The Heat-Flux Vector in Nonflow Systems

When added together these give for the polymer contribution to the heat-flux vector ADEFPXCTVo  

The contribution of the solute to the thermal conductivity of the solution is then defined as the coefficient of the temperature gradient in Eq. (16.32). If we neglect 

This definition of thermal conductivity is consistent with that given in Refs. [30a], [11], and [12]. It should be noted that the spring constant H does not appear in the result. 

Van den Brule [31, Dissertation, Eq. (a.39), p. 76] was the first to obtain an expression for the thermal conductivity for Hookean dumbbells. His result, for small has the same form as Eq. (16.33), but with 7/4 replaced by 3/2. 

However, in his theory he did not take into account all three contributions to the heat-flux vector. Results analogous to Eqs. (16,28-16,33) have also been obtained for FENE dumbbells [31a]. 

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