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U = \frac{\lambda_{ann}}{d_h} \, {\rm Nu}_h{ann}

where

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body--uriencoded--\lambda_%7Bann%7D

thermal conductivity of flowing of fluid in the annulus

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body--uriencoded--d_h%7Bann%7D

annular hydraulic diameter

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body--uriencoded--%7B\rm Nu%7D_h%7Bann%7D

dimensionless Nusselt number (Nu)

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The Nusselt number (Nu) correlations are:

Stagnant fluidNatural ConvectionForced Convection
OEIS sequence A282581
J. DIRKER & J. P. MEYER


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{\rm Nu}=3.6568



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{\rm Nu} = \frac{2 \cdot \epsilon({\rm Ra})}{\ln (r_{out}/r_{in})}



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{\rm Nu}= c \cdot \mbox{Re}_D^p \cdot \mbox{Pr}^{0.4}\cdot \left( \frac{\mu}{\mu_w} \right)^{0.14}




wherewhere


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body--uriencoded-- \mbox%7BRe%7D

 Reynolds number 

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body--uriencoded--\epsilon(%7B\rm Ra%7D)

Natural Convection Heat Transfer Multiplier 
LaTeX Math Inlinebodyc

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body--uriencoded-- \

displaystyle c = \frac%7B0.03 \, a%5e%7B1.86%7D%7D%7B0.063 \, a%5e3 -0.674 \, a%5e2 +2.225 \, a - 1.157 %7D

mbox%7BPr%7D = \nu / a

Prandtl number 

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body--uriencoded--%7B\rm Ra%7D

Rayleigh number 

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body

\nu

kinematic viscosity



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bodya

thermal diffusivity
p


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body

p = 1.013 \cdot\exp \left[ -0.067 \cdot a \right]

--uriencoded--r_%7Bout%7D

inner radius of outer pipe


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body

--uriencoded--r_%7Bin%7D

outer radius of inner pipe
a


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body--uriencoded--

a

\zeta = r_%7Bout%7D/r_%7Bin%7D





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bodyp = 1.013 \cdot\exp \left[ -0.067 \cdot \zeta \right]



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body--uriencoded--\displaystyle c = \frac%7B0.03 \, \zeta%5e%7B1.86%7D%7D%7B0.063 \, \zeta%5e3 -

\mbox%7BPr%7DPrandtl number 

0.674 \, \zeta%5e2 +2.225 \, \zeta - 1.157 %7D


See also

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Physics / Thermodynamics / Heat Transfer /  Heat Transfer Coefficient (HTC) / Heat Transfer Coefficient (HTC) @model

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