Heat transfer large Reynolds number

The results of our tentative calculations [formulas (41)—(43)] of the distance at which a stabilized regime is established and the braking and heat transfer cover the entire cross-section show the opposite whereas in the stabilized flow the dependence on the Reynolds number disappears, the distance at which this stabilization occurs is very strongly dependent on the Reynolds number. At our large Reynolds numbers, long before stabilization, at a distance of 5 105d/Re turbulization of the boundary layer takes place. 

Chapter I I Heat and Mass Transfer at Large Reynolds Number... 

We saw in Chapter 10 that the boundary-layer structure, which arises naturally in flows past bodies at large Reynolds numbers, provides a basis for approximate analysis of the flow. In this chapter, we consider heat transfer (or mass transfer for a single solute in a solvent) in the same high-Reynolds-number limit for problems in which the velocity field takes the boundary-layer form. We saw previously that the thermal energy equation in the absence of significant dissipation, and at steady state, takes the dimensionless form... 

Figure 11-2. The temperature profile for heat transfer from a horizontal flatplate at large Reynolds number (large Peclet number) for several values of the Prandtl number, 0.01 < Pr < 100.

Equation 56 states that when the Brinkman number increases, the Nusselt number decreases in other words, the viscous dissipation tends to reduce significantly the value of the convective heat transfer at large Reynolds numbers when the hydraulic diameter decreases. On the contrary, for low values of the Reynolds number, the mean value of the Nusselt number coincides theoretically with the fully developed value of the Nusselt number because the entrance region is very short and the effects of the viscous dissipation are unimportant in this region. 

Heat Transfer In general, the fluid mechanics of the film on the mixer side of the heat transfer surface is a function of what happens at that surface rather than the fluid mechanics going on around the impeller zone. The impeller largely provides flow across and adjacent to the heat-transfer surface and that is the major consideration of the heat-transfer result obtained. Many of the correlations are in terms of traditional dimensionless groups in heat transfer, while the impeller performance is often expressed as the impeller Reynolds number. 

If the surface over which the fluid is flowing contains a series of relatively large projections, turbulence may arise at a very low Reynolds number. Under these conditions, the frictional force will be increased but so will the coefficients for heat transfer and mass transfer, and therefore turbulence is often purposely induced by this method. 

Fluid flow and reaction engineering problems represent a rich spectrum of examples of multiple and disparate scales. In chemical kinetics such problems involve high values of Thiele modulus (diffusion-reaction problems), Damkohler and Peclet numbers (diffusion-convection-reaction problems). For fluid flow problems a large value of the Mach number, which represents the ratio of flow velocity to the speed of sound, indicates the possibility of shock waves a large value of the Reynolds number causes boundary layers to be formed near solid walls and a large value of the Prandtl number gives rise to thermal boundary layers. Evidently, the inherently disparate scales for fluid flow, heat transfer and chemical reaction are responsible for the presence of thin regions or "fronts in the solution. 

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