Convective fluid, dynamic viscosity

Convective heat transmission occurs within a fluid, and between a fluid and a surface, by virtue of relative movement of the fluid particles (that is, by mass transfer). Heat exchange between fluid particles in mixing and between fluid particles and a surface is by conduction. The overall rate of heat transfer in convection is, however, also dependent on the capacity of the fluid for energy storage and on its resistance to flow in mixing. The fluid properties which characterize convective heat transfer are thus thermal conductivity, specific heat capacity and dynamic viscosity. 

Viscous dissipation. The mixing efficiency of a viscous fluid is related to the viscous dissipation d> since = t D = 2r] D D where 17 is the dynamic viscosity. Maps of viscous dissipation can, therefore, be used to qualitatively predict the differences in mixing efficiency between different regions of the mantle, or between different models of mantle convection (Figure 10). 

Experience shows that convection heal transfer strongly depends on the fluid properties dynamic viscosity p., thermal conductivity k, density p, and specific heat c, as well as the fluid velocity V. It also depends on the geometry and the roughness of the solid surface, in addition to the type of fluid flow (such as being streamlined or turbulent). Thus, we expect the convection heat transfer relations to be rather complex because of the dependence of convection on so many variables. This is not surprising, since conveclion is die most complex mechanism of heat transfer. 

Here, k, Cp, p, and p are, respectively, the thermal conductivity, specific heat at constant pressure, density, and dynamic viscosity of the convective fluid V is the relative velocity between fluid and solid and L is a geometry dependent, characteristic length dimension for the system. Note that the Pr is composed exclusively of fluid properties and that the Re will increase in direct proportion to the relative velocity between fluid and solid surface. Example applications are shown in Fig. 2. 

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. 

Although these eddy diffusivities act in the same manner as the kinematic viscosity and thermal diffusivity in laminar flow, the critical difference is that the eddy diffusivities are not properties of the fluid but are dependent largely on the dynamic behavior of the fluid motion. In this section the fluid dynamic bases for evaluating these eddy diffusivities are given. They will then be used in a variety of convective heating situations to yield formulas useful in engineering computations. 

For non-Newtonian fluids the viscosity p is fitted to flow curves of experimental data. The models for this fit are discussed in the next chapter. The energy equation is also implemented in the code and can be used for temperature-dependent problems, but it is not needed for the simulation of fluid dynamic problems like jet breakup due to the uncoupling of the density in the incompressible formulation. The finite volume scheme uses the Marker and Cell (MAC) method to discretize the computational domain in space. The convective and diffusive terms are discretized with second-order accuracy and the fluxes are calculated with a Godunov-type scheme. 

Under plug flow conditions the convective transport is completely dominant over the diffusive mass transport term. The fluid moves like a plug and the diffusive term can be neglected. The conditions for plug flow are closely satisfied for narrow and long tubular reactors when the viscosity is low. However, this approximation is clearly best for fully developed turbulent flow, for which the velocity profiles are relatively fiat. For dynamic conditions, the species mass balance is a PDF with z and t as the independent variables. The Eulerian species mass balance (1.301) reduces further to ... 

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