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{\rm Nu}=3.66 + \frac{ 0.065 \cdot {\rm Re} \cdot {\rm Pr} \cdot {D/L} }{ 1 + 0.04 \cdot ({\rm Re} \cdot {\rm Pr} \cdot {D/L})^{2/3} }

{\rm Nu}=0.023 \cdot \mbox{Re}_D^{3/4} \cdot \mbox{Pr}^{0.4}

{\rm Nu}=\frac{ (f/8) \, ({\rm Re} - 1000) {\rm Pr}  }{ 1 + 12.7 \, (f/8)^{1/2} \, ({\rm Pr}^{2/3} -1) }

{\rm Nu}=0.3 + \frac{0.62 \, \mbox{Re}^{1/2} \, \mbox{Pr}^{1/3} }
{\left[ 1+ (0.4/\mbox{Pr})^{2/3} \right]^{1/4}}
\left[ 1 + \left( \frac{\mbox{Re}}{282000} \right)^{5/8}\right]^{4/5}

Relation

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to Biot Number  

Both numbers naturally arise in modelling the heat exchange between solid body and fluid.

Both numbers have similar definition except that Nusselt number is based on  thermal conductivity of the fluid while Biot Number is based on  thermal conductivity of the solid body.

Normally, Nusselt number indicates The real difference betweeh the two are;
Nusselt number confirms whether conductive or convective heat transfer dominates across the fluid-solid interface while Biot number, interface between solid body and fluid.

While Biot Number indicates whether significant thermal gradients gradient will develop inside a a solid by body based on the ratio of heat transfer away from the surface of a a solid body to heat transfer within the solid body.

See also

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Physics / Thermodynamics / Heat Transfer

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