![]() ![]() Finally, the general case is demonstrated using Green's functions. Both a geometrical and a mathematical argument are introduced to show that shape factors are invariant under conformal mapping. Then, conformal mapping is used to relate known configurations for squares and rectangles to the solutions for the disk. The canonical case of the interior and exterior of a disk is examined first. In this paper, we show that known shape factors for the interior of two-dimensional objects are identical to the corresponding shape factors for the exterior of those objects. However, the analytical determination of shape factors for any but the simplest configurations can quickly come to involve complicated mathematics, and, for that reason, it is desirable to extend the available results as far as possible. Many shape factors have been tabulated, and most undergraduate heat transfer books cover their derivation and use. Shape factors for steady heat conduction enable quick and highly simplified calculations of heat transfer rates within bodies having a combination of isothermal and adiabatic boundary conditions. Journal of Verification, Validation and Uncertainty Quantification.Journal of Thermal Science and Engineering Applications.Journal of Offshore Mechanics and Arctic Engineering.Journal of Nuclear Engineering and Radiation Science.Journal of Nondestructive Evaluation, Diagnostics and Prognostics of Engineering Systems.Journal of Nanotechnology in Engineering and Medicine.Journal of Micro and Nano-Manufacturing.Journal of Manufacturing Science and Engineering.Journal of Engineering Materials and Technology.Journal of Engineering for Sustainable Buildings and Cities.Journal of Engineering for Gas Turbines and Power.Journal of Engineering and Science in Medical Diagnostics and Therapy.Journal of Electrochemical Energy Conversion and Storage.Journal of Dynamic Systems, Measurement, and Control.Journal of Computing and Information Science in Engineering.Journal of Computational and Nonlinear Dynamics.Journal of Autonomous Vehicles and Systems.ASME Letters in Dynamic Systems and Control.ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part B: Mechanical Engineering.Mechanical Engineering Magazine Select Articles.
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