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CHEMICAL ENGINEERING METHODS AND TECHNOLOGY H C EAT ONDUCTION M , A ETHODS PPLICATIONS R AND ESEARCH No part of this digital document may be reproduced, stored in a retrieval system or transmitted in any form or by any means. The publisher has taken reasonable care in the preparation of this digital document, but makes no expressed or implied warranty of any kind and assumes no responsibility for any errors or omissions. No liability is assumed for incidental or consequential damages in connection with or arising out of information contained herein. This digital document is sold with the clear understanding that the publisher is not engaged in rendering legal, medical or any other professional services. C E M HEMICAL NGINEERING ETHODS T AND ECHNOLOGY Additional books and e-books in this series can be found on Nova’s website under the Series tab. CHEMICAL ENGINEERING METHODS AND TECHNOLOGY H C EAT ONDUCTION M , A ETHODS PPLICATIONS R AND ESEARCH JORDAN HRISTOV AND RACHID BENNACER EDITORS Copyright © 2019 by Nova Science Publishers, Inc. All rights reserved. No part of this book may be reproduced, stored in a retrieval system or transmitted in any form or by any means: electronic, electrostatic, magnetic, tape, mechanical photocopying, recording or otherwise without the written permission of the Publisher. We have partnered with Copyright Clearance Center to make it easy for you to obtain permissions to reuse content from this publication. Simply navigate to this publication’s page on Nova’s website and locate the “Get Permission” button below the title description. This button is linked directly to the title’s permission page on copyright.com. Alternatively, you can visit copyright.com and search by title, ISBN, or ISSN. For further questions about using the service on copyright.com, please contact: Copyright Clearance Center Phone: +1-(978) 750-8400 Fax: +1-(978) 750-4470 E-mail: [email protected]. NOTICE TO THE READER The Publisher has taken reasonable care in the preparation of this book, but makes no expressed or implied warranty of any kind and assumes no responsibility for any errors or omissions. No liability is assumed for incidental or consequential damages in connection with or arising out of information contained in this book. The Publisher shall not be liable for any special, consequential, or exemplary damages resulting, in whole or in part, from the readers’ use of, or reliance upon, this material. Any parts of this book based on government reports are so indicated and copyright is claimed for those parts to the extent applicable to compilations of such works. Independent verification should be sought for any data, advice or recommendations contained in this book. In addition, no responsibility is assumed by the publisher for any injury and/or damage to persons or property arising from any methods, products, instructions, ideas or otherwise contained in this publication. This publication is designed to provide accurate and authoritative information with regard to the subject matter covered herein. It is sold with the clear understanding that the Publisher is not engaged in rendering legal or any other professional services. If legal or any other expert assistance is required, the services of a competent person should be sought. FROM A DECLARATION OF PARTICIPANTS JOINTLY ADOPTED BY A COMMITTEE OF THE AMERICAN BAR ASSOCIATION AND A COMMITTEE OF PUBLISHERS. Additional color graphics may be available in the e-book version of this book. Library of Congress Cataloging-in-Publication Data Names: Hristov, Jordan, editor. | Bennacer, Rachid, editor. Title: Heat conduction: methods, applications and research / editors, Jordan Hristov, Ph.D., D.Sc., Department of Chemical Engineering, University of Chemical Technology and Metallurgy, Sofia, Bulgaria and Rachid Bennacer, University of Paris-Saclay, Orsay, France. Description: Hauppauge, New York, USA: Nova Science Publishers, Inc., [2019] | Series: Chemical engineering methods and technology | Includes bibliographical references and index. Identifiers: LCCN 2018050907 (print) | LCCN 2018053628 (ebook) | ISBN 9781536146745 (ebook) | ISBN 9781536146738 | ISBN 9781536146745 (ebook) Subjects: LCSH: Heat--Conduction. Classification: LCC QC321 (ebook) | LCC QC321 .H43 2019 (print) | DDC 536/.23--dc23 LC record available at https://lccn.loc.gov/2018050907 Published by Nova Science Publishers, Inc. † New York CONTENTS Preface vii Chapter 1 Approximate Solutions to the One-Phase Stefan 1 Problem with Non-Linear Temperature-Dependent Thermal Conductivity Julieta Bollati, María F. Natale, José A. Semitiel and Domingo A. Tarzia Chapter 2 Application of Variational Integral Method to 21 Analyze Variety of Rewetting Problems Manish Kumar Agrawal and Santosh Kumar Sahu Chapter 3 The Heat Radiation Diffusion Equation with 67 Memory: Constitutive Approach and Approximate Integral-Balance Solutions Jordan Hristov Chapter 4 Fundamental Solutions to the Cauchy and Dirichlet 95 Problems for a Heat Conduction Equation Equipped with the Caputo-Fabrizio Differentiation Derya Avci, Mehmet Yavuz and Necati Özdemir Chapter 5 About the Heat Conduction Impact on the 109 Thermosolutal Stability within Annulus: Silicon Carbide Ceramic Case Karim Ragui, Youb Khaled Benkahla and Rachid Bennacer vi Contents Chapter 6 Hygrothermal Transfers in Porous Media 145 Kamilia Abahri and Xiaoyan Ma Chapter 7 Energy Storage Using Phase Change Materials 175 Xiaoyan Ma, Jianfei Song and Bin Liu About the Editors 209 Index 211 PREFACE Heat conduction problems are classic challenges for engineers and scientist with consciously emerging challenging problems to be solved. Among the multifaceted applications of heat conduction problem there principle, say classical, problems that are always challenging to develop new solutions, among them: transient heat conductions with non-linear heat conductivities, Stefan problems, phase change materials, porous media heat conduction with convection, etc. This collection of studies arranged as a book was suggested by the publisher and when we, the editors, were invited there was an ambiguity what exactly to be included as topic. Then, we decided to invite authors who are appearing in journal publications and the responses as chapters arranged in this book clearly indicate what some of the modern trend in conduction studies are. Following these introductory notes we may mention three chapters applying the integral-balance method, which is one of the most powerful engineering methods in heat conduction. In Chapter 1, Bolati et al. applied different approximations for the one- dimensional one-phase Stefan problem corresponding to the fusion process of a semi-infinite material with a temperature boundary condition at the fixed face and non-linear temperature-dependent thermal conductivity. A refined balance integral method, assuming a quadratic temperature profile in space is successfully applied. Agrawal and Sahu, in Chapter 2, applied the variational integral method to analyze variety of rewetting problems. The analysis is extended to include the effect of precursory cooling, variation in heat transfer in multiple step functions, exponential functions and variation in property. Based on the viii Jordan Hristov and Rachid Bennacer analysis, closed form solution for the temperature field and rewetting velocity are developed. In Chapter 3, Hristov applied a constitutive approach to modeling of heat shock waves described by the diffusion approximation in radiation heat transfer in terms of time fractional derivatives. Approximate closed-form analytical solutions by a double integration method concerning a step change of the surface temperature and two classical problems with time-dependent boundary are developed for special case of time-depended boundary conditions. Avci et al. (Chapter 4), considered the heat conduction equation in terms of Caputo-Fabrizio operator with a nonsingular exponential kernel in problems formulated in a line segment. The solutions developed by the Laplace transform in time and the finite sin-Fourier transform in space allowed demonstrating the effect of the fractional parameters controlling the memory kernel, thus, elucidating what really as physics the Caputo-Fabrizio operator models in heat conduction. In Chapter 5, Raguii et al. summarize some recent results on the conduction-limit impact within a double-diffusive convection of a Bingham plastic fluid which occurs within a Silicon Carbide Ceramic annulus; contained between a cold “and less concentric” outer circular cylinder and a hot “and concentric” inner one. Predictions of a such critical limit, into these few pages, will be a function of some relevant parameters; such as the boundary layers’ ratio, known generally as Lewis number and the thermosolutal buoyancy one; which is a pure relation between the thermosolutal gradients and its expansion coefficients, as long as the geometry aspect ratio is developed. Abahri and Ma consider in Chapter 6 the current state of knowledge related to transport of heat, fluid (air) and mass (moisture) in porous construction materials. Finally, Ma et al. (Chapter 7) consider the energy storage properties of Phase Change Materials (PCMs) related to energy consumption in buildings. Analytical solution in semi-infinity domain, a short time solution in 2D rectangular corner, a semi-analytical solution for a bounded domain, the multi- phase problem in a Cartesian domain, and the phase change problem in a cylindrical domain are developed. After these brief outlines of the main results presented in the chapters collected we may express out warm appreciations to all author contributing the book. Moreover, last but not least, we like to express our gratitude to the publishing office for their understanding about the problems emerging during