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A282581 Decimal expansion of the limiting Nusselt Number for laminar flow in a cylindrical pipe with constant wall temperature 0
3, 6, 5, 6, 7, 9, 3, 4, 5, 7, 7, 6, 3, 2, 9, 2, 3, 6, 1, 9, 7, 9, 4, 3, 7, 5, 0, 6, 0, 8, 8, 4, 5, 2, 4, 3, 9, 5, 2, 2, 7, 4, 5, 2, 0, 4, 6, 4, 8, 8, 1, 4, 5, 4, 9, 8, 1, 6, 2, 0, 3, 5, 1, 8, 8, 3, 7, 1, 3, 9, 1, 6, 3, 7, 2, 1, 8, 0, 2, 1, 8, 4, 3, 0, 9, 1, 9, 9, 6, 9, 6, 8, 5, 9, 5, 3, 6, 0, 0, 3 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Study of the heat transfer in cylindrical pipes with fully-developed laminar flow lwith constant inlet temperature and constant wall temperature (the Graetz-Nusselt problem) leads to the dimensionless equation 2 * (1-r^2) * dT/dz = 1/r * dT/dr + d^2T/dr^2 subject to the boundary conditions T(z=0) = 1, T(r=1) = 0, (dT/dr)(r=0) = 0.

The solution to this equation, obtained using separation of variables, is (where M is Kummer's M function and beta an eigenvalue) T = M(1/2 - 1/2 * beta, 1, 2*beta*r^2) * exp(- beta*r^2) * exp( - beta^2*z).

The first eigenvalue is calculated from the condition that the function value is zero for r=1: M(1/2 - 1/2 * beta[1], 1, 2*beta[1]) = 0.

The Nusselt number then is Nu = 2*beta[1]^2.

The Nusselt number was named after the German engineer Wilhelm Nusselt (1882-1957). - Amiram Eldar, May 18 2021

REFERENCES

Theodore L. Bergman and Adrienne S. Lavine, Fundamentals of Heat and Mass Transfer, Wiley, 2017, section 8.4, p. 491.

LINKS

Table of n, a(n) for n=1..100.

Hans Dieter Baehr and Karl Stephan, Wärme- und Stoffübertragung, Springer Vieweg, 2013.

Wikipedia, Nusselt number.

EXAMPLE

Nu = 3.6567934577632923619...

MAPLE

fsolve(KummerM(1/2-1/2*beta, 1, 2*beta), beta=1..2)^2*2

MATHEMATICA

RealDigits[2 * (x /. FindRoot[Hypergeometric1F1[1/2 - x/2, 1, 2*x], {x, 1}, WorkingPrecision -> 120])^2, 10, 100][[1]] (* Amiram Eldar, May 18 2021 *)

CROSSREFS

Sequence in context: A245652 A106109 A275925 * A247581 A322887 A175650

Adjacent sequences:  A282578 A282579 A282580 * A282582 A282583 A282584

KEYWORD

nonn,cons

AUTHOR

Thomas König, Feb 19 2017

EXTENSIONS

a(100) corrected by Amiram Eldar, May 18 2021

STATUS

approved

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Last modified May 22 09:50 EDT 2022. Contains 353949 sequences. (Running on oeis4.)