Viscous-convective regime

The distribution of a decaying scalar field advected by a turbulent flow was studied by Corrsin (1961) who generalized the Obukhov-Corrsin theory of passive scalar turbulence for the linear decay problem F(C) = S(x) — bC. As in the case of the passive non-decaying scalar field, depending on the length scales considered, one can identify inertial-convective and viscous-convective regimes with qualitatively different characteristics. 

Gases are likely to be in the dispersion regime, not the pure convection regime. Liquids can well be in one regime or another. Very viscous liquids such as polymers are likely to be in the pure convection regime. If your system falls in the no-man s-land between regimes, calculate the reactor behavior based on... 

In this lecture, a variety of results for convective heat transfer in microtubes and microchannels in the slip flow regime under different conditions have been presented. Both constant wall temperature and constant wall heat flux cases have been analyzed in microtubes, including the effects of rarefaction, axial conduction, and viscous dissipation. In rough microchannels the abovementioned effects have also been investigated for the constant wall temperature boundary condition. Then, temperature-variable dynamic viscosity and thermal conductivity of the fluid were considered, and the results were compared with constant property results for microchannels, with the effects of rarefaction and viscous dissipation. 

It is also essential that the period of the ac stimulus not be so long that convection becomes a factor within a few cycles. The lower frequency limit was set here at 1 Hz because convection would become a problem in the range of several seconds in most liquid systems with water-like viscosity. Current equipment for EIS can operate at much lower frequencies (as low as 10 jU,Hz) and can be usefully applied in the low-frequency (long-time) regime when the processes being examined are not controlled by convection. Examples include transport or reaction at a solid-solid interfaces or diffusion and reaction in extremely viscous media, such as glasses or polymers. 

In the limit of vanishingly small Reynolds numbers, forces due to convective momentum flux are negligible relative to viscous, pressure, and gravity forces. Equation (12-4) is simplified considerably by neglecting the left-hand side in the creeping flow regime. For fluids with constant /r and p, the dimensionless constitutive relation between viscons stress and symmetric linear combinations of velocity gradients is... 

In this entry the effect of the viscous heating in microchannels is highlighted by means of two examples. First of all, a steady-state liquid flow in the laminar regime through a microchannel with an imposed constant linear heat flux at the walls q is considered (HI boundary condition see Convective Heat Transfer in Microchannels ). Then, the case of a steady-state liquid flow in the laminar regime through a microchannel with an axially constant outer wall temperature, while the wall heat flux is linearly proportional to the difference between the external temperature and the wall temperature, is considered. This is the case of a microchannel cooled by convection of an external fluid (T3 botmdary condition see Convective Heat Transfer in Microchannels ). 

The heat transfer in microchannels is expected to agree with conventional theory provided that the discussed continuum assumptions can be made. For example, under fully developed laminar flow conditions at low Re, Nu is constant. However, many experimental data show large deviations between each other and inconsistency with classical theory exists. There is an increase in Nu with increasing Re measured. According to Herwig and Hausner [37], a common theoretical basis on forced convection for macro- and microchannels can be used to describe forced convection of liquids in the laminar regime. However, there are effects which are more pronounced and which are of more importance on the microscale, such as surface tension, viscous forces and electrostatic forces [38]. These effects are called scaling effects with respect to standard macroscale analysis. 

In order to study the forced convection of liquids in the laminar regime a common theoretical basis for macro- and microflows can be used nevertheless, certain effects can be of different importance for microsystems if compared with macrosystems. These effects can be defined as scaling effects with respect to a standard macroanalysis. At the microscale, since different forces have different length dependences, the surface forces (like surface tensions, viscous forces or electrostatic forces) become more important and even dominant as the scale is reduced. Tscous heating, like pressure drop, tends to increase dramatically when the dimensions of tnicrochannels are decreased. 

Singh, R, Gupta, C.B., 2005. MHD free convective flow of viscous fluid through a porous medium bounded by an oscillating porous plate in slip flow regime with mass transfer. Indian J. Theor. Phys. 53, 111 120. 

Solving this flow model for the velocity the pressure is calculated from the ideal gas law. The temperature therein is obtained from the heat balance and the mixture density is estimated from the sum of the species densities. It is noted that the viscous velocity is normally computed from the pressure gradient by use of a phenomenologically derived constitutive correlation, known as Darcy s law, which is based on laminar shear flow theory [139]. Laminar shear flow theory assumes no slip condition at the solid wall, inducing viscous shear in the fluid. Knudsen diffusion and slip flow at the solid matrix separate the gas flow behavior from Darcy-type flow. Whenever the mean free path of the gas molecules approaches the dimensions of pore diameter, the individual gas molecules are in motion at the interface and contribute an additional flux. This phenomena is called slip flow. In slip flow, the layer of gas next to the surface is in motion with respect to the solid surface. Strictly, the Darcy s law is valid only when the flow regime is laminar and dominated by viscous forces. The theoretical foundation of the dusty gas model considers that the model is applied to a transition regime between Knudsen and continuum bulk diffusion. To estimate the combined flux, the model is based on the assumption that the combined flux can be expressed as a linear sum of the Knudsen flux and the convective flux due to laminar flow. 

---