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The Nusselt number is the ratio of total heat transfer (convection + conduction) to conductive heat transfer across a boundary. The convection and conduction heat flows are parallel to each other and to the surface normal of the boundary surface, and are all perpendicular to the mean fluid flow in the simple case.
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 .
h = convection heat transfer coefficient; G = mass flux of the fluid; ρ = density of the fluid; c p = specific heat of the fluid; u = velocity of the fluid; It can also be represented in terms of the fluid's Nusselt, Reynolds, and Prandtl numbers: = where Nu is the Nusselt number;
Often it can be estimated by dividing the thermal conductivity of the convection fluid by a length scale. The heat transfer coefficient is often calculated from the Nusselt number (a dimensionless number). There are also online calculators available specifically for Heat-transfer fluid applications.
In the situation of laminar flow in circular tubes, several dimensionless numbers are used such as Nusselt number, Reynolds number, and Prandtl number. The commonly used equation is =. Natural or free convection is a function of Grashof and Prandtl numbers. The complexities of free convection heat transfer make it necessary to mainly use ...
The Sherwood number (Sh) (also called the mass transfer Nusselt number) is a dimensionless number used in mass-transfer operation. It represents the ratio of the total mass transfer rate ( convection + diffusion) to the rate of diffusive mass transport, [ 1 ] and is named in honor of Thomas Kilgore Sherwood .
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fluid dynamics (free convection within immiscible fluids; ratio of surface tension to momentum-transport) Lewis number: Le = = heat and mass transfer (ratio of thermal to mass diffusivity) Lift coefficient: C L =