Laminar heat transfer external flow

The laminar heat transfer coefficient for flow over a flat plate is the most-often-used expression for computing external-flow heat transfer. The flat plate, which can be a substrate or a package heated over its entire sm-face, has a Nusselt number ... 

The purpose of this chapter is to illustrate some of the ways in which the equations derived in the previous chapter can be used to obtain heat transfer rates for situations involving external laminar flows. External flows involve a flow, which is essentially infinite in extent, over the outer surface of a body as shown in Fig. 3.1. 

As with external mixed convection, the influence of buoyancy forces on the flow depends on the angle that the buoyancy forces makes to the direction of the forced flow. The heat transfer rate also, of course, depends on the duct cross-sectional shape as well as on whether the flow is laminar or turbulent. 

B Develop an intuitive understanding of friction drag and pressure drag, and evaluate the average drag and convection coefficients in external flow, a Evaluate the drag and heat transfer associated with flow over a flat plate for both laminar and turbulent flow,... 

Film condensation on a horizontal tube. For a curvilinear surface, in particular, for a horizontal circular cylinder along which a condensate film flows, the angle 6 is a nonconstant variable. By taking into account the fact that 6(6) d, where d is the diameter of a circular cylinder, and proceeding by analogy with (5.7.7), one can readily obtain the following formula for the heat transfer coefficient averaged over the external surface of the tube provided that the flow in the condensate film is laminar [200] ... 

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. 

Vertical Surfaces. If the laminar flow direction is downward and gravity-controlled, heat transfer coefficient for internal condensation inside vertical tubes can be predicted using the correlations for external film condensation—see Table 17.23. The condensation conditions usually occur under annular flow conditions. Discussion of modeling of the downward internal convective condensation is provided in Ref. 76. 

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. 

In this entry the effect of the viscous heating in microchannels is highlighted by means of two examples. First of all, a steady-state liquid flow in the laminar regime through a microchannel with an imposed constant linear heat flux at the walls q is considered (HI boundary condition see Convective Heat Transfer in Microchannels ). Then, the case of a steady-state liquid flow in the laminar regime through a microchannel with an axially constant outer wall temperature, while the wall heat flux is linearly proportional to the difference between the external temperature and the wall temperature, is considered. This is the case of a microchannel cooled by convection of an external fluid (T3 botmdary condition see Convective Heat Transfer in Microchannels ). 

Acrivos, A. 1958. Combined laminar free and forced convection heat transfer in external flows. AIChE Journal. 4. 285-289. 

External Natural Flow for Various Geometries For vertical walls, Churchill and Chu [Inf. J. Heat Mass Transfer, 18,1323 (1975)] recommend, for laminar and turbulent flow on isothermal, vertical walls with height L,... 

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. 

The /th species mass flux, j, and the total heat flux, q, can be expressed in terms of transfer coefficients. This is useful in situations where the liquid or gas phase is not completely resolved, or when the flow conditions are not exactly known. Often, these transfer coefficients are determined experimentally for a particular flow situation. For instance, different expressions are used, depending on whether the transfer is due to pure conduction or whether it is dominated by ccaivection. Also, the type of convection plays a role, that is, if the convection is forced or non-forced. A forced convection has a non-zero relative velocity between droplet and environment, whereas for a non-forced convection, the relative drop-gas velocity is zero and only the Stefan flow dominates. Note that the natural convection due to gravity is taken to be zero since gravity is an external force, and external forces are neglected in this article. In addition, in forced convection, the nature of the flow, that is, whether the flow is laminar or turbulent, plays an important role. These issues will be discussed in more detail in the following subsections. 

Derive steady-state and nonsteady-state mass and energy balances for a catalyst monolith channel in which several chemical reactions take place simultaneously. External and internal mass transfer limitations are assumed to prevail. The flow in the chaimel is laminar, but radial diffusion might play a role. Axial heat conduction in the solid material must be accounted for. For the sake of simplicity, use cylindrical geometry. Which numerical methods do you recommend for the solution of the model ... 

The specialized literature, and especially Paul et al. [4], provide details on close-clearance impellors (for example, anchors and helical ribbons) and correlations suitable for deep laminar flow. As a generalization, heat and mass transfer to the external environment is very low in such devices. However, it is usually possible to achieve a sufficiently high circulation rate in the vessel for the tank to be reasonably well mixed. 

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