On the solution of local nonsimilar boundary-layer equations for standard and inverse flows

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With the recent advances in numerical techniques and with the availability of high speed computers, the numerical solution of the boundary-layer equations does not impose much difficulty. The governing equations for momentum transfer and heat transfer can be solved accurately and efficiently in their partial differential equation form. Despite this capability, however, there are some problems in engineering in which it is still advantageous as well as convenient to obtain the solution of the boundary-layer equations by using approximate methods, such as Pohlhausen's method, ref. (1), local similarity methods (see ref. (2), for example) and local nonsimilarity methods, ref. (3). These methods avoid the complexity of solving partial differential equations and consider the solution of ordinary differential equations. In this note we discuss the solution of the boundary-layer equations by using the local nonsimilarity method of ref. (3). We consider two-dimensional incompressible laminar flows and obtain their solutions for standard and inverse boundary-layer flows by using an efficient and accurate numerical method described in ref. (4). The method can easily be extended to solve the energy equation, ref. (5), since the solution of that equation is independent of the momentum equation and being a linear ordinary differential equation, can be solved by simple integration methods once the solution of the momentum equation is obtained.