ORIGINAL M. Asbik Æ O. Ansari Æ B. Zeghmati Numerical study of boundary layer transition in flowing film evaporation on horizontal elliptical cylinder Received: 25 July 2003 / Published online: 15 September 2004 Ó Springer-Verlag 2004 Abstract A numerical study of the onset of longitudinal transition between turbulent and laminar regimes during the evaporation of a water film is presented. These water film streams along a horizontal elliptical tube under the simultaneous effects of gravity, pressure gradients, caused by the vapor flow and curvature, and viscous forces. At the interface of water vapor, the shear stress is supposed to be negligible. Outside the boundary layer, the vapor phase velocity is obtained from potential flow. In the analysis Von Karman’s turbulence model is used and the inertia and convection terms are retained. Transfers equations are discretised by using the implicit Keller method. The effects of an initial liquid flow rate per unit of length, Froude number, temperature differ- ence between the wall and the liquid–vapor interface and ellipticity on the transition position have been evaluated. The transition criterion has been given in term of the critical film Reynolds number (Re G ) C . List of symbols a ellipse semi-major axis length, m b ellipse semi-minor axis length, m Bo liquid Bond number q L d 2 g r Cp L specific heat, J kg 1 K 1 d effective diameter, d=a+b ,m e ellipticity, b/a Fr Froude number U 0 2 /gd g acceleration of gravity, m s 2 h(h) local heat transfer coefficient, W m 2 K 1 h fg specific enthalpy of evaporation, J kg 1 n, j index for nodes Ja Jacob number, Cp L Dt/h fg Nu L local Nusselt number, Eq. 24b p pressure, Pa q heat flux, W m 2 Pr Prandtl number, Cp L l L /k L r radial distance, m R(h) radius of curvature, Eq. 4, m Re L two-phase Reynolds number, U 0 d/m L Re G film Reynolds number, 4G/l L t* temperature in the liquid film, K Dt (t* w t* 0 ), K u* velocity (x-axis), m s 1 v* velocity (y-axis), m s 1 U s friction velocity, m s 1 x*,y* (see Fig. 1), m Greek letters G mass flow per unit of length, kg m 1 s 1 G 0 initial mass flow per unit of length, kg m 1 s 1 d* liquid film thickness, m d + (see Eq. 23a) g transformed coordinate, Eq. 12b g 5 (see Eq. 23b) h parametric angle (see Fig. 2), deg or rad k thermal conductivity, W m 1 K 1 l dynamic viscosity, kg m 1 s 1 m kinematic viscosity, m 2 s 1 q density, kg m 3 r surface tension, N m 1 s shear stress, N m 2 / polar angle, deg or rad h ktr angular position corresponds to transition point, deg or rad Subscripts–superscripts c critical e edge of the vapor boundary layer L liquid phase qs quasi-static t turbulent M. Asbik Æ O. Ansari Faculte´ des Sciences et Techniques, UFR de Mode´lisation en Exploitation Rationnelle des Ressources Naturelles, B. P. 509, Boutalamine, Errachidia, Morocco B. Zeghmati (&) Centre d’Etudes Fondamentales (G.M.A.I.-C.E.F.), EA 2986 Universite´ de Perpignan, 52, avenue de Villeneuve, 66860 Perpignan cedex, France E-mail: zeghmati@univ-perp.fr Heat Mass Transfer (2005) 41: 399–410 DOI 10.1007/s00231-004-0554-0