Accurate solution for fluid heat flux distribution near a steady state

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Abstract
A solution, exact to terms of second order in the temperature gradient, Del T, is obtained to a Fokker-Planck-type equation previously derived for the distribution g(v) in values v of the local heat flux in a large, homogeneous fluid phase. The solution assumes Del T is applied at time t=0, causing the heat flow to build up and relax toward a steady state. An exact expression for the steady value of (v2) is obtained to order ( Del T)2 to test an earlier result, obtained by an approximate expansion of g. The exact solution is more useful than the earlier one, which involved truncation errors, for calculating correlation functions, relaxing terms in g are also calculated.

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