# Relaxation Model

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3. GOVERNING EQUATIONS
In this paper, relaxation model is employed to account for thermal non-equilibrium between the phases. This model is presented by Downar-Zapolski et al. [16] and is employed by several authors to numerically simulate steady flashing flows [17-19]. Barret et al. [20] used this model to compute unsteady flashing flows in variable cross section ducts.
Relaxation model consists of three conservation laws (mass, momentum, energy) for the two-phase mixture in addition to the mass balance law for the vapor phase: ∂U/∂t+∂F/∂z=S where, U=[■(ρ@ρu@■(E@ρx))],F=[■(ρu@ρu^2+p@■(u(E+p)@ρux))],S=[■(0@(-2fρu^2)⁄d@■((4h_TP (T_w-T_L ))⁄d@(-ρ(x-x ̅ ))⁄θ))] where, ρ, p, u, x, x ̅, θ, f and hTP represent respectively mixture density,