In the area of heat conduction and diffusion, many analytical solutions are available already in classic books on the subject. The authors of such books have assumed that the mathematical expression is all the reader needs, when in fact for engineering applications, considerable additional work can be required in order to obtain numerical values. Practically speaking, such analytical solutions, like imported furniture packed flat in a box, should come with instructions and tools needed to assemble them into a usable form.
This project is concerned with repackaging analytical solutions, by adding information and tools, to make them better suited for engineering applications, and to make these widely available. We propose to develop the EXact Analytical Conduction Toolbox, or EXACT. This project will draw upon the experience of senior researchers in the area of heat conduction and diffusion, to capture their perishable knowledge. Because the field of heat conduction is mature, and attracting fewer new researchers, it is important to act now, to harvest and store the knowledge of experienced researchers, before this knowledge passes away. Although research on heat conduction solutions may be going out of style, analytical solutions themselves will never go out of style, because of the ongoing need for verification of fully-numeric solutions, and, as direct solvers in support of experimental measurement of thermal properties and heat flux. This project will take advantage of the vast digital storage capacity in the ?cloud?, combined with instantaneous world-wide communication, and combined with cross-platform data-and-software compatibility, to disseminate the results in ways impossible only a few years ago.
The information to be assembled for each exact solution will draw upon several areas of intellectual merit. Some analytical solutions have the form of infinite series, and regarding the number of series terms required, it is possible just to take a large number and see if it is sufficient. This common procedure may be satisfactory for 1D problems, but not for 2D or 3D problems, so specific methods to address convergence will be included. Efficient computation of eigenvalues will be addressed, with algorithms and computer programs supplied. Tied in with the evaluation of infinite series is the concept of time partitioning which is not well-known. A further related concept is ?intrinsic verification?, in which the solution itself contains the means for checking that the numerical results are accurate and precise. A numbering system for heat conduction will be applied to both new and existing solutions to make them easy to identify, store, and retrieve. The number system is transformative, because it provides a new way of viewing the entire body of solutions in heat conduction and diffusion.
The results of this project will serve a wide community, including researchers, working engineers, educators, and students, through improved access to precise numerical values, from verified algorithms, for a variety of applications. For example, experimentalists, including biologists, could utilize the solutions in many ways to determine thermal and mass transfer properties. Because computations based on analytic solutions are very accurate, sensitivities to boundary conditions, thermal properties, and so on can be investigated with precision, something that cannot be done with finite element, finite difference, and other fully-numeric methods. Success in this project will serve as a model for harvesting and storing knowledge in other mature fields of science and engineering. In particular the numbering system, presently applied to heat conduction and diffusion, could be extended to any field for which analytical solutions have impact, for example in electromagnetics, acoustics, and fluid flow. This project will have an impact on traditional publishing, as the project results will provide a paradigm for moving from the publishing present -- where books and databases are perhaps of equal importance -- to the publishing future, where computer databases will be ascendant.
This project provides opportunity for many younger researchers to work closely with a few senior researchers who are at or past retirement age. This affords a significant opportunity to directly transfer expertise and sustain the flow of knowledge across generations in the field of heat transfer.
