Customer Reviews

The Mathematics of Diffusion

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This classic diffusion text continues where many other texts end, and covers a broad variety of problem types. This is an excellent resource for diffusion solutions for less-common boundary conditions and assumptions, including thorough mathematical developments of the solutions and many references to the original works. Non-mathematicians will often need to roll up their sleeves to digest portions of the derivations, but the insight into the solution processes is often very revealing. This makes this book an invaluable reference, although it is probably not well suited as your only book on diffusion.

Crank's Mathematics of diffusion is a comprehensive summary of solutions to several diffusion related problems. The insights offered are clear and logical, mathematics is at a level that anyone with a college level understanding of calculus (and differential equations) can comprehend and appreciate. The book is particularly useful for researchers and experimentalists who wish to design measurements to understand diffusion behavior into pratically realizable substrates. Time dependent, concentration dependent and temperature dependent effects are included and non-Fickian behavior is discussed. Moving boundaries, sorption and problems involving diffusion in heterogeneous media are also described. Of course, the discussions are neither exhaustive nor recent results feature in the book, for which one must look on his own. This is more like a basic text, and must be used likewise.

The book does not discuss mass transfer under convective flow conditions, and does not incorporate discussion of experimental methods used to measure concentration gradients. Yet it is an essential text to compare many observed concentration profiles to the known solutions plotted in the book. Mass Transfer by Hines and Maddox can be used as supplement for looking at chemical engineering type mass transfer problems. For anyone familiar with an excellent text by Carslaw and Jaegar on the Conduction of heat in solids, Crank's text provides a nice mapping of heat transfer problems discussed in that book to diffusion related problems. The mathematics of diffusion, once mastered, is useful in understanding similar problems in heat problems, momentum transport etc. For everyone involved in studies involving diffusion, Crank's treatise is a must have, must read book.

This book is a classic, collecting analytical solutions to common differential equations arising from common problems in mass transport.

I am a computational biologist. I have very little love for math books, because they seem to be written for gifted people, and my mathematical intuition is quite limited. Often, I must consult many different textbooks and websites, and try and fail many times, before I understand how something works. In this case, I was trying to write a numerical integrator for the heat equation as part of a larger model.

This book was an unexpected gift! The chapter on numerical methods lays the whole thing out, crystal clear, never skipping a step. I had very little experience with partial differential equations before my current project, and I was still able to figure it out in no time. After many wasted hours on Wikipedia, the way forward is clear from this decades-old book.

Highly, highly recommended!

If you are looking for mathematical solutions to diffusion equation under diffrent boundary conditions this is a good reference to have. For people interestted in numerical solutions and techniques this book may not serve the purpose other than getting analytical or approximate solutions to compare with their numerical implementation. There is a chapter on numerical methods, but the coverage is limited and it is introductory. Also, the book is not really about "mathematics" of diffusion - it is about "solutions to diffusion equation". To gain insights into solutions this is a very good book to read. In particular, there are discussions in this book on modeling diffusion in polymers that handle relevant aspects of the problem outside of just the math involved.

Crank has presented diffusion mathematics almost as well as Carslaw and Jaeger have presented heat conduction, although a bit less well explained.

This text is a great resource for understanding diffusion. It is accessible to your average scientist (my background is soil science), but you will have to do some work if your not a mathematician. Don't let that stop you though, this is THE text on diffusion maths. It's an invaluable tool.

This book does it all. Any problems you have Crank has got you. Don't read it without knowing transport though, he solves mad prolems but that's really it. No insight or anything like that. Who cares he does MAD problems