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Mass transfer coefficients can be estimated from many different theoretical equations, correlations, and analogies that are functions of material properties, intensive properties and flow regime (laminar or turbulent flow). Selection of the most applicable model is dependent on the materials and the system, or environment, being studied.
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 .
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;
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 empirical relations from experimental data. [12] Heat transfer is analyzed in packed beds, nuclear reactors and heat exchangers.
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. Experimental assessment of the heat transfer coefficient poses some challenges especially when small fluxes are to be measured (e.g. < 0.2 W/cm 2). [1] [2]
is a convective heat transfer coefficient [W/(m 2 ·K)] L {\displaystyle {L}} is a characteristic length [m] of the geometry considered. (The Biot number should not be confused with the Nusselt number , which employs the thermal conductivity of the fluid rather than that of the body.)
The constant of proportionality is the heat transfer coefficient. [7] The law applies when the coefficient is independent, or relatively independent, of the temperature difference between object and environment. In classical natural convective heat transfer, the heat transfer coefficient is dependent on the temperature.
The Be number plays in forced convection the same role that the Rayleigh number plays in natural convection. In the context of mass transfer . the Bejan number is the dimensionless pressure drop along a channel of length L {\displaystyle L} : [ 4 ]