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A larger Nusselt number corresponds to more active convection, with turbulent flow typically in the 100–1000 range. [2] A similar non-dimensional property is the Biot number, which concerns thermal conductivity for a solid body rather than a fluid. The mass transfer analogue of the Nusselt number is the Sherwood number.
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In convective heat transfer, the Churchill–Bernstein equation is used to estimate the surface averaged Nusselt number for a cylinder in cross flow at various velocities. [1] The need for the equation arises from the inability to solve the Navier–Stokes equations in the turbulent flow regime, even for a Newtonian fluid .
is the gas film Lewis number (-), is the gas film specific heat at constant pressure (J.Kg −1.K −1) The droplet vaporization rate can be expressed as a function of the Sherwood number. The Sherwood number describes the non-dimensional mass transfer rate to the droplet and is defined as: [3]
The relative magnitudes of the Grashof number and the square of the Reynolds number determine which form of convection dominates. If G r / R e 2 ≫ 1 {\displaystyle {\rm {Gr/Re^{2}\gg 1}}} , forced convection may be neglected, whereas if G r / R e 2 ≪ 1 {\displaystyle {\rm {Gr/Re^{2}\ll 1}}} , natural convection may be neglected.
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Pr L is the Prandtl number of the liquid, Re b is the bubble Reynolds number, =, where: G b is the average mass velocity of the vapor leaving the surface; μ L is the liquid viscosity. Rohsenow has developed the first and most widely used correlation for nucleate boiling, [3]
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