Semiclassical statistical mechanics of two-dimensional hard-body fluids

The problem of calculating the thermodynamic properties of two-dimensional semiclassical hard-body fluids is studied. Explicit expressions are given for the first-order quantum corrections to the free energy, equation of state, and virial coefficients. The numerical results are calculated for the planar hard dumbbell fluid. Significant features are the increase in quantum corrections with increasing eta and increasing L*=L/sigma(0).     

Equilibrium theory of two-dimensional simple liquids

Using the Wigner-Kirkwood expansion and bare Lennard-Jones (LJ) (12-6) potential, an effectiveLJ potential is derived, which includes the quantum effects through the expressions of the effective diameter∂(T, λ) and well-depth (T, λ). We use theWCA perturbation theory to calculate the free energy and pressure for theLJ and effectiveLJ potentials. Simple analytic expressions are given for the reference system and the first order correction calculated. The results are quite good at high density. The quantum effects on the free energy and pressure are also discussed.     

Fluctuating boundary layers in combined convection flows along a vertical surface

The effect of buoyancy force on laminar boundary layer in two dimensional flow and heat transfer along a semi-infinite vertical surface, when the velocity of the on-coming stream oscillates in magnitude about a steady mean, is analysed. Two separate solutions valid for low and high frequency ranges are developed. It is found that for low frequency oscillations the phase angles of oscillatory components of skin friction and the rate of heat transfer increase as the Grashof number increases. For very high frequencies, the velocity field is of shear-wave type unaffected by the mean flow; the phase lead in the skin friction is, then, /4 and the rate of heat transfer fluctuation indicates a phase lag of /2 over that of the free stream oscillations.The authors are thankful to referee for many useful suggestions.