The Time Delay for a Perceptible Thermal Disturbance in a Slab

[+] Author and Article Information
M. G. Davies

School of Architecture and Building Engineering, The University, Liverpool L69 3BX, UK

J. Heat Transfer 121(4), 1072-1075 (Nov 01, 1999) (4 pages) doi:10.1115/1.2826058 History: Received September 25, 1998; Revised May 02, 1999; Online December 05, 2007


If a thermal disturbance such as a step change in temperature is applied at each surface of a homogeneous slab of thickness 2L, the effect of cooling at x = +L at first has no effect at x = −L but is clearly evident after a time described by a Fourier number F0 = λt/ρcp L2 of around 0.2. To establish the time of a perceptible change the minimum value of φi − (φ1 + (φ2 ) is sought, where φ1 is the flux into a semi-infinite solid and φ1 and φ2 are the first and second eigenfunction contributions to the solution for a slab of finite thickness. Cooling throughout the slab is determined virtually by the first eigenfunction alone after F0 = 0.22. For a fluid-cooled slab these values are larger.

Copyright © 1999 by The American Society of Mechanical Engineers
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