Forced Convection Flow of Power-Law Fluids Over a Flat Plate Embedded in a Darcy-Brinkman Porous Medium

Abstract

The steady forced convection flow of a power-law fluid over a horizontal plate embedded in a saturated Darcy-Brinkman porous medium is considered. The flow is driven by a constant pressure gradient. In addition to the convective inertia, also the "porous Forchheimer inertia" effects are taken into account. The pertinent boundary value problem is investigated analytically, as well as numerically by a finite difference method. It is found that far away from the leading edge, the velocity boundary layer always approaches an asymptotic state with identically vanishing transverse component. This holds for pseudoplastic (0 < n < 1), Newtonian (n = 1), and dilatant (n > 1) fluids as well. The asymptotic solution is given for several particular values of the power-law index n in an exact analytical form. The main flow characteristics of physical and engineering interest are discussed in the paper in some detail.Keywords Power-law fluids · Darcy-Brinkman medium · Porous inertia · Steady laminar flow · Asymptotic state · Exact solutions List of symbols C F Forchheimer coefficient Da Darcy number F Forchheimer number K permeability m 2 K * modified permeability m n+1 L length unit (m)

Prediction and verification for the models of temperature rising by medium bubbles in hydraulic system

“…When cavitation occurs in the hydraulic system, it may cause the problems for instance the instable pulsations of pressure and flow, the increases of noise and vibration, the slowness of response, the acceleration of oil degradation, etc. 2,3 During the processes of generation, development, and collapse of the bubbles, the thermal imbalance comes out as well, 4 which directly leads to the increase of temperature in the hydraulic oil. The oil temperature rise of hydraulic system caused by the process from bubble compression to collapse is one of the significant performances of bubble thermal effect.…”