By Baehr H.D., Stephan K.
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Additional info for Heat and Mass Transport
22) with a new quantity, the local heat transfer coeﬃcient, deﬁned by α := q˙W . 23) This deﬁnition replaces the unknown heat ﬂux q˙W , with the heat transfer coefﬁcient, which is also unknown. This is the reason why many researchers see the introduction of α as unnecessary and superﬂuous. Nevertheless the use of heat 2 Ludwig Prandtl (1875–1953) was Professor for Applied Mechanics at the University of G¨ottingen from 1904 until his death. He was also Director of the Kaiser-Wilhelm-Institut for Fluid Mechanics from 1925.
In a ﬂat vessel wall the temperature changes linearly, however the straight line moves according to time. 38 1 Introduction. Technical Applications Fig. 17: Temperature proﬁle for the cooling of a thin walled vessel The process of cooling, as in Fig. 17, will now be considered.
The density of the ﬂuid adjacent to the wall is lowered, causing an upward ﬂow in the gravitational ﬁeld to develop. In free convection, the characteristic (forced) velocity w0 does not apply. The new physical quantity is the acceleration due to gravity g. 50) known as the Galilei number. As the density changes with temperature ν = η/ must be calculated with a constant density 0 = (ϑ0 ) using a ﬁxed reference temperature ϑ0 . All other ﬂuid properties are assumed to be constant. 1 The diﬀerent types of heat transfer 23 At least one new characteristic number K is required to describe the density changes with temperature.