In this work, the Blasius equation is studied. Homotopy perturbation method (HPM) and homotopy analysis method (HAM) are applied to obtain its solution. Comparison with variational iteration method (VIM) is made to highlight the significant features of employed methods and their capability of handling nonlinear problems. The outcome shows the success of (HPM) and (HAM) for solving nonlinear pro...

This article covers several aspects of respiratory fluid mechanics that have been actively investigated by our group over the years. For the most part, the topics involve two-phase flows in the respiratory system with applications to normal and diseased lungs, as well as therapeutic interventions. Specifically, the topics include liquid plug flow in airways and at airway bifurcations as it rela...

where σ is the stress tensor, ǫ = 12 (∇u +∇u) T is the strain tensor, f is a body force per unit mass (gravity is a typical example), qT is a volume source (it may model chemical reactions, Joule effects, radioactive decay, etc.), and jT is the heat flux. In addition to the above three fundamental conservation equations, one may also have to add L equations that accounts for the conservation of...

When anticommuting Grassmann variables are introduced into a fluid dynamical model with irrotational velocity and no vorticity, the velocity acquires a nonvanishing curl and the resultant vorticity is described by Gaussian potentials formed from the Grassmann variables. Upon adding a further specific interaction with the Grassmann degrees of freedom, the model becomes supersymmetric.

Extreme sports such as canyoneering have expanded greatly since the turn of the century yet little scientific attention has been paid to the analyses of the dangers of those activities. The author was much involved in promoting one such sport, namely canyoneering, and presents this paper as an example of the kind of fluids engineering analyses that are needed in order to objectively quantify th...

where x = φ(X, T ) is the position of the material point X at time T . We will refer to X as a material, or Lagrangian point, and x as a spatial or Eulerian point. If Ω ⊂ B is a material region, we denote by ΩT = φ (Ω, T ) the spatial region occupied by the material points in Ω at time T . We assume that the deformation φ is smooth, with a smooth inverse X = Φ(x, t). Here, we write T = t for th...