

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
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OFFSET

1,1


COMMENTS

Study of the heat transfer in cylindrical pipes with fullydeveloped laminar flow lwith constant inlet temperature and constant wall temperature (the GraetzNusselt problem) leads to the dimensionless equation 2 * (1r^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 (18821957).  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(1/21/2*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



