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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
aostrogo@iit.edu

Borivoje B. Mikic

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

1Corresponding author.

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

Abstract

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.

Copyright (c) 2018 by ASME
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