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A new evaluation method for Nusselt numbers in naphthalene sublimation experiments in rotating-disk systems

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Abstract

A comparative analysis of theoretical and empirical relations, as well as experimental data for mass transfer of a rotating disk in laminar, transitional and turbulent flows for naphthalene sublimation in air was done. New correlations between local and average Sherwood numbers for the entire disk were offered. A new evaluation approach for Nusselt numbers based on the experimental data for naphthalene sublimation in laminar, transitional and turbulent flows was developed.

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Abbreviations

a :

thermal diffusivity

b :

outer radius of disk

C :

concentration

D m :

diffusion coefficient

h m :

mass transfer coefficient

h m,av :

average mass transfer coefficient \( {\left( { = \frac{2} {{b^{2} }}{\int\limits_0^b {h_{{\text{m}}} rdr} }} \right)} \)

k :

thermal conductivity

K 1 :

constant in Eqs. (1), (2)

K 2 :

constant in Eqs. (1), (2)

n R :

exponent in Eqs. (1), (2)

Nu :

Nusselt number (=q w r/[k(T w − T ∞)])

Nu av :

average Nusselt number (=q w,av b/[k(T w − T ∞)av])

Pr :

Prandtl number (=ν/a)

q w :

local heat flux at the wall

q w,av :

average heat flux at the wall \( {\left( { = {{\int\limits_0^b {q_{{\text{w}}} rdr} }} \mathord{\left/ {\vphantom {{{\int\limits_0^b {q_{{\text{w}}} rdr} }} {{\int\limits_0^b {rdr} }}}} \right. \kern-\nulldelimiterspace} {{\int\limits_0^b {rdr} }}} \right)} \)

r, φ, z :

radial, tangential and axial coordinate

Re ω :

local Reynolds number (=ωr 2/ν)

Re φ :

Reynolds number at r = b (=ωb 2/ν)

Sc :

Schmidt number (=ν/D m)

Sh :

Sherwood number (=h m r/D m)

Sh av :

average Sherwood number (=h m,av b/D m)

(T w − T ∞)av :

average temperature difference \( {\left( { = {{\int\limits_0^b {(T_{{\text{w}}} - T_{\infty } )rdr} }} \mathord{\left/ {\vphantom {{{\int\limits_0^b {(T_{{\text{w}}} - T_{\infty } )rdr} }} {{\int\limits_0^b {rdr} }}}} \right. \kern-\nulldelimiterspace} {{\int\limits_0^b {rdr} }}} \right)} \)

T :

temperature

ν:

kinematic viscosity

ω :

angular speed of rotation of the disk

av:

average value

tr:

transition

w:

wall (z = 0)

∞:

infinity

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Acknowledgments

The research results that laid the foundation of the present work were obtained in part due to the gratefully acknowledged support of the Research Fellowship of the Alexander von Humboldt Foundation taken by the author at TU Dresden.

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  1. Institut für Thermodynamik der Luft- und Raumfahrt, Universität Stuttgart, Pfaffenwaldring 31, 70569, Stuttgart, Germany

    Igor V. Shevchuk

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  1. Igor V. Shevchuk
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Correspondence to Igor V. Shevchuk.

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Shevchuk, I.V. A new evaluation method for Nusselt numbers in naphthalene sublimation experiments in rotating-disk systems. Heat Mass Transfer 44, 1409–1415 (2008). https://doi.org/10.1007/s00231-008-0376-6

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