Transient Diffusion in Triangular Cylinders (Advances in Applied Mathematics and Mechanics, 2021)
A heated triangular cylinder is suddenly cooled in a constant temperaturebath. The transient heat conduction problem is transformed to the Helmholtz equationrelated to the vibration of membranes. Using the membrane analogy, exact analyticsolutions for the transient heat conduction problem for three triangular cross sectionsare found.