Semi-infinite solid solution extended to cylindrical and spherical solids, using time dependent participating volume-to-surface ratio and erfc solutions

[+] Author and Article Information
Aleksandar G. Ostrogorsky

ASME Fellow, Illinois Institute of Technology, Room 246, MANE E1, Illinois Institute of Technology, Chicago, IL 60616

Borivoje B. Mikic

ASME Fellow, Massachusetts Institute of Technology, Room 5-214, Massachusetts Ave., Cambridge, MA 02139

1Corresponding author.

ASME doi:10.1115/1.4039688 History: Received December 04, 2017; Revised March 02, 2018


Time dependent participating volume to surface ratio, V(t)/A, was used to derive "extended time" model, Fo+, for heat conduction transients in cylindrical and spherical solids. Fo+ model is valid for temperature, flux and convection boundary conditions. It extends the time span of the semi-infinite solid solution by ~10 times, up to Fo~0.05 or d ~R (d is transient penetration depth). For comparison, in cylindrical and spherical solids, the planar semi-infinite solid solution is valid for d<<R. For constant heat flux boundary condition imposed on the sphere, erfc series solution is derived using Laplace transforms. A set of simple and approximations, useful up to Fo<0.1, was obtained by splitting in half the first term of the erfc series.

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