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DISCUSSION

Discussion: “An Integral Equation for the Dual-Lag Model of Heat Transfer” (Kulish, V. V., and Novozhilov, V. B., 2004, ASME J. Heat Transfer, 126, pp. 805–808) OPEN ACCESS

[+] Author and Article Information
D. Milov

 RRA, 56 Burlington Street, Lexington, MA 02420

J. Heat Transfer 129(7), 927 (Jan 30, 2006) (1 page) doi:10.1115/1.2227044 History: Received May 26, 2005; Revised January 30, 2006
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In this paper, the authors claim in the abstract and the conclusion that the “solution with dual phase lag depends only on the difference between the two lags.” Then, they proceed to derive an integral solution for the temperature history.

I show first that this conclusion is erroneous and second that the Laplace transform method they use is incorrect.

The authors claim that the system of the dual lag Eqs. (1) and (3) in their paper is equivalent to the new system of Eqs. (6) and (7) in their paper. This is quite incorrect for the following reasons:
  • To obtain Eq. (6) from Eq. (1), the authors perform the shift in time told+τqtnew, where told corresponds to the time in Eq. (1) and tnew is the time in Eq. (6).With this shift Eq. (3) becomes using the new time
    Tt(x,tτq)=1ρcpq(x,tτq)x
    whereas the authors assume that Eq. (3) does not change with the transformation of time applied to obtain Eq. (6) from Eq. (1).
  • It follows that the derivation of Eq. (7) is wrong. Equation (7) is correct only if τq=0.

Thus, their conclusion that the “solution with dual phase lag depends only on the difference between the two lags” is wrong.

The solution that follows Eq. (7) can be applicable only when τq=0 as pointed out in the previous discussion. In this case, Eq. (8) is fine but its Laplace transform Eq. (10) is not.

To find the Laplace of Eq. (8), we multiply both sides by est and then integrate over time from Δτ to infinity following the notation in the subject paper.

The result is not Eq. (10) as the authors claim but the following equation

d2Θdx2=sesΔτΔτθ(x,t)estdtθ(x,Δτ).

Here the Laplace transform of the temperature rise is defined as

Θ(x,s)=0θ(x,t)estdt

I suggest that the subject paper be retracted.

Copyright © 2007 by American Society of Mechanical Engineers
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