On the spatial stability of free-convection flows in a saturated porous medium. (English) Zbl 0609.76092
We consider the free-convection boundary-layer flow in a saturated porous medium adjacent to an impermeable vertical surface. It is assumed that the surface is supplying heat to the porous medium in a prescribed way, which varies along the surface. The problem, which relates to the spatial stability of the known similarity solutions of the boundary-layer equations, is formulated and certain analytical results are presented for special cases. For this special class of flows we are able to determine analytically the first eigenvalue for all relevant parameter values and thereby show that such flows are spatially stable.
Keywords:
free-convection boundary-layer flow; saturated porous medium; impermeable vertical surface; stability; similarity solutions; boundary-layer equations; eigenvalueReferences:
| [1] | Cheng, P. and Minkowycz, W.J.: Free convection about a vertical flat plate embedded in a porous medium with application to heat transfer from a dike, J. Geophys. Res. 82 (1977) 2040-2044. · doi:10.1029/JB082i014p02040 |
| [2] | Merkin, J.H.: Mixed convection boundary layer flow on a vertical surface in a saturated porous medium, J. Engng. Math. 14 (1980) 301-313. · Zbl 0433.76078 · doi:10.1007/BF00052913 |
| [3] | Merkin, J.H.: A note on the solution of a differential equation arising in boundary-layer theory, J. Engng. Math. 18 (1984) 31-36. · Zbl 0532.76038 · doi:10.1007/BF00042897 |
| [4] | Daniels, P.G. and Simpkins, P.G.: The flow induced by a heated vertical wall in a porous medium, Q. Jl. Mech. Appl. Math. 37 (1984) 339-354. · Zbl 0563.76093 · doi:10.1093/qjmam/37.2.339 |
| [5] | Banks, W.H.H. and Zaturska, M.B.: Eigensolutions in boundary-layer flow adjacent to a stretching wall, I.M.A.J. Appl. Math. 36 (1986) 263-273. · Zbl 0619.76011 |
| [6] | Abramowitz, M. and Stegun, I.A.: Handbook of Mathematical Functions. Dover, New York (1970). · Zbl 0171.38503 |
| [7] | Jahnke, E., Emde, F. and Lösch, F.: Tables of Higher Functions. McGraw-Hill Book Company Inc. (1962). · Zbl 0087.12801 |
| [8] | Slater, L.J.: Confluent Hypergeometric Functions. Cambridge University Press (1960). · Zbl 0086.27502 |
| [9] | Zaturska, M.B. and Banks, W.H.H.: A note concerning free-convective boundary-layer flow, J. Engng. Math. 19 (1985) 247-249. · Zbl 0578.76085 · doi:10.1007/BF00042537 |
| [10] | Riley, N.: Asymptotic expansions in radial jets, J. Math. Phys. XLI (1962) 132-146. · Zbl 0113.41303 |
| [11] | Banks, W.H.H.: Similarity solutions of the boundary-layer equations for a stretching wall, J. de Mècan. Thèor. et Appl. 2 (1983) 375-392. · Zbl 0538.76039 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
