Hydrodynamic mechanism of temperature gradient formation in thin nematic films

The temperature gradient formation mechanism in an initially uniformly heated hybrid-oriented liquid-crystal (HOLC) channel of microscopic sizes upon exposure to a steady hydrodynamic flow is theoretically studied within the nonlinear generalization of the Ericksen–Leslie theory, taking into account the heat conduction equation. The case of total thermal insulation of one of the HOLC channel is considered provided that a constant temperature is maintained on the other surface. It is shown that the temperature difference $\chi_{\operatorname{max}}(\zeta)$ in the HOLC channel section, caused by the horizontal steady flow with the “triangular” velocity profile $u(z, \zeta$) is significantly affected by the position $\zeta$ of the maximum velocity. It is shown that, in the case of the LC system formed by 4-$n$-pentyl-$n'$-cyanobiphenyl molecules, the hydrodynamic flow characterized by the peak position $\zeta$ = 0.98 of the velocity $u(z,\zeta$ = 0.98) $\sim$ 0.9 $\mu$m/s forms a maximum temperature difference $\chi_{\operatorname{max}}(\zeta)$ = 0.03 ($\sim$9 K) over the HOLC channel section.