No Arabic abstract
In present analysis, nanofluid transport near to a stagnation region over a bidirectionally deforming surface is scrutinized. The region is embedded with Darcy-Forchheimer medium which supports permeability. The porous matrix is suspended with nanofluid, and surface is under the influence of inconsistent heat source/sink. Using similarity functions, framed governing equations are switched to a collection of ordinary differential equations. Output is procured via optimal homotopy asymptotic method (OHAM). Basic notion of OHAM for a vector differential set-up is presented along with required convergence theorems. At different flow stagnation strengths, nanofluid behavior is investigated with respect to variations in porosity parameter, Forchheimer number, Brownian motion, stretching ratio, thermophoretic force, heat source/sink and Schimdt number. Stagnation flow strength invert the pattern of boundary layer profiles of primary velocity. Heat transfer has straightforward relation with Forchheimer number when stagnation forces dominate stretching forces
Viscoelastic flows through porous media become unstable and chaotic beyond critical flow conditions, impacting industrial and biological processes. Recently, Walkama textit{et al.} [Phys. Rev. Lett. textbf{124}, 164501 (2020)] have shown that geometric disorder greatly suppresses such chaotic dynamics. We demonstrate experimentally that geometric disorder textit{per se} is not the reason for this suppression, and that disorder can also promote choatic fluctuations, given a slightly modified initial condition. The results are explained by the effect of disorder on the occurrence of stagnation points exposed to the flow field, which depends on the initially ordered geometric configuration.
In this article we consider the linear stability of the two-dimensional flow induced by the linear stretching of a surface in the streamwise direction. The basic flow is a rare example of an exact analytical solution of the Navier-Stokes equations. Using results from a large Reynolds number asymptotic study and a highly accurate spectral numerical method we show that this flow is linearly unstable to disturbances in the form of Tollmien-Schlichting waves. Previous studies have shown this flow is linearly stable. However, our results show that this is only true for G{o}rtler-type disturbances.
The mixing effectiveness, i.e., the enhancement of molecular diffusion, of a flow can be quantified in terms of the suppression of concentration variance of a passive scalar sustained by steady sources and sinks. The mixing enhancement defined this way is the ratio of the RMS fluctuations of the scalar mixed by molecular diffusion alone to the (statistically steady-state) RMS fluctuations of the scalar density in the presence of stirring. This measure of the effectiveness of the stirring is naturally related to the enhancement factor of the equivalent eddy diffusivity over molecular diffusion, and depends on the Peclet number. It was recently noted that the maximum possible mixing enhancement at a given Peclet number depends as well on the structure of the sources and sinks. That is, the mixing efficiency, the effective diffusivity, or the eddy diffusion of a flow generally depends on the sources and sinks of whatever is being stirred. Here we present the results of particle-based simulations quantitatively confirming the source-sink dependence of the mixing enhancement as a function of Peclet number for a model flow.
In this chapter, we analyze the steady-state microscale fluid--structure interaction (FSI) between a generalized Newtonian fluid and a hyperelastic tube. Physiological flows, especially in hemodynamics, serve as primary examples of such FSI phenomena. The small scale of the physical system renders the flow field, under the power-law rheological model, amenable to a closed-form solution using the lubrication approximation. On the other hand, negligible shear stresses on the walls of a long vessel allow the structure to be treated as a pressure vessel. The constitutive equation for the microtube is prescribed via the strain energy functional for an incompressible, isotropic Mooney--Rivlin material. We employ both the thin- and thick-walled formulations of the pressure vessel theory, and derive the static relation between the pressure load and the deformation of the structure. We harness the latter to determine the flow rate--pressure drop relationship for non-Newtonian flow in thin- and thick-walled soft hyperelastic microtubes. Through illustrative examples, we discuss how a hyperelastic tube supports the same pressure load as a linearly elastic tube with smaller deformation, thus requiring a higher pressure drop across itself to maintain a fixed flow rate.
Channel formation and branching is widely seen in physical systems where movement of fluid through a porous structure causes the spatiotemporal evolution of the medium in response to the flow, in turn causing flow pathways to evolve. We provide a simple theoretical framework that embodies this feedback mechanism in a multi-phase model for flow through a fragile porous medium with a dynamic permeability. Numerical simulations of the model show the emergence of branched networks whose topology is determined by the geometry of external flow forcing. This allows us to delineate the conditions under which splitting and/or coalescing branched network formation is favored, with potential implications for both understanding and controlling branching in soft frangible media.