Abstract: The classical theory of small amplitude shallow water waves is applied to regular polygonal basins. The natural frequencies of the basins are related to the eigenvalues of the Helmholtz equation. Exact solutions are presented ...

Abstract: The fully developed forced convection with H1 and/or H2 conditions in a semi-elliptic duct is studied. Such ducts model conduits attached to a flat surface and etched microfluidic channels. Due to differences in materials, ...

Abstract: The basic problem of steady-state heat conduction in a ring with internal heat generation and convective boundary conditions is considered. An exact solution is found for the ring with a rectangular cross section and an ...

Abstract: The Falkner–Skan flow over a wedge is classic in boundary layer theory. We consider the heat or mass transfer from a source at the vertex of the wedge. The interactions of the thermal boundary layer and momentum boundary ...

Abstract: The N-segment circular arch with rigid members and semirigid joints under external pressure is studied. The problem is formulated in coupled difference equations. An efficient initial value method is presented to solve the ...

Abstract: Using an efficient Ritz method, the thermoconvective stability of a bottom-heated porous layer in vertical elliptic and semi-elliptic enclosures with adiabatic side walls is studied. The stability mosaics for the critical ...

Abstract: Liquid or gas seeps into one side of a porous layer. Coriolis forces affect the flow due to system rotation. The problem models seepage flow into a porous rock fault under planetary rotation. Using similarity, the ...

Abstract: The Darcy–Brinkman flow through a tapered channel or cone, including the flow through a slit or hole on a plate, is studied for the first time. Assuming small Darcy numbers, the solution is found to third order error using ...

Abstract: Fluid flow in saturated porous media imbedded with a solid inclusion may be described by the Darcy–Brinkman equation. When the Darcy number is small, a boundary-layer theory, similar to Prandtl's theory for viscous flow, ...

Abstract: Liquid or gas seeps into one side of a porous layer. Coriolis forces affect the flow due to system rotation. The problem models seepage flow into a porous rock fault under planetary rotation. Using similarity, the ...