Single-Phase Fluid Flow Energy Balance

1 Single—Phase Fluid Flow Energy Balance 

R constant volume superheater inside radius e = void fraction = thermal diffusion 

The scaling arguments are as described earlier in this text. First, all the variables are made dimensionless by the introduction of scale factors. The differential equations are then transformed by substitution of the dimensionless variables. The dimensionless variables and derivatives are of order one. Typical values for the scale factors and parameters are used, and then the relative importance of the various terms in the differential equation can be determined. 

Scale factors are used to define the following dimensionless variables  

The variables with the zero subscripts are the characteristic values of the variables. The characteristic values and parameter values are given in Table 7.1. 

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A momentum balance for the flow of a two-phase fluid through a horizontal pipe and an energy balance may be written in an expanded form of that applicable to single-phase fluid flow. These equations for two-phase flow cannot be used in practice since the individual phase velocities and local densities are not known. Some simplification is possible if it... 

Negligible pressure gradient in the single-phase fluid flow regime. This allows us to modify the derivation of the fluid thermal energy balance by assuming constant pressure. 

Estimate thermofluid characteristics of liquid-vapor phase change and related heat transfer processes such as circulation rate in natural or forced internal or external fluid circulation, pressure drops, and single- and two-phase vapor-liquid flow conditions. The initial analysis should be based on a rough estimation of the surface area from the energy balance... 

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