login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (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/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 3-540-60374-3

LINKS

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

Wikipedia, Nusselt number

EXAMPLE

Nu = 3.6567934577632923619...

MAPLE

fsolve(KummerM(1/2-1/2*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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 25 23:48 EDT 2019. Contains 322465 sequences. (Running on oeis4.)