Definition of Heat Transfer Coefficients

If we substitute these expressions into Eq. 11.2.1 for the rate of entropy production per 

This leads us to conclude that A 0, in addition to the constraint (Eq. 2.3.21) for the positive definiteness of the Maxwell-Stefan diffusion coefficients at infinite dilution )°y. 

Equations 11.2.5 and 11.2.6 are the complete forms of the constitutive relations for simultaneous mass and energy transport. The reader is referred to the treatise by Hirschfelder et al. (1964) and to the papers by Merk (1960) and Standart et al. (1979) for further background to these derivations. 

By analogy with Eq. 7.1.3, we may define heat transfer coefficients, in either fluid phase, by 

It is more conventional to define the heat transfer coefficients as 

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From the temperature profile given by Equation 7.58, the heat flux at the wall, the total rate of heat transfer, and the bulk temperature of the fluid at the exit can be evaluated. Also, using the arithmetic mean of terminal temperature differences together with the definition of heat transfer coefficient, the arithmetic mean Nusselt number can be expressed as a function of the Graetz number. Similarly, the logarithmic Nusselt number can also be obtained as a function of the Graetz number [12]. 

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