

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, 6
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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/dz + 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.


REFERENCES

Baehr H.D.; Stephan K: Wärme und Stoffübergang. 2. Auflage, ISBN 3540603743


LINKS

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


EXAMPLE

Nu = 3.6567934577632923619...


MAPLE

fsolve(KummerM(1/21/2*beta, 1, 2*beta), beta=1..2)^2*2


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


STATUS

approved



