward model is then replaced with artificial neural network (ANN) as data reduction, which is developed using several computational fluid dynamics solutions, and the inverse estimation is accomplished. The results indicate that a quick solution can be obtained using ANN with a limited number of experiments. © 2020, Indian Academy of Sciences.