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In the traditional similarity theory the influence of temperature-and pressure-dependent fluid properties on the flow field and heat transfer is not described by the basic dimensionless parameters, i.e. Prandtl, Reynolds, Rayleigh, . . . number. We present an extended similarity theory that not only takes into account the variable material properties but also can handle small variations in other parameters of the physical model like small changes in the (reference) Prandtl number. The method has general applicability that is suitable for a wide variety of fluid dynamic and heat transfer situations in which variable properties with a strong dependence on temperature and pressure play a significant role. It is especially useful in predicting the behaviour of a certain fluid based on the results for a different one. As an example the Nußelt number of a lid driven heated cavity is determined with fluid properties being temperature dependent. (2000). Primary 76M55; Secondary 80A20. Mathematics Subject Classification

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Let u denote the relative rounding error of some floating-point format.Recently it has been shown that for a number of standard Wilkinson-type bounds the typical factors γ k := ku/(1−ku) can be improved into ku, and that the bounds are valid without restriction on k. Problems include summation, dot products and thus matrix multiplication, residual bounds for LU-and Cholesky-decomposition, and triangular system solving by substitution.In this note we show a similar result for the product k i=0 x i of real and/or floatingpoint numbers x i , for computation in any order, and for any base β 2. The derived error bounds are valid under a mandatory restriction of k. Moreover, we prove a similar bound for Horner's polynomial evaluation scheme.