Heat transfer in falling-film boiling

The correlation of Kunz and Yerazunis (H. R. Kunz and S. Yerazunis, An Analysis of Film Condensation, Film Evaporation, and Single-Phase Heat Transfer for Liquid Prandtl Numbers From 0.001 to 10000, J. Heat Transfer / Volume 91 / Issue 3, 413-421, doi:10.1115/1.3580203 (?)), also cited in Perry, Chemical Engineers Handbook 7th ed. page 11-16 can be used to predict the heat transfer coefficient for falling-film evaporators.

The correlation is presented in the form of a graph, which makes its application in a computer system unpractical:

This graph can be digitized using the excellent utility ScanIt. The resulting digitized plot can be fitted using gnuplot to this expression:

a(x) = ((aa*x + ab)*x + ac)
b(x) = ((ba*x + bb)*x + bc)
c(x) = ((ca*x + cb)*x + cc)
d(x) = ((da*x + db)*x + dc)
e(x) = (ea*x + eb)
f(x) = (fa*x + fb)
g(x,y) = (a(y)*x+b(y))*(0.5-atan((x-e(y))*f(y))/3.14159265)+(c(y)*x+d(y))*(atan((x-e(y))*f(y))/3.14159265+0.5)

The expression g(x,y) returns the base-10 logarithm of the graph abscissa h / (K^3*rho^2*g/mu^2)^(1/3) as a function of:

  • 1 < x = log10(Re) < 5
  • 0 < y=log10(Pr) < 3.

The numerical values for the coefficients are:

aa -0.112754
ab 0.047577
ac -0.613718
ba 0.197783
bb -0.0809519
bc 0.614201
ca -0.00307804
cb 0.0140499
cc 0.290747
da 0.0255274
db 0.127306
dc -1.0811
ea -1.15207
eb 2.44218
fa 0.286347
fb 0.439599

The expression is smooth and qualitatively reproduces the original plot:

The deviation in term of graph abscissa are on average 1.2%, and less than 1% for more than half of the sampled points (370).

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4 Responses to Heat transfer in falling-film boiling

  1. Pingback: Digitize scanned graphs : ScanIt!

  2. juan carlos gallardo says:

    Dear sirs:Just trying of using your useful regression formula for some heat exchange design.Loading it at a xls file, the results doesn’t coincide with the original chart.e.g NRe 1000, NPr 20, results 0.722 instead of 0.62. Any mistyping error ? I understood that (a(y)*x+b(y)) means (a(x)*y+b(x)). Thanks in advance.JCG.

  3. paolog says:

    Actually from the chart for Re=1000 and Pr=20 I read something less than 0.6, while the correlation yields 0.6233708625. Unfortunately the fit of the Pr=20 curve, especially in the Re=[500..10000] range, is quite bad, as you can see in the last figure (pink line against cyan-filled dots).

    Beware that in the formulas above the expression a(x) is later used passing y (the log(Pr)) as argument – think of x as a replaceable argument. For your convenience I have put two spreadsheet implementations of the formula here:

    ODF (LibreOffice)
    XLS (Microsoft Excel 2003 or later)

    • juan carlos gallardo says:

      Dear Paolog: You are great…. Thank you very much for your kind and fast reply. Your attached xls file clarify my misunderstanding for the: ((aa*D31+ab)*d31 +ac)…..notation… With my best Regards. Juan Carlos.

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