Laminar boundary layer, external flow

Acrivos, A., Shah, M. J., and Petersen, E. E., Momentum and heat transfer in laminar boundary-layer flows of non-Newtonian fluids past external surfaces, AIChE J., Vol. 6, No. 2, pp. 312-317, 1960. 

In electrochemical reactors, the externally imposed velocity is often low. Therefore, natural convection can exert a substantial influence. As an example, let us consider a vertical parallel plate reactor in which the electrodes are separated by a distance d and let us assume that the electrodes are sufficiently distant from the reactor inlet for the forced laminar flow to be fully developed. Since the reaction occurs only at the electrodes, the concentration profile begins to develop at the leading edges of the electrodes. The thickness of the concentration boundary layer along the length of the electrode is assumed to be much smaller than the distance d between the plates, a condition that is usually satisfied in practice. 

Some of the commonly used methods for obtaining solutions to problems involving laminar external flows have been discussed in this chapter. Many such problems can be treated with adequate accuracy using the boundary layer equations and similar ity integral and numerical methods of solving these equations have been discussed. A brief discussion of the solution of the full governing equations has also been presented. 

One approach to the solution of this equation is to assume that the pressure does not vary with v, and so it is specified by the external velocity distribution, v is computed from the continuity equation, leaving a differential equation in u to be integrated. However, this holds only for the laminar flow since turbulent boundary layers are inherently unsteady. The subsequent sections deal with the solutions of these equations in more detail. 

Consider two-dimensional steady-state mass transfer in the liquid phase external to a solid sphere at high Schmidt numbers. The particle, which contains mobile reactant A, dissolves into the passing fluid stream, where A undergoes nth-order irreversible homogeneous chemical reaction with another reactant in the liquid phase. The flow regime is laminar, and heat effects associated with the reaction are very weak. Boundary layer approximations are invoked to obtain a locally flat description of this problem. 

Much of the research activity in this area has related to heat transfer to inelastic non-Newtonian fluids in laminar flow in circular and non-circular ducts. In recent years, some consideration has also been given to heat transfer to/from non-Newtonian fluids in vessels fitted with coils and jackets, but little information is available on the operation of heat exchange equipment with non-Newtonian fluids. Consequently, this chapter is concerned mainly with the prediction of heat transfer rates for flow in circular tubes. Heat transfer in external (boundary layer) flows is discussed in Chapter 7, whereas the cooling/heating of non-Newtonian fluids in stirred vessels is dealt with in Chapter 8. First of all, however, the thermo-physical properties of the commonly used non-Newtonian materials will be described. 

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