Pressure-driven flow in a thin pipe with rough boundary

Stationary incompressible Newtonian fluid flow governed by external force and external pressure is considered in a thin rough pipe. The transversal size of the pipe is assumed to be of the order $$\varepsilon $$ ε , i.e., cross-sectional area is about $$\varepsilon ^{2}$$ ε 2 , and the wavelength in longitudinal direction is modeled by a small parameter $$\mu $$ μ . Under general assumption $$\varepsilon ,\mu \rightarrow 0$$ ε , μ → 0 , the Poiseuille law is obtained. Depending on $$\varepsilon ,\mu $$ ε , μ -relation ($$\varepsilon \ll \mu $$ ε ≪ μ , $$\varepsilon /\mu \sim \mathrm {constant}$$ ε / μ ∼ constant , $$\varepsilon \gg \mu $$ ε ≫ μ ), different cell problems describing the local behavior of the fluid are deduced and analyzed. Error estimates are presented.

Three dimensional fluid flow within a rectangular channel with several cylindrical (and/or) elliptical blocks: lattice boltzmann investigation

Through this paper, we investigate numerically a Three-dimensional laminar flow of an incompressible Newtonian fluid within a rectangular channel; including several adiabatic partitions of a cylindrical (and/or) elliptical shape. To do so, a numerical code based on the Lattice Boltzmann approach is used. In other words, three dimensions D3Q19 model is adopted all based on a cubic Lattice, where each pattern of the latter is characterized by nineteen discrete speeds. Our numerical code has been successfully validated after a wide comparison between the present results and those of the literature. By taking into account the Reynolds number, the partitions’ shape impact on the flow fields within the channel is taking all attention and that throughout the time’ Streamlines and the velocity profiles. The pressure drop within our channel is also investigated to come out with the best arrangement of these kinds of partitions within.

Flow behavior in weakly permeable micro-tube with varying viscosity near the wall

Weakly permeable micro-tubes are employed in many applications involving heat and/or mass transfer. During these processes, either solute concentration builds up (mass transfer) or steep change in temperature (heat transfer) takes place near the permeable wall causing a change in the viscosity of the fluid. Results of the present work suggest that such change in viscosity leads to a considerable alteration in the flow behavior, and the commonly assumed parabolic velocity profile no longer exists. To solve the problem numerically, the equation of motion was simplified to represent permeation of incompressible, Newtonian fluid with changing viscosity through a micro-tube. Even after considerable simplification, the accuracy of the results was the same as that obtained by previously reported results for some specific cases using rigorous formulation. The algorithm developed in the present work is found to be numerically robust and simple so that it can be easily integrated with other simulations.