Numerical Study of Vertical Wall Jets: Influence of the Prandtl Number
This paper is a numerical investigation of a laminar
isothermal plane two dimensional wall jet. Special attention has been
paid to the effect of the inlet conditions at the nozzle exit on the
hydrodynamic and thermal characteristics of the flow. The
behaviour of various fluids evolving in both forced and mixed
convection regimes near a vertical plate plane is carried out. The
system of governing equations is solved with an implicit finite
difference scheme. For numerical stability we use a staggered non
uniform grid. The obtained results show that the effect of the Prandtl
number is significant in the plume region in which the jet flow is
governed by buoyant forces. Further for ascending X values, the
buoyancy forces become dominating, and a certain agreement
between the temperature profiles are observed, which shows that the
velocity profile has no longer influence on the wall temperature
evolution in this region. Fluids with low Prandtl number warm up
more importantly, because for such fluids the effect of heat diffusion
is higher.
[1] Conférences C.E.A., E.D.F, Phènomènes thermiques et hydrauliques
non stationnaires, Jouy-en-Josas, Proc. Eyrolles Editeur, 1976.
[2] Nizou P.Y., Analogie entre transfert de chaleur et de quantité de
mouvement dans un jet pariètal plan turbulent, Int. J. Heat Mass Tran.
1984, Vol. 27, pp 1737-1748.
[3] Nizou P.Y., Tida T., Transfert de chaleur et de quantité de mouvement
dans les jets pariétaux plans turbulents, Int. J. Heat Mass Tran. 1995,
Vol. 38, pp 1187-1200.
[4] Leduc B., Joumotte A., Refroidissement d-une plaque plane par jet et
injection pariètaux, Revue générale de thermique. N┬░ 166, 1975, pp 692-
697.
[5] Lauder BE., Splanding DB, The numerical computation of turbulent
flow, Comput Methods appl Mech Eng. Vol. 3, 1974, pp 269-289.
[6] Ljuboja M., Rodi W., Calculation of turbulent wall jets with an algebric
Reynolds stress model, J. Fluid Eng.. Vol. 102, 1980, pp 350-356.
[7] Kechiche J., Mhiri H., Le Palec G., Bournot P., Etude numérique du
transfert de chaleur et de quantité de mouvement dans un jet pariètal
plan turbulent, P.c.n2004.
[8] Kechiche J., Mhiri H., Le Palec G., Bournot P., Numerical study of the
inlet conditions on a turbulent plane two-dimensional wall jets. Energy
conversion and management. Vol. 45, 2004, pp 2931-2949.
[9] Schlichting H., Boundary layer theory, 1979 , Mc Graw Hill.
[10] Gorla R.S., Combined natural and forced convection in a laminar wall
jet a long a vertical plates with uniform surface heat flux, Appl. Scient.
Res. Vol. 31, 1976, pp. 455-465
[11] Savage S.B., Chan G.K., The buoyant two dimensional laminar vertical
jets, Q.J. Mech. Appl. Math. 1970, Vol. 23, pp 413-430.
[12] Wilks G., Hunt R., The two dimensional laminar vertical jet with
positive or adverse buoyancy, Numerical heat tran. 1985, Vol. 8, pp 449-
468.
[13] Yu W.S., Lin H.T., Rigorous numerical solutions and correlations for
two dimensional laminar buoyant jets, Int. J. Heat Mass Tran. 1992, Vol.
35, pp 1131-1141.
[14] Mhiri H., Golli S., Le Palec G., Bournot P., Influence des conditions
d-émission sur un écoulement de type jet plan laminaire isotherme ou
chauffé, Revue générale de thermique. 1998, Vol. 37, pp 898-910.
[15] Marzouk S., Mhiri H., Le Palec G., Bournot P., Numerical study of
momentum and heat transfer in a pulsed laminar jet, Int. J. Heat Mass
Tran. 2003, Vol. 46, pp 4319-4334.
[16] Kechiche J., Application des modèles de turbulence ├á bas nombre de
Reynolds pour l-étude des jets pariétaux turbulents, Ph.D. thesis,
Université de la méditerrannée Aix MarseilleII, France - Université de
Monastir, Tunisie, 2006.
[17] Habli S., Mhiri H., Golli S., Le Palec G., Bournot P., Etude numérique
des conditions d-émission sur un écoulement de type jet axisymétrique
turbulent, Int. J. Therm. Sci. Vol. 40, 2001, pp 497-511.
[18] Mokni A., Kechiche J., Mhiri H., Le Palec G.,. Bournot P, Inlet
conditions influence on laminar plane wall jets, 3th international
Conference on diffusion in solids and liquids DSL2007, Portimao-
Portugal.
[1] Conférences C.E.A., E.D.F, Phènomènes thermiques et hydrauliques
non stationnaires, Jouy-en-Josas, Proc. Eyrolles Editeur, 1976.
[2] Nizou P.Y., Analogie entre transfert de chaleur et de quantité de
mouvement dans un jet pariètal plan turbulent, Int. J. Heat Mass Tran.
1984, Vol. 27, pp 1737-1748.
[3] Nizou P.Y., Tida T., Transfert de chaleur et de quantité de mouvement
dans les jets pariétaux plans turbulents, Int. J. Heat Mass Tran. 1995,
Vol. 38, pp 1187-1200.
[4] Leduc B., Joumotte A., Refroidissement d-une plaque plane par jet et
injection pariètaux, Revue générale de thermique. N┬░ 166, 1975, pp 692-
697.
[5] Lauder BE., Splanding DB, The numerical computation of turbulent
flow, Comput Methods appl Mech Eng. Vol. 3, 1974, pp 269-289.
[6] Ljuboja M., Rodi W., Calculation of turbulent wall jets with an algebric
Reynolds stress model, J. Fluid Eng.. Vol. 102, 1980, pp 350-356.
[7] Kechiche J., Mhiri H., Le Palec G., Bournot P., Etude numérique du
transfert de chaleur et de quantité de mouvement dans un jet pariètal
plan turbulent, P.c.n2004.
[8] Kechiche J., Mhiri H., Le Palec G., Bournot P., Numerical study of the
inlet conditions on a turbulent plane two-dimensional wall jets. Energy
conversion and management. Vol. 45, 2004, pp 2931-2949.
[9] Schlichting H., Boundary layer theory, 1979 , Mc Graw Hill.
[10] Gorla R.S., Combined natural and forced convection in a laminar wall
jet a long a vertical plates with uniform surface heat flux, Appl. Scient.
Res. Vol. 31, 1976, pp. 455-465
[11] Savage S.B., Chan G.K., The buoyant two dimensional laminar vertical
jets, Q.J. Mech. Appl. Math. 1970, Vol. 23, pp 413-430.
[12] Wilks G., Hunt R., The two dimensional laminar vertical jet with
positive or adverse buoyancy, Numerical heat tran. 1985, Vol. 8, pp 449-
468.
[13] Yu W.S., Lin H.T., Rigorous numerical solutions and correlations for
two dimensional laminar buoyant jets, Int. J. Heat Mass Tran. 1992, Vol.
35, pp 1131-1141.
[14] Mhiri H., Golli S., Le Palec G., Bournot P., Influence des conditions
d-émission sur un écoulement de type jet plan laminaire isotherme ou
chauffé, Revue générale de thermique. 1998, Vol. 37, pp 898-910.
[15] Marzouk S., Mhiri H., Le Palec G., Bournot P., Numerical study of
momentum and heat transfer in a pulsed laminar jet, Int. J. Heat Mass
Tran. 2003, Vol. 46, pp 4319-4334.
[16] Kechiche J., Application des modèles de turbulence ├á bas nombre de
Reynolds pour l-étude des jets pariétaux turbulents, Ph.D. thesis,
Université de la méditerrannée Aix MarseilleII, France - Université de
Monastir, Tunisie, 2006.
[17] Habli S., Mhiri H., Golli S., Le Palec G., Bournot P., Etude numérique
des conditions d-émission sur un écoulement de type jet axisymétrique
turbulent, Int. J. Therm. Sci. Vol. 40, 2001, pp 497-511.
[18] Mokni A., Kechiche J., Mhiri H., Le Palec G.,. Bournot P, Inlet
conditions influence on laminar plane wall jets, 3th international
Conference on diffusion in solids and liquids DSL2007, Portimao-
Portugal.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:58213", author = "Amèni Mokni and Hatem Mhiri and Georges Le Palec and Philippe Bournot", title = "Numerical Study of Vertical Wall Jets: Influence of the Prandtl Number", abstract = "This paper is a numerical investigation of a laminar
isothermal plane two dimensional wall jet. Special attention has been
paid to the effect of the inlet conditions at the nozzle exit on the
hydrodynamic and thermal characteristics of the flow. The
behaviour of various fluids evolving in both forced and mixed
convection regimes near a vertical plate plane is carried out. The
system of governing equations is solved with an implicit finite
difference scheme. For numerical stability we use a staggered non
uniform grid. The obtained results show that the effect of the Prandtl
number is significant in the plume region in which the jet flow is
governed by buoyant forces. Further for ascending X values, the
buoyancy forces become dominating, and a certain agreement
between the temperature profiles are observed, which shows that the
velocity profile has no longer influence on the wall temperature
evolution in this region. Fluids with low Prandtl number warm up
more importantly, because for such fluids the effect of heat diffusion
is higher.", keywords = "Forced convection, Mixed convection, Prandtl
number, Wall jet.", volume = "3", number = "3", pages = "311-8", }
