Development of an efficient model for inverse conjugate heat transfer problems

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DEVELOPMENT OF AN EFFICIENT MODEL FOR INVERSE CONJUGATE HEAT TRANSFER

PROBLEMS

by

AJIT KUMAR PARWANI Department of Mechanical Engineering

Submitted

In fulfillment of the requirements of the degree of DOCTOR OF PHILOSOPHY

to the

INDIAN INSTITUTE OF TECHNOLOGY DELHI

JULY 2013

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Dedicated to my late father Shri D.R. Parwani.

His words of inspiration and encouragement

in pursuit of excellence, still linger on.

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CERTIFICATE

The thesis entitled DEVELOPMENT OF AN EFFICIENT MODEL FOR

INVERSE CONJUGATE HEAT TRANSFER PROBLEMS being submitted by Mr. Ajit Kumar Parwani to the Indian Institute of Technology Delhi for award of the degree of Doctor of Philosophy is a record of original bonafide research work carried out by him. He has worked under our guidance and supervision, and has fulfilled the requirements for the submission of this thesis, which has attained the standard required for a Ph.D. degree of this Institute.

The results represented in this thesis have not been submitted elsewhere for the award of any degree or diploma.

Dr. Prabal Talukdar Dr. P. M. V. Subbarao

Associate Professor, Professor,

Dept. of Mechanical Engineering Dept. of Mechanical Engineering

Indian Institute of Technology Indian Institute of Technology

Delhi Delhi

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ACKNOWLEDGEMENTS

One of the joys of completion is to look over the journey of past years and remember all those who have helped and supported me along this long but fulfilling road.

Throughout these years, I have received a lot of support from my family, supervisors and friends. Indeed, my doctoral thesis is a dream of my late father Shri D.R. Parwani coming true and I am sure he would be the most happiest and proud person for my title of PhD.

I have been very fortunate with my supervisors Dr. Prabal Talukdar and Professor P.M.V. Subbarao. I could not have asked for better role models. Dr. Prabal Talukdar is a young, dynamic and a great researcher in computational heat transfer. He always encouraged and motivated me to write the outcomes into publications. Professor P.M.V. Subbarao is very strong in the fundamentals of engineering and his high scientific standards set an example. He helped and guided me for conducting the experiments on wind tunnel. I would like to thank to my both supervisors for bearing my mistakes and correcting them time and again with patience.

I wish to thank the entire faculty of Mechanical Engineering Department, Indian Institute of Technology (IIT), Delhi for the enormous amount that I learned from them.

Special thanks to my research committee members Professor Anjan Ray, Dr. B.

Premachandran and Professor Anupam Dewan who provided encouraging and constructive feedback. I would also thank to the many anonymous reviewers of my publications for helping to shape and guide the direction of the work with careful and instructive comments.

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I am very thankful to the Refrigeration and Air Conditioning lab staff Mr. Prem Singh and Mr. Shambhu Prasad for their constant help throughout this research work. I am also indebted to my colleagues and friends I had the pleasure to work with. They have been an invaluable support day in, day out, during all these years. Special thanks to Dr. V.P. Chandra Mohan, Mr. Vinayak Hemadri, Mr. Naveen Jina, Mr. Abhinav Bhadauria, Mr. Bappi, Mr. Rinku, Mr. Udayraj, Mr. Vipul and Mr. Raj Kumar.

I truly acknowledge to my wife Mansi Parwani, for her love, comprehension and allowed me to spend most of the time on this thesis and to my daughter Alisha, for her smiles that made me to forget much tougher situations. My great and lovely mother, I really don‟t want to say „thanks‟ to her because it never expresses my feeling for her;

I just simply wish her to be with me and the rest of the family healthier and happier ever. I also want to thank to my sisters and family; Mr. and Mrs. Damani, Mr. and Mrs.

Raichandani and to my parent in-law Mr. and Mrs. Bharwani for their unconditional support.

I gratefully acknowledge the funding sources from IIT, Delhi and SERC division of Department of Science and Technology, Government of India that made my Ph.D. work possible. The funding has also enabled me to attend various well-situated conferences including my first ever foreign visit to Poland, where I could exchange research results and ideas with numerous interesting colleagues from all around the world.

At the end, I thank the Lord Ganesha for showering me blessings and moral strength to carry out my work without which I would not have done it.

Ajit Kumar Parwani July 2013

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ABSTRACT

The motivation for applying an inverse technique may be manifold. Sometimes, especially in the field of thermal engineering, one wants to calculate the temperature or heat flux on the surface of a body or boundary of the flowing medium. However, it may be the case that the surface for some reason is inaccessible to direct measurements with the aid of some measurement device. Sometimes though, these kinds of devices may be an inappropriate choice. It could be the case that the installation of any such device may disturb the experiment or the conditions at the surface are very extreme (like reentry of space vehicle into the atmosphere) such that the installation of the devices if not impossible but could be difficult. In these situations one is directed to using an inverse method based on interior measurements in the body, and in which the desired temperature or heat flux is calculated by a numerical procedure.

Because of the ill-posed nature of inverse heat transfer problems, solutions of these types of problems are always difficult. The conjugate gradient method (CGM) is extensively used in the literature because of its fast convergence. However, there are limitations with CGM like inability to handle discontinuity, inability of prediction at the final time step etc. The additional complexity with the CGM is that its formulation changes with every problem. In the recent time stochastic methods (genetic algorithm, particle swam optimization technique, differential evolution algorithm etc.) are gaining popularity because of their simplicity of implementation. However, these methods are not fully implemented for different class of inverse heat transfer problems. The implementation of these methods and their comparison with the deterministic methods like CGM is necessary to examine the pros and cons of these methods. The present thesis considers differential evolution algorithm to examine its applicability and

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performance in comparison to the CGM. In addition, the CGM is also applied for certain problems which were not taken in the past. In this thesis, inverse heat transfer methods are developed for the estimation of unknown conditions like boundary heat flux, inlet temperature or source term in different areas of heat transfer. The numerical models based on conjugate-gradient method (CGM) with an adjoint equation and differential evolution algorithm (DEA) are developed for solving various inverse heat transfer problems through the minimization of a performance function, which is expressed by the sum of square residuals between calculated and observed temperature.

The methods are discussed in detail and their performances are assessed comparatively for the estimation of unknown conditions. In order to take the merits of both of these methods, a hybrid differential evolution method (HDM) with a local optimization algorithm is also proposed in this work for minimization of the performance function.

The CGM is used as a local optimization algorithm to speed up the convergence.

The above mentioned techniques are applied in conjugate heat transfer medium where conduction-convection or radiation-conduction occurs simultaneously. The attention is focused on the estimation of functional variation of boundary conditions (heat flux or inlet temperature) or source term. There is no more prior information regarding the functional variation of quantities to be estimated. CGM is applied successfully for the estimation of spacewise variation of unknown quantities (heat flux, inlet temperature or source term). DEA and HDM are more accurate than CGM for the estimation of timewise variation of unknown quantities.

The finite volume method is applied for the discretization of the governing partial differential equations. Computer codes have been developed for all these problems. To check the reliability of the models, one set of experiments is performed.

An experimental set up is built wherein a turbulent flow through a channel is

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considered with the imposition of constant heat flux at the upper boundary. The temperature data measured close to the upper boundary are used in the numerical model to predict the heat flux applied at the upper boundary. A reasonably good prediction is observed showing the reliability of the numerical model developed in this work.

Keywords: Inverse heat transfer, Conjugate gradient method with adjoint equation, Differential evolution algorithm, Hybrid differential evolution, unknown conditions

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Development of an efficient model for inverse conjugate heat transfer problems