Skip to main content Accessibility help
×
Home

Buoyancy effects in a wall jet over a heated horizontal plate

  • R. Fernandez-Feria (a1) and F. Castillo-Carrasco (a1)

Abstract

A similarity solution of the boundary layer equations for a wall jet on a heated horizontal surface at constant temperature taking into account the coupling of the temperature and velocity fields by buoyancy is described. This similarity solution exists for any value of ${\it\Lambda}=Gr/Re^{2}$ , characterizing this coupling between natural and forced convection over the horizontal plate, where $Gr$ is a Grashof number and $Re$ is a Reynolds number, provided that the plate temperature is higher than the ambient temperature ( ${\it\Lambda}>0$ , say). Two main qualitative differences are found in the flow structure in relation to the well-known Glauert’s similarity solution for a wall jet without natural convection effects (i.e. when ${\it\Lambda}=0$ ): the first is that the similarity variable and structure of the horizontal velocity and temperature have the same functional form for both a radially spreading jet and a two-dimensional jet; the second is that the maximum of the horizontal velocity increases as the jet spreads over the surface, instead of decreasing like in Glauert’s solution, as the radial or horizontal distance to the power $1/5$ . To check this similarity solution we solve numerically the boundary layer equations for the particular case of a jet with constant velocity and temperature emerging from a slot of height ${\it\delta}$ and radius $r_{0}$ (in the radially spreading case). An approximate, analytical similarity solution near the jet exit is also found that helps to start the numerical integration. Far from the jet exit the numerical solution tends to the similarity solution for any set of values of the non-dimensional parameters governing the problem, provided that the plate is heated ( ${\it\Lambda}>0$ ). No similarity solution is found numerically for the case of a cooled plate ( ${\it\Lambda}<0$ ). For ${\it\Lambda}=0$ Glauert’s similarity solution is recovered.

Copyright

Corresponding author

Email address for correspondence: ramon.fernandez@uma.es

References

Hide All
Afzal, N. & Hussain, T. 1984 Mixed convection over a horizontal plate. Trans. ASME J. Heat Transfer 106, 240241.
Boyd, J. P. 2000 Chebyshev and Fourier Spectral Methods, 2nd edn. Dover.
Daniels, P. G. 1992 A singularity in thermal boundary-layer flow on a horizontal surface. J. Fluid Mech. 242, 419440.
Daniels, P. G. & Gargaro, R. J. 1992 Numerical and asymptotic solutions for the thermal wall jet. J. Engng Maths 26, 493508.
Daniels, P. G. & Gargaro, R. J. 1993 Buoyancy effects in stably stratified horizontal boundary-layer flow. J. Fluid Mech. 250, 233251.
Denier, J. P., Duck, P. W. & Li, J. 2005 On the growth (and suppression) of very short-scale disturbances in mixed froce-free convection boundary layers. J. Fluid Mech. 526, 147170.
Deswita, L., Nazar, R., Ishak, A., Ahmad, R. & Pop, I. 2010 Similarity solutions for mixed convection boundary-layer flow over a permeable horizontal plate. Appl. Maths Comput. 217, 26192630.
Fernandez-Feria, R. & Ortega-Casanova, J. 2014 A pseudospectral based method of lines for solving integro-differential boundary-layer equations. Appl. Maths Comput. 242, 388396.
Fernandez-Feria, R., del Pino, C. & Fernandez-Gutierrez, A. 2014 Separation in the mixed convection boundary-layer radial flow over a constant temperature horizontal plate. Phys. Fluids 26, 103603.
Gill, W. N. & del Casal, E. 1962 A theoretical investigation of natural convection effects in forced horizontal flows. AIChE J. 8, 513518.
Glauert, M. B. 1956 The wall jet. J. Fluid Mech. 1, 625643.
Higuera, F. J. 1997 Opposing mixed convection flow in a wall jet over a horizontal plate. J. Fluid Mech. 342, 355375.
Leal, L. G. 1973 Combined forced and free convection heat transfer from a horizontal flat plate. Z. Angew. Math. Phys. 24, 2042.
Lessen, M.1949 On the stability of the free laminar boundary layer between parallel streams. NACA Tech. Rep. NACA-R-979.
Schlichting, H. & Gersten, K. 2000 Boundary Layer Theory, 8th edn. Springer.
Schneider, W. 1979 A similarity solution for the combined forced and free convection flow over a horizontal plate. Intl J. Heat Mass Transfer 22, 14011406.
Schneider, W. & Wasel, M. G. 1985 Breakdown of the boundary-layer approximation for mixed convection above a horizontal plate. Intl J. Heat Mass Transfer 28, 23072313.
Sparrow, E. M., Eichhorn, R. & Gregg, J. L. 1959 Combined forced and free convection in a boundary-layer flow. Phys. Fluids 2, 319328.
Steinrück, H. 1994 Mixed convection over a cooled horizontal plate: non-uniqueness and numerical instabilities of the boundary-layer equations. J. Fluid Mech. 278, 251265.
Steinrück, H. 1995 Mixed convection over a horizontal plate: self-similar and connecting boundary-layer flows. Fluid Dyn. Res. 15, 113127.
Stewartson, K. 1958 On the free convection from a horizontal plate. Z. Angew. Math. Phys. IXa, 276282.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

JFM classification

Buoyancy effects in a wall jet over a heated horizontal plate

  • R. Fernandez-Feria (a1) and F. Castillo-Carrasco (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed