Thermal boundary layer, definition

As with the velocity boundary layer, the thermal boundary layer is assumed to have a definite thickness, dr, and outside this boundary layer the temperature is assumed to be constant. 

The above definition of the lithosphere equates the lithosphere with a thermal boundary layer... 

Solving Eq. (S-58 numerically for the temperature profile for different Prandtl numbers, and using the definition of the thermal boundary layer, it is determined that 8/S, = Pr. Then the thermal boundary layer thickness becomes... 

In Fig. 12.1a it is assumed that the entire plate is heated and that both boundary layers start at the leading edge of the plate. If the first section of the plate is not heated and if the heat-transfer area begins at a definite distance Xq from the leading edge, as shown by line O B in Fig 12.16, a hydrodynamic boundary layer already exists at Xg, where the thermal boundary layer begins to form. 

If T terface and Tbuik replace Ca, equilibrium and Ca, bulks respectively, in the definition of the dimensionless profile P, and the thermal diffusiv-ity replaces a. mix. then the preceding equation represents the thermal energy balance from which temperature profiles can be obtained. The tangential velocity component within the mass transfer boundary layer is calculated from the potential flow solution for vg if the interface is characterized by zero shear and the Reynolds number is in the laminar flow regime. Since the concentration and thermal boundary layers are thin for large values of the Schmidt and Prandtl... 

Two definitions of the thickness S of the thermal boundary layer (but also of the boundary layer of concentration in mass transport and velocity in hydrodynamics) are mostly used ... 

As discussed in Chapters 2 and 3, in the integral method it is assumed that the boundary layer has a definite thickness and the overall or integrated momentum and thermal energy balances across the boundary layer are considered. In the case of flow over a body in a porous medium, if the Darcy assumptions are used, there is, as discussed before, no velocity boundary layer, the velocity parallel to the surface near the surface being essentially equal to the surface velocity given by the potential flow solution. For flow over a body in a porous medium, therefore, only the energy integral equation need be considered. This equation was shown in Chapter 2 to be ... 

In contrast, for experiments with liquid layers having a free surface, the boundary conditions have been somewhat less definite. In most of them, the solid surface could be described accurately in terms of boundary conditions (i)a, (ii)b, and (iii)a of Table III, while the upper surface could perhaps be described fairly well by means of (i)a and (ii)a however, experimental evidence may be cited which casts doubt on the appropriateness of both of these. The general thermal boundary condition, (iii)c, of which (iii)a and b are merely limiting cases, is usually required to complete the description of the free surface. 

Next we have to define the boundary and the initial conditions. For so called zero flux sensors there is no transport of any of the participating species across the sensor/enzyme layer boundary. Such condition would apply to, e.g., optical, thermal or potentiometric enzyme sensors. In that case the first space derivatives of all variables at point x are zero. On the other hand amperometric sensors would fall into the category of non-zero-flux sensors by this definition and the flux of at least one of the species (product or substrate) would be given by the current through the electrode. 

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