Heat transfer coefficient, boundary layer theory

Experimental data from various sources (C5, K2, G4, S16) were taken for comparison. Kauh (K2) determined the drying schedules for balsa wood slabs of various thicknesses (, j, f in.) at different wind velocities (100-124 ft/min). It was not possible to apply boundary-layer theory to calculate heat- and mass-transfer coefficients because the length of the slabs was not recorded. 

Garud s (G4) data on the drying of welding electrodes show agreement within 15%, (Fig. 12) although the critical moisture content was not known accurately. Whenever data were not sufficient to calculate heat-and mass-transfer coefficients by boundary-layer theory, initial drying rate data was used for the purpose. 

The convective heat transfer coefficient generally depends on conditions in the boundary layer, surface geometry, fluid motion, and thermodynamic and transport properties of the fluid. A thorough examination of the heat transfer coefficient theory and many examples are given by Bird et al [15], Kays and Crawford [71], Middleman [102] and Incropera and DeWitt [60]. 

The Colburn y-factor is another representation of the heat-transfer coefficient and arises from a boundary layer theory model. It is defined as... 

Boundary Layer Concept. The transfer of heat between a solid body and a liquid or gas flow is a problem whose consideration involves the science of fluid motion. On the physical motion of the fluid there is superimposed a flow of heat, and the two fields interact. In order to determine the temperature distribution and then the heat transfer coefficient (Eq. 1.14) it is necessary to combine the equations of motion with the energy conservation equation. However, a complete solution for the flow of a viscous fluid about a body poses considerable mathematical difficulty for all but the most simple flow geometries. A great practical breakthrough was made when Prandtl discovered that for most applications the influence of viscosity is confined to an extremely thin region very close to the body and that the remainder of the flow field could to a good approximation be treated as inviscid, i.e., could be calculated by the method of potential flow theory. 

Hence, the local mass transfer coefficient scales as the two-thirds power of a, mix for boundary layer theory adjacent to a solid-liquid interface, and the one-half power of A, mix for boundary layer theory adjacent to a gas-liquid interface, as well as unsteady state penetration theory without convective transport. By analogy, the local heat transfer coefficient follows the same scaling laws if one replaces a, mix in the previous equation by the thermal conductivity. 

Mass transfer coefficient (fe) A measure of the solute s mobility due to forced or natural convection in the system. Analogous to a heat transfer coefficient, it is measured as the ratio of the mass flux to the driving force. In membrane processes the driving force is the difference in solute concentration at the membrane surface and at some arbitrarily defined point in the bulk fluid. When lasing the film theory to model mass transfer, k is also defined as D/S, where D is solute diffusivity and d is the thickness of the concentration boundary layer. 

The cooling heat transfer of the electrical heater can be treated like cooling a plate on one side in surface flow. Here, the influence of the surrounding channel walls is neglected for simplicity. With the help of the boundary layer theory, the wall heat transfer is described by the dimensionless heat transfer coefficient, the local Nusselt number Nu [7] ... 

The classical approach to analysis of this problem still relies on Eq. (1). Consider the cooling of a solid surface by a fluid. One hypothesizes a stagnant film of the fluid that possesses all the fluid-phase resistance to heat transfer. The properties of the fluid and the thickness of the film determine the magnitude of the resistance. Boundary-layer theory enables estimation of various film thicknesses, but normal engineering practice is based on the use of individual coeflflcients that are empirically determined. Thus, the local individual coefficient for the film at a surface is defined by the Newton relation... 

The theory of Jephson (1) assumes a perfect scraping of the barrel surface by the screw flight. In practice a gap exists between the flight and the barrel wall. Therefore a layer of material remains at the wall with a thickness, approximately equal to the flight clearance (8/) that forms an extra thermal resistance to heat transfer. Janeschitz-Kriegl et al. (3) solved this problem by adjusting the boundary conditions for the Jephson model. They assumed a linear variation of temperature over the remaining layer of material from the wall temperature to the bulk temperature and derived for the heat transfer coefficient ... 

High mass transfer rates will influence not only the mass transfer coefficient but also the heat transfer coefficients and friction factor. Analysis of film theory penetration theory and boundary layer theory (21) show that the relation of the various coefficients at high (k ) and low mass transfer (kj ) can be given by 0 s ... 

---