Page 51 - Process Equipment and Plant Design Principles and Practices by Subhabrata Ray Gargi Das

2.7 Estimation of overall design heat transfer coefficient 47

T w ¼ wall temperature ( C)

T sat ¼ saturation temperature ( C) of boiling liquid

P w ; P sat ¼ saturation pressure corresponding to T w and T sat
P ¼ operating pressure (bar)
P c ¼ critical pressure of the liquid (bar)
2
Q ¼ heat flux (W/m )
The estimation of individual heat transfer coefficients using
equations provided in Table 2.6 requires fluid physical properties
namely density, viscosity and thermal conductivity. These prop-
erties vary with temperature and since the formulae involve a
Caloric Temperature
single value of property, either an averaging or a correction to the
average property value is necessary. Whenever the range of
temperature change of a fluid is small, arithmetic averaging of the
property at the outlet and inlet temperatures for the fluid suffices as a good approximation. For
some fluids like heavy petroleum hydrocarbon fractions, the thermophysical properties are a
strong function of temperature. Particularly the kinematic viscosity for high viscous liquids (e.g.,
heavy petroleum cuts, reduced crude oil, short residue, lubricating oil distillates, etc.) varies
significantly with temperature. When these fluids flow through exchangers and the temperature
change is large, there is substantial variation of heat transfer coefficient along the exchanger. In
such exchanger calculations, evaluating the heat transfer coefficients at the arithmetic average
temperature generates unsatisfactory results. This is avoided by introducing the concept of caloric
temperature, a hypothetical temperature between the inlet and outlet at which the fluid thermo-
physical properties are used to calculate the heat transfer coefficient. One may note that the caloric
temperature values are different for the shell and the tube fluids such that evaluation and use of the
individual heat transfer coefficients at respective caloric temperatures satisfy the basic equation.
(2.25)
Q ¼ U caloric AðDTÞ
The caloric temperature concept is based on an assumption that the overall heat transfer coefficient
varies linearly with temperature between the terminal points. The procedure therefore should include a
characteristic nature of variation of the thermophysical properties (primarily viscosity) with temper-
ature for the fluids involved. The procedure for estimating the caloric temperature is detailed in
Chapter 5 of ‘Process Heat Transfer’ by D. Q. Kern for petroleum fluids.
Based on the discussions presented in this chapter, the
design of double-pipe and shell and tube heat exchangers is
discussed in Chapters 3 and 4. Chapter 5 deals with heat
Organisation of Section II exchanger network analysis and Chapters 6 and 7 deal with the
design of two typical heat exchange equipment involving phase
change namely design of an evaporator and cooling tower. One
may refer to the book (see Further Reads) by Shah and Sekulic
and Towler and Sinnott for design of other types of exchanger.