Topic
Method of matched asymptotic expansions
About: Method of matched asymptotic expansions is a research topic. Over the lifetime, 4233 publications have been published within this topic receiving 73311 citations.
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TL;DR: In this article, boundary and interior layer phenomena exhibited by solutions of certain singularly perturbed third-order boundary value problems which govern the motion of thin liquid films subject to viscous, capillary and gravitational forces are derived.
Abstract: This paper studies boundary and interior layer phenomena exhibited by solutions of certain singularly perturbed third-order boundary value problems which govern the motion of thin liquid films subject to viscous, capillary and gravitational forces. Precise conditions specifying where and when the third-order derivative terms in the differential equations can be neglected are derived, and improved estimates for the actual solutions in terms of solutions of the lower-order models are constructed. The paper also contains a technique for replacing a third-order problem with an asymptotically equivalent second-order one that may have wider applicability.
61 citations
TL;DR: In this paper, it is shown that the free convection boundary layer approaches a singular character if the Prandtl number tends to zero, and the method of matched asymptotic expansions is used to integrate the equations for this extreme case.
Abstract: In this paper it is shown that the free convection boundary layer approaches a singular character if the Prandtl number tends to zero. The method of matched asymptotic expansions is used to integrate the equations for this extreme case. An expression is derived for the Nusselt—Grashof relation and the results are compared with those of previous investigations which attack the problem in a different way.
61 citations
TL;DR: In this article, the problem of heat transfer to a strip of finite length in a uniform shear flow is considered, and the mathematical problem is solved by the method of matched asymptotic expansions and expressions for the local and overall dimensionless heat transfer rate from the strip are found.
Abstract: The problem of heat transfer (or mass transfer at low transfer rates) to a strip of finite length in a uniform shear flow is considered. For small values of the Peclet number (based on wall shear rate and strip length), diffusion in the flow direction cannot be neglected as in the classical Leveque solution. The mathematical problem is solved by the method of matched asymptotic expansions and expressions for the local and overall dimensionless heat-transfer rate from the strip are found. Experimental data on wall mass-transfer rates in a tube at small Peclet numbers have been obtained by the well-known limiting-current method using potassium ferrocyanide and potassium ferricyanide in sodium hydroxide solution. The Schmidt number is large, so that a uniform shear flow can be assumed near the wall. Experimental results are compared with our theoretical predictions and the work of others, and the agreement is found to be excellent.
60 citations
TL;DR: In this article, the matched asymptotic expansion method was applied to several long-wave problems including the scattering of acoustic waves by a grating of cylinders and the scatter of water waves incident on horizontal cylinders.
Abstract: The method of matched asymptotic expansions is applied to several long-wave problems including the scattering of acoustic waves by a grating of cylinders and the scattering of water waves incident on horizontal cylinders. It is shown that a naive application of the method can lead to incorrect results. A modified expansion procedure is developed and applied to a number of problems.
60 citations
60 citations