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Nusselt number correlations for heat transfer to small spheres in thermal plasma flows

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Abstract

Seven different equations predicting heat transfer rates to small spheres in plasma flows are examined considering argon and nitrogan as plasma gases from 300 to 21,000 K at 1 atm. For argon there is a general consensus up to 9000 K, beyond which wide deviations in behavior occur. For nitrogen, the seven correlations are in good agreement up to 4000 K, but show substantial deviations beyond this value. Comparisons with the sparsely available experimental data are made for argon from 300 to 17,000 K and for nitrogen up to 5500 K. Disagreement between the various correlations and experiment can exceed one order of magnitude.

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Abbreviations

C p :

specific heat at constant pressure

D :

sphere diameter

h :

heat transfer coefficient

i :

enthalpy

Nu:

Nusselt number

Pr:

Prandtl number

\(\dot q\) :

heat flow [W]

\(\dot {q}^"\) :

heat flux [W/m2]

Re:

Reynolds number

S ∞ :

\(S_\infty = \int_{T_0 }^{T_\infty } {\kappa dT}\) = heat conductivity potential at free-stream conditions

S w :

\(S_w = \int_{T_0 }^{T_w } {\kappa dT}\) = heat conductivity potential at the walll

T :

temperature

T 0 :

300 K

U :

velocity

K :

thermal conductivity

ρ:

density

μ:

viscosity

ν:

kinematic viscosity

∞:

free-stream conditions, also referred to as gas or plasma

w:

wall conditions, at sphere's surface

f:

film conditions, refers to the arithmetic mean of wall and plasma temperatures

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of Minnesota, Minneapolis, Minnesota

    R. M. Young & E. Pfender

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  1. R. M. Young
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  2. E. Pfender
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Young, R.M., Pfender, E. Nusselt number correlations for heat transfer to small spheres in thermal plasma flows. Plasma Chem Plasma Process 7, 211–229 (1987). https://doi.org/10.1007/BF01019179

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  • DOI: https://doi.org/10.1007/BF01019179

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