Summary
The mixed convective heat and mass transfer over a horizontal plate has been investigated. A diffusion equation with a chemical reaction source term is taken into account. By applying transformation group theory to the analysis of the governing equations, we obtain a similarity solution of the problem in the case that the temperature and concentration at the wall and the moving speed of the plate are proportional to power distributions along the distance from the leading edge. Furthermore the similarity equations have been solved numerically by a fourth-order Runge-Kutta scheme. The numerical results obtained for various values of the Schmidt number, chemical reaction parameter and buoyancy parameters reveal the influence of the parameters on the flow, heat and mass transfer behavior.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Abbreviations
- a :
-
parameter of the group
- C :
-
concentration of the fluid
- D :
-
diffusion coefficient
- Gr T , Gr c :
-
Grashof numbers
- h T ,h T :
-
local and average heat transfer coefficient at the wall
- k :
-
chemical reaction rate constant
- K 1 :
-
buoyancy parameter related to temperature difference
- K 2 :
-
buoyancy parameter related to concentration difference
- K 3 :
-
chemical reaction parameter
- l :
-
reference length of the plate
- n :
-
reaction order
- Nu x, T , Nu T :
-
local and average Nusselt numbers
- p :
-
pressure of the fluid
- Pr:
-
Prandtl number
- q w(x):
-
heat flux at the wall
- Q w :
-
total heat transfer between the plate and the fluid
- Re, Re x :
-
Reynolds number, local Reynolds number
- Sc:
-
Schmidt number
- Sh x , Sh:
-
local and average Sherwood number
- St:
-
Stanton number
- St* :
-
total heat flux in terms of St
- T :
-
temperature of the fluid
- U 0 :
-
reference moving speed of the plate
- U(x) :
-
stretching speed of the plate
- u, v :
-
velocity components inx, y direction respectively
- x, y :
-
Cartesian coordinates
- α:
-
thermal diffusity
- β T ,β c :
-
volumetric coefficients of expansion
- θ:
-
non-dimensional temperature
- ν:
-
kinematic viscosity
- ϱ:
-
density
- ϕ:
-
non-dimensional concentration
- ψ:
-
stream function
- χ:
-
thermal conductivity
- W :
-
at the wall
- ∞:
-
at infinity
- C :
-
of concentration
- T :
-
of temperature
References
Sparrow, E. M., Minkowycz, W. J.: Buoyancy effects on horizontal boundary-layer flow and heat transfer. Int. J. Heat Mass Transfer5, 505–511 (1962)
Chen, T. S., Sparrow, E. M., Mucoglu, A.: Mixed convection in boundary layer flow on a horizontal plate. ASME J. Heat Transfer99, 66–71 (1977).
Schneider, W.: A similarity solution for combined forced and free convection flow over a horizontal plate. Int. J. Heat Mass Transfer22, 1041–1046 (1979).
Dey, J.: Mixed convection flow over a semi-infinite horizontal plate with vectored mass transfer. ASME J. Heat Transfer104, 558–560 (1982).
de Hoog, F. R., Laminger, B., Weiss, R.: A numerical study of similarity solutions for combined forced and free convection. Acta Mech.51, 139–149 (1984).
Afzal, N., Hussain, T.: Mixed convection over a horizontal plate. ASME J. Heat Transfer106, 240–241 (1984).
Ramachandran, N., Armaly, B. F., Chen, T. S.: Mixed convection over a horizontal plate. ASME J. Heat Transfer105, 420–423 (1983).
Merkin, J. H., Ingham, D. B.: Mixed convection similarity solutions on a horizontal surface. ZAMP38, 102–115 (1987).
Morgan, A. J. A.: The reduction by one of the number of independent variables in some systems of partial differential equations. Q. J. Math. Oxford Ser.2, 250–259 (1952).
Hansen, A. G.: Similarity analysis of boundary value problems in engineering. Englewood Cliffs: Prentice-Hall 1964.
Ames, W. F.: Nonlinear partial differential equations in engineering. vol. II. New York: Academic Press. 1972.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Fan, J.R., Shi, J.M. & Xu, X.Z. Similarity solution of mixed convection with diffusion and chemical reaction over a horizontal moving plate. Acta Mechanica 126, 59–69 (1998). https://doi.org/10.1007/BF01172799
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01172799