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I'm looking for a Physics-oriented book on heat transfer - mainly on conduction - starting from basic definitions such as heat flux or thermal resistance. I'd prefer a book with a set of solved problems included so that I can test my understanding of the subject. Could you help me?

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I'm currently using a book called "A course in Classical Physics 2-Fluids and Thermodynamics" by Alessandro Bettini which you could try, however the topic you are looking for is only present in one chapter at the end of the book, so I'm not sure if this book will provide sufficient information. It does have what you are requesting for though.

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This book covers convection, conduction and radiation. It introduces the topics well and provides the equations and concepts that are used to derive the relationships.

It covers concepts from simple one-dimensional steady-state conduction to more complicated problems that involve combinations of heat transfer types and complicated geometries. It provides a general framework to solve everything from simple to fairly complex heat transfer problems. The chapters are well divided so that you can likely read only the relevant chapters on conduction and build up from simple steady state one-dimensional to whatever complexity you require.

It also covers mass transfer, which has many analogous processes and formulations.

As far as I know this is one of the standard heat transfer textbooks. It has many example questions. I don't think the answers are provided with the text; but they are readily available online.

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The gold standard for conductive heat transfer is Conduction of Heat in Solids by Carslaw and Jaeger.

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