Heat transfer boundary layers

This dimensionless group is recognized as the Prandtl number, which is currently used in heat transfer processes. This number is very important when the boundary layer theory is applied because it shows the relationship between the corresponding thickness of the heat transfer boundary layer and the hydrodynamic boundary layer [6.12]. 

J9A,mix in the expressions for 5c and Sc represents a diffusivity instead of a molecular transport property, one must replace a, mix by the thermal diffusivity 0 (= kidpCp, where p = density, Cp = specific heat, and kjc = thermal conductivity) to calculate the analogous heat transfer boundary layer thickness Sj and the Prandtl number [i.e., Pr = d/p)ja. In the creeping flow regime, where g 9) = I sine. 

The approximation in the equation of continuity introduces no error at the cylindrical interface, where r = R and rj = 1. This error increases as one moves farther away from the interface, because curvature becomes more important at larger r, yet the approximation under consideration neglects the effect of curvature. Hence, the maximum error introduced into the Equation of Continuity occurs at the outer edge of the mass and heat transfer boundary layers, where maximum — R + S nnd maximum — 1 T 9/R. At 0 = 7t j 2 S jR = 2.8 X 10, r maximiim —... 

Since a, mix appears everywhere in part (a) as a diffusivity, not a molecular transport properly, the corresponding heat transfer boundary layer thickness is calculated from the preceding equation via replacement of A,mix by a. 

Consider the locally flat description of heat transfer by convection and conduction from a hot plate to an incompressible fluid at high Peclet numbers with two-dimensional laminar flow in the heat transfer boundary layer adjacent to the hot surface. The tangential fluid velocity component Vx is only a function of position x parallel to the interface. 

Equation (17.28) holds if the mass transfer boundary layer is fully developed, which is verified for the following condition (see [22] for the case of the heat transfer boundary layer) ... 

Mass transfer from a surface to the gas-solid suspension is significantly higher than that for particle-free conditions. This increase is due to a possible reduction of the mass transfer boundary layer and an increase in the interstitial gas velocity when particles are present. The effect on heat transfer is even more significant as solid particles also act as heat carriers. 

Boundary layer mass transfer Boundary layer heat transfer... 

Boundary layei—mass transfer Boundary layer—heat transfer... 

The Schmidt number for the mass transfer is analogous to the Prandtl number for heat transfer. Its physical implication means the relative thickness of the hydrodynamic layer and mass-transfer boundary layer. The ratio of the velocity boundary layer (S) to concentration boundary layer (Sc) is governed by the Schmidt number. The relationship is given by... 

But before the virtues of the results and the approach are extolled, the method must be described in detail. Let us therefore return to a systematic development of the ideas necessary to solve transport (heat or mass transfer) problems (and ultimately also fluid flow problems) in the strong-convection limit. To do this, we begin again with the already-familiar problem of heat transfer from a solid sphere in a uniform streaming flow at sufficiently low Reynolds number that the velocity field in the domain of interest can be approximated adequately by Stokes solution of the creeping-flow problem. In the present case we consider the limit Pe I. The resulting analysis will introduce us to the main ideas of thermal (or mass transfer) boundary-layer theory. 

We now consider bar element, and the element length is f. Two nodes are denoted by i,j. The trial function of temperature field is linear distribution. Under the convective heat transfer boundary condition, the finite element basic equation of steady heat conduction in the three-layered composite plate is [8]... 

Answer Begin with the equation of continuity and the mass transfer equation in cylindrical coordinates with two-dimensional flow (i.e., Vr and vq) in the mass transfer boundary layer and no dependence of Ca on z because the length of the cylinder exceeds its radius by a factor of 100. Heat transfer results will be generated by analogy with the mass transfer solution. The equations of interest for an incompressible fluid with constant physical properties are... 

If the heat and mass transfer Peclet numbers are large, then it is reasonable to neglect molecular transport relative to convective transport in the primary flow direction. However, one should not invoke the same type of argument to discard molecular transport normal to the interface. Hence, diffusion and conduction are not considered in the X direction. Based on the problem description, the fluid velocity component parallel to the interface is linearized within a thin heat or mass transfer boundary layer adjacent to the high-shear interface, such that... 

Use the following boundary condition at the outer edge of the mass transfer boundary layer in the liquid phase Ca = 0 at r = t2. At the solid-liquid boundary where r = ri, Ca is given by its equilibrium solubility in the liquid. The thickness of the mass transfer boundary layer is T2 — n. Hint Think about your experience with heat transfer coefQcients because you have used the solution to this problem several times in the past in other courses that focus on heat transfer. 

The viscosity /j and density p used are the actual flowing mixture of solute A and fluid B. If the mixture is dilute, properties of the pure fluid B can be used. The Prandtl number c pjk for heat transfer is analogous to the Schmidt number for mass transfer. The Schmidt number is the ratio of the shear component for diffusivity pip to the diffusivity for mass transfer and it physically relates the relative thickness of the hydrodynamic layer and mass-transfer boundary layer. 

Figure 540 Schematic of fluid flowing over heated interface showing local conduction at interface and advection of heat through boundary layer. The sum of the molecular-level interaction conduction and heat transfer by bulk motion (advection) is terms the convection heat transfer.

Optical Imaging Lens resolution-can be sub-micron Limited to camera resolution, can be >1000 fps Lens field-of-view Yes—with a modified cell to allow optical access Accurate tool for flow for channel-level flow only. Catalyst layer images require alteration of the diffusion media and heat transfer boundary conditions. 

Heat and Mass Transfer Boundary Layers Temperature and Concentration Polarization Effects... 

Camera-Roda, G., Boi, C., Saavedra, A., and Sarti, G. C. (1994). Heat and mass transfer boundary layers in radial creeping flow. Int. J. Heat Mass Tranter 37, 2145. 

The relationship between heat transfer and the boundary layer species distribution should be emphasized. As vaporization occurs, chemical species are transported to the boundary layer and act to cool by transpiration. These gaseous products may undergo additional thermochemical reactions with the boundary-layer gas, further impacting heat transfer. Thus species concentrations are needed for accurate calculation of transport properties, as well as for calculations of convective heating and radiative transport. 

Another concept sometimes used as a basis for comparison and correlation of mass transfer data in columns is the Clulton-Colbum analogy (35). This semi-empirical relationship was developed for correlating mass- and heat-transfer data in pipes and is based on the turbulent boundary layer model... 

Third, design constraints are imposed by the requirement for controlled cooling rates for NO reduction. The 1.5—2 s residence time required increases furnace volume and surface area. The physical processes involved in NO control, including the kinetics of NO chemistry, radiative heat transfer and gas cooling rates, fluid dynamics and boundary layer effects in the boiler, and final combustion of fuel-rich MHD generator exhaust gases, must be considered. 

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