Heat and mass transfer for turbulent pipe flow

Abstract

NOTATION a, b = constants, Equation ( 3 ) H o = enthalpy of ideal gas, B.t.u./lb.-mole H = enthalpy, B.t.u./lb.-mole P = pressure, Ib./sq. in. abs. R = gas constant T = absolute temperature, O R . D = molar volume z = compressibility factor Greek Letters K = constant, Equation ( 3 ) T Su brcripts c = critical = internal pressure, lb./sq. in. abs. T = constant temperature z, = constant volume LITERATURE CITED 1. 2. 3. 4. 5. 6.Beattie, J. A., and 0. C. Bridgeman, Proc. Am. Acad. ArtsHeat and mass transfer coefficients for turbulent flow in smooth circular pipes have been represented by empirical equations of the form N N u = a ( N R e ) (NPr)'(1)with various values of the constants a, b, and c to correlate experimental data. EARLY RESEARCHThe equations of Colburn (1 ) , Dittus and Boelter ( 2 ) , ( 3 ) , and Sieder and Tate ( 4 ) are representative of the significant differences in the constants for Equation ( 1). These constants represent data for fluids with Prandtl numbers with the approximate range of 1 to 100. Interest in liquid metals as heat transfer media resulted in experimental data which showed that these data for very low Prandtl number fluids could not be predicted by correlations of the form of Equation (1). This difference occurs because the wall region, with characteristics of laminar flow, provides the resistance for heat transfer with Prandtl numbers greater than one, but the fully turbulent core region represents much of the resistance for the liquid metals. Drexel and McAdams

Particle−Liquid Mass Transfer Coefficient in Two-/Three-Phase Stirred Tank Reactors

“…Some attempts have been made theoretically and experimentally to evaluate particle-fluid effective relative velocity in turbulent dispersions and to correlate k SL using it. 47,50,68,[74][75][76][77][78]102,103 These studies modified and used the equation of motion for small spherical particles suspended in a turbulent flow given by Tchen. 84 The equation of motion proposed by Tchen is In eq 19, subscripts P and f refer to the particle and fluid, respectively.…”

Mass Transfer Modeling for Salt Transport in Amphoteric Nanofiltration Membranes

“…Considering that the total flux of solute S is the sum of a diffusive flux and a convective flux, being the former the sum of two contributions, the molecular and the eddy diffusion Introducing this flux equation in eq 1 The integral of both members over the limits of the polarization concentration layer is To carry out the integration a correlation between the eddy diffusivity, ε ( t ) , and the dimensionless distance, y + , has to be introduced. We selected one recommended for the region near the wall and used in the adjustment of heat and mass transfer data obtained by several authors Introducing this correlation and the friction factor given by the Blasius formula, which is valid for fully developed turbulent flow in long, smooth, circular tubes, the solute concentration in the interface feed solution−membrane is finally obtained …”

A Three‐Dimensional Three‐Phase Model of Gas Injection in AOD Converters

“…Their work includes an extensive analysis of the effect of the dispersed‐phase viscosity on droplet size as well as the relative influence of viscosity and interfacial tension on droplet size. The starting point in their derivation is an equation that was originally developed by Hughmark, which expresses the disruptive energy due to continuous phase turbulence, : where is the stabilizing cohesive energy due to interfacial tension and is the cohesive energy due to the dispersed‐phase viscosity. By expressing the energy balance in such a way that it could be related to the maximum stable droplet diameter, the following equation was derived.…”