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1/d ratios ad-hoc approximation application of mathematical applied mathematician Applied Mathematics art of approximation asymptology blockage boundary conditions boundary layer sheet cerebrospinal fluid coefficient convective corner region Cough pulse Davenport profile denotes dimensionless drag coefficient drag force effective collision cross-section elastic dura employed exp i cot Experimental vertical velocity Figure fluid mechanics formulated front face frontal vortex gradient height Grashof number ground level ground surface Gunn and Kinzer heat conducting heat transfer horizontal inflow investigation irrational approximation lim e f oo located lumbar and cisternal lumbar region mathematical model Maxwell method of Fluxions nonlinear partial differential observed partial differential equations physical plane plate potential flow region pressure wave problem rate of rainfall rational approximation theory rear scaling self-similar solution spinal cord temperature theoretical thermal trajectory turbulent flow field UNIVERSITY OF HULL viscosity volume of water wave propagation wave speed width of building x-direction yields