Gases Prandtl numbers

Both the recuperator and gas cooler are laminar flow heat exchangers with a low Prandtl number working fluid (HeXe) on at least one side. The NRPCT was unable to locate a well documented convection coefficient correlation that was applicable to both laminar flow and low Prandtl number gases. The Kays... 

Von Arx, A. V. and Ceyhan, I. Laminar Heat Transfer for Low Prandtl Number Gases", S Symposium Space Nuclear Power Systems, Albuquerque, AlP Conference Proceeding, pp. 719-722, 1991. 

Prf frozen Prandtl number, gas properties weighted over all species present PrM effective Prandtl number, Eq. 6.182... 

The model of the recuperator uses the default volume control flags except for the following 1) the vertical stratification model is not used (since not relevant to single phase flow), 2) the ORNL ANS narrow channel model heat transfer correlation Is applied, and 3) wail friction is not computed along the direction of flow. The ORNL ANS model provides the best approximation of experimental data for the low Prandtl number gas being used and the laminar flow regime. The Nusselt number from the ORNL ANS model is adjusted for both compact heat exchanger effects and Reynolds number... 

PHYSICAL AND CHEMICAL DATA TABLE 2-309 Specific Heat at Constant Pressure, Thermal Conductivity, Viscosity, and Prandtl Number of R32 Gas... 

In die dehnition of the Prandtl number, Cp is the heat capacity of the gas at constant pressure. 

A = Surface area ft based on tube ID C = Gas specific heat. Btu/lb°F d = Tube inner diameter, in. k = Gas thermal conductivity, Btu/ft-h°F L = Tube length, ft N = Total number of tubes in boiler Pr = Gas Prandtl number Q = Duty of the boiler. Btu/h... 

HETP = height equivalent to a theoretical plate, ft HTU = height of a transfer unit, ft L = liquid mass velocity, Ib/hr-ft m = exponent a 1.0 n = exponent 0.44 Pr = Prandtl number, dimensionless Sc = Schmidt number dimensionless U, = linear velocity of gas based on total column cross-sectional area, ft/sec... 

Sc = Schmidt number, dimensionless Pr = Prandtl number, dimensionless Cg = gas specific heat, Btu/lb-°F a = interfacial area, fti/fti Q, = sensible heat transfer duty, Btu/hr Qj. = total heat transfer duty, Btu/hr... 

The average Nusselt number is not very sensitive to changes in gas velocity and Reynolds number, certainly no more than (Re)I/3. The Sherwood number can be calculated with the same formula as the Nusselt number, with the substitution of the Schmidt number for the Prandtl number. While the Prandtl number of nearly all gases at all temperatures is 0.7 the Schmidt number for various molecules in air does depend on temperature and molecular type, having the value of 0.23 for H2, 0.81 for CO, and 1.60 for benzene. 

Nusselt and Reynolds numbers are based on the diameter of the heating element, the conductivity and viscosity of the liquid, and the nominal gas velocities. The heat-transfer coefficient is constant for nominal liquid velocities above 10 cm/sec. The results were obtained for Prandtl numbers from 5 to 1200, but no effect of this variation was observed. 

In Chapter 12 it is shown that when the Schmidt and Prandtl numbers for a mixture of gas and vapour are approximately equal to unity, the Lewis relation applies, or ... 

The gas-phase wall heat-transfer coefficient can be evaluated by using the gas-phase Reynolds number and Prandtl number in Eq. (33). The thermal conductivities of liquids are usually two orders of magnitude larger than the thermal conductivities of gases therefore, the liquid-phase wall heat-transfer coefficient should be much larger than the gas-phase wall heat-transfer coefficient, and Eq. (34) simplifies to... 

The second approach assigns thermal resistance to a gaseous boundary layer at the heat transfer surface. The enhancement of heat transfer found in fluidized beds is then attributed to the scouring action of solid particles on the gas film, decreasing the effective film thickness. The early works of Leva et al. (1949), Dow and Jacob (1951), and Levenspiel and Walton (1954) utilized this approach. Models following this approach generally attempt to correlate a heat transfer Nusselt number in terms of the fluid Prandtl number and a modified Reynolds number with either the particle diameter or the tube diameter as the characteristic length scale. Examples are ... 

In a supersonic gas flow, the convective heat transfer coefficient is not only a function of the Reynolds and Prandtl numbers, but also depends on the droplet surface temperature and the Mach number (compressibility of gas). 154 156 However, the effects of the surface temperature and the Mach number may be substantially eliminated if all properties are evaluated at a film temperature defined in Ref. 623. Thus, the convective heat transfer coefficient may still be estimated using the experimental correlation proposed by Ranz and Marshall 505 with appropriate modifications to account for various effects such as turbulence,[587] droplet oscillation and distortion,[5851 and droplet vaporization and mass transfer. 555 It has been demonstrated 1561 that using the modified Newton s law of cooling and evaluating the heat transfer coefficient at the film temperature allow numerical calculations of droplet cooling and solidification histories in both subsonic and supersonic gas flows in the spray. 

Pr (Cp/Lt/X) is constant for most gases over wide ranges of temperature and pressure and this fact may be used to estimate the thermal conductivity at high temperatures. The Prandtl number is between 0.65 and 1.0, depending on the molecular complexity of the gas. 

The gas film coefficient is dependent on turbulence in the boundary layer over the water body. Table 4.1 provides Schmidt and Prandtl numbers for air and water. In water, Schmidt and Prandtl numbers on the order of 1,000 and 10, respectively, results in the entire concentration boundary layer being inside of the laminar sublayer of the momentum boundary layer. In air, both the Schmidt and Prandtl numbers are on the order of 1. This means that the analogy between momentum, heat, and mass transport is more precise for air than for water, and the techniques apphed to determine momentum transport away from an interface may be more applicable to heat and mass transport in air than they are to the liquid side of the interface. 

Equation (4.36) provides a simple method for estimating an important heat transfer dimensionless group called the Prandtl number. Recall from general chemistry and thermodynamics that there are two types of molar heat capacities, C , and the constant pressure heat capacity, Cp. For an ideal gas, C = 3Cpl5. The Prandtl number is... 

The diffusion coefficient as defined by Fick s law, Eqn. (3.4-3), is a molecular parameter and is usually reported as an infinite-dilution, binary-diffusion coefficient. In mass-transfer work, it appears in the Schmidt- and in the Sherwood numbers. These two quantities, Sc and Sh, are strongly affected by pressure and whether the conditions are near the critical state of the solvent or not. As we saw before, the Schmidt and Prandtl numbers theoretically take large values as the critical point of the solvent is approached. Mass-transfer in high-pressure operations is done by extraction or leaching with a dense gas, neat or modified with an entrainer. In dense-gas extraction, the fluid of choice is carbon dioxide, hence many diffusional data relate to carbon dioxide at conditions above its critical point (73.8 bar, 31°C) In general, the order of magnitude of the diffusivity depends on the type of solvent in which diffusion occurs. Middleman [18] reports some of the following data for diffusion. 

For gas-solid fluidized beds, Wen and Fane (1982) suggested that the determination of the bed-to-surface mass transfer coefficient can be conducted by using the corresponding heat transfer correlations, replacing the Nusselt number with the Sherwood number, and replacing the Prandtl number by Sc(cpp)/(cpp)/(l — a). Few experimental results on bed-to-surface mass transfer are available, especially for gas-solid fluidized beds operated at relatively high gas velocities. 

Gas flow has little effect on heat transfer in a mechanically agitated vessel containing power-law fluid. While for turbine stirrers the heat-transfer coefficient for a power-law fluid can be obtained from Eq. (7.7), a more generalized form Nu = a[Re /(m)]2/3 Pr1/3 should be preferred. Here the expression given by Metzner and Otto (1957) for Re /(m) should be used and the viscosity in Prandtl number must be the constant viscosity value at high shear rates. 

In heat-exchanger applications, it is frequently important to match heat-transfer requirements with pressure-drop limitations. Assuming a fixed total heat-transfer requirement and a fixed temperature difference between wall and bulk conditions as well as a fixed pressure drop through the tube, derive expressions for the length and diameter of the tube, assuming turbulent flow of a gas with the Prandtl number near unity. 

Natural convection occurs when a fluid is in contact with a solid surface of different temperature. Temperature differences create the density gradients that drive natural or free convection. In addition to the Nusselt number mentioned above, the key dimensionless parameters for natural convection include the Rayleigh number Ra = p AT gx3/ va and the Prandtl number Pr = v/a. The properties appearing in Ra and Pr include the volumetric coefficient of expansion p (K-1) the difference AT between the surface (Ts) and free stream (Te) temperatures (K or °C) the acceleration of gravity g(m/s2) a characteristic dimension x of the surface (m) the kinematic viscosity v(m2/s) and the thermal diffusivity a(m2/s). The volumetric coefficient of expansion for an ideal gas is p = 1/T, where T is absolute temperature. For a given geometry,... 

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