On laminar flow through a uniformly porous pipe

Asymptotic solution of a laminar flow in a porous channel with large suction: A nonlinear turning point problem

“…In particular, the case 0 < e <C 1, which corresponds to large suction, (i.e., R > 1) leads to three such problems, one of which is the subject of this paper. This problem and related problems have been studied by Berman [3], Proudman [12], Yuan and Finkelstein [21], Terrill [16], Terrill and Thomas [17], Robinson [13], Skalak and Wang [15], and Zaturska et al [22]. The importance of exponentially small terms in some of the analyses was commented on by Van Dyke [18].…”

Perturbation solutions for a micropolar fluid flow in a semi-infinite expanding or contracting pipe with large injection or suction through porous wall

“…Here it should be noted that direct use of the method of variation of parameters will cause a singularity in the third-order derivative of f 1 [17][18][19]. In order to eliminate the singularity and to simplify the equation of f 1 , we can set…”

“…For large injection, analytical solutions are constructed using the Lighthill method, which eliminates singularity of the solution in the high order derivative [17][18][19];a series expansion matching method is used for large suction. The accuracy of the analytical solutions for each case is compared with its numerical results.…”

Internal Flows Driven by Wall-Normal Injection

“…This is illustrated in Figure 1 for the special cases of porous channels and tubes. In general, one is required to solve a reduced-order form of the equations of motion for a bounded fluid in order to retrieve a meaningful solution (Terrill & Thomas, 1969). For a general three dimensional setting, this effort leads to a formidable task that is often intractable.…”