Heat and Mass Transfer at Large Reynolds Number

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 

In Chap. 9, we considered the solution of this equation in the limit Re 1, where the velocity distribution could be approximated by means of solutions of the creeping-flow equations. When Pe 1, we found that the fluid was heated (or cooled) significantly in only a very thin thermal boundary layer of 0(Pe l/3) in thickness, immediately adjacent to the surface of a no-slip body, or () Pe l/2) in thickness if the surface were a slip surface with finite interfacial velocities. We may recall that the governing convection di ffusion equation for mass transfer of a single solute in a solvent takes the same form as (111) except that 6 now stands for a dimensionless solute concentration, and the Peclet number is now the product of Reynolds number and Schmidt number, 

In this chapter, we consider heat transfer from heated (or cooled) bodies in the dual limit Re 1 and Pe l.1 For simplicity, we restrict most of the discussion to solid bodies with 

Although the dependence of the thermal boundary-layer thickness on the independent parameters Re and Pr (or Pe) remains to be determined, we may anticipate that the magnitudes of Re and Pe will determine the relative dimensions of the two boundary layers. If Pe yp Re yp 1, both the momentum and thermal layers will be thin, but it seems likely that the thermal layer will be much the thinner of the two. Likewise, if Pe Pe 1, we can guess that the momentum boundary layer will be thinner than the thermal layer. In the analysis that follows in later sections of this chapter, we consider both of the asymptotic limits Pr — oc (Pe yy Re y D and Pr 0 (Re yy Pe p 1). We shall see that the relative dimensions of the thermal and momentum layers, previously anticipated on purely heuristic grounds, will play an important and natural role in the theory. 

---

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

Effective mass and heat transfer between gas and catalyst phase. Because the BSR geometry induces transition to turbulent flow at relatively low Reynolds numbers (as low as 500), mass and heat transfer between gas and catalyst phase is faster than in monolithic reactors. This is because the flow in a monolithic reactor is usually laminar. The advantage of the BSR can be exploited in processes with a large heat effect, where heat transfer through the film layer is generally more important than intraparticle heat and mass transfer. 

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. 

---