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This book contains mathematical aspects of direct and inverse thermoelastic problems. The concept of direct and inverse thermoelastic problems are the central theme of this book, find its roots and applications in branches of mathematics, aeronautical sciences and mechanical engineering which is helpful for students and researchers. All the results are obtains in terms of Bessel's function in the form of infinite series. The numerical results are derived and depicted graphically. The mathematical approach of this book is to study new dimensions of thermoelastic problems in different areas.