## Abstract

We investigate the effect of the wall-scalar fluctuations on passive scalar turbulent fields for a moderate Reynolds number Rτ = 395 and for several Prandtl numbers ranging from the very low value Pr = 0.01 to the high value Pr = 10 by means of direct numerical simulation (DNS) simulations. Several cases of plane channel flows are considered. Case I is a channel flow heated on both walls with a constant imposed heat flux qw. We consider for this case two different types of boundary conditions. For the first one, the isoscalar boundary condition θw = 0 is imposed at the wall implying that its fluctuation and therefore its rms scalar fluctuations $θrms=⟨θ′θ′⟩$ is zero at the wall whereas in the second type, θw is not prescribed to a fixed value so that it is fluctuating in time at the wall leading to nonzero rms fluctuations. In this latter case, as the heat flux is maintained constant in time at the wall, the fluctuating heat flux $q′w$ reduces to zero at the wall. For illustration purpose, in addition to case I, we also consider case II, which is a plane channel heated only from one wall but cooled from the other one at the same rate taking into account of the freestream scalar boundary condition at the wall $θ′w≠0$ with $q′w=0$. The distributions of the mean scalar field, root-mean-square fluctuations, turbulent heat flux, correlation coefficient, turbulent Prandtl number, and Nusselt number are examined in detail. Moreover, some insights into the flow structure of the scalar fields are provided. As a result of interest, it is found that the mean scalar field $⟨θ⟩$ is not affected by the scalar fluctuations at the wall. But owing to the different boundary conditions applied at the wall, significant differences in the evolution of the rms scalar fluctuations θrms are observed in the immediate vicinity of the wall. Surprisingly, the maximum rms intensity remains almost unchanged in the near wall region whatever the type of boundary condition is applied at the wall. In addition, the turbulent heat fluxes that play a major role in heat transfer are found to be independent of the wall scalar fluctuations. This study demonstrates that the impact of the wall scalar fluctuations is appreciable mainly in the near wall region. This outcome must be taken into account when simulating industrial flows with thermal boundary conditions involving different fluid/solid combinations.

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