Abstract
It is shown that frequently used dimensional estimation of a layer thermal relaxation time, tr, as L2/κ based on the layer thickness, L, and thermal diffusivity, κ, strongly overestimates tr. The correct estimate tr=L2/π2κ should contain a factor of 1/π2 which is of the order of 0.1.
Highlights
Notwithstanding the correct way to estimate thermal and diffusional relaxation time is well known and straightforward, in some publications estimates of thermal relaxation time contain major errors
Most typically, when estimating the thermal relaxation time based upon dimensional analysis, tr=CL2ț, where L is a layer thickness and κ is heat diffusivity, one assumes by default that the numerical factor, ɋ, is of the order of unity while for a 1D geometry it is, 1/π2
A statement that a characteristic thermal relaxation time for a lithosphere of, say, L=200 km thickness is of the order of a billion years is incorrect
Summary
Institute of Geophysics, National Academy of Sciences of Ukraine, Kiev, Ukraine Received October 12, 2015 Показано, что часто используемая размерная оценка времени тепловой релаксации tr=L2ț, где L — мощность слоя, а κ — температуропроводность, дает сильно завышенное Правильная оценка tr=L2ʌ2ț должна содержать множитель 1/π2 порядка 0,1. значение tr. Ключевые слова: характерное время, тепловая релаксация.
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