By Baehr H.D., Stephan K.

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**Example text**

The walls of the room are treated as black surroundings which are at temperature ϑS = ϑA = 18 ◦ C. The tube gives oﬀ heat to the air by free convection and to the surrounding walls by radiation. 66) where αm is the mean heat transfer coeﬃcient for free convection. 55 2 . W. S. 67) which has the same form as Eq. 56), that of N um = f (Gr, P r). 57) the Grashof number is gβ (ϑW − ϑL ) d3 . Gr = ν2 The expansion coeﬃcient β has to be calculated for the air temperature ϑ A . 00344 K−1 . To take the temperature dependence of the material properties into account, ν, λ and P r all have to be calculated at the mean temperature ϑm = 12 (ϑW + ϑA ).

Only tubes with the same value of L/d can be said to be geometrically similar. These geometry based dimensionless numbers will not be explicitly considered here, but those which independently of the geometry, determine the velocity and temperature ﬁelds, will be derived. g. the entry velocity in a tube or the undisturbed velocity of a ﬂuid ﬂowing around a body, along with the density and viscosity η of the ﬂuid. While density already plays a role in frictionless ﬂow, the viscosity is the ﬂuid property which is characteristic in friction ﬂow and in the development of the boundary layer.

The number of dimensionless quantities is notably smaller than the total number of all the relevant physical quantities. The number of experiments is signiﬁcantly reduced because only the functional relationship between the dimensionless numbers needs to be investigated. Primarily, the values of the dimensionless numbers are varied rather than the individual quantities which make up the dimensionless numbers. The theoretical solution of a heat transfer problem is structured more clearly when dimensionless variables are used.