Turbulent heat transfer external flow

In forced convection, circulating currents are produced by an external agency such as an agitator in a reaction vessel or as a result of turbulent flow in a pipe. In general, the magnitude of the circulation in forced convection is greater, and higher rates of heat transfer are obtained than in natural convection. 

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. 

Fig. 24.6. Inside an acid cooler. Fig. 9.5 gives an external view. Tubes start through the tube sheet , shown here. They extend almost to the far end of the cooler where there is another tube sheet . Cool water enters at this end and flows through the tubes to the far end. Between the tube sheets , the tubes are surrounded by warm acid moving turbulently around them. Heat transfers from the warm acid to the cool water (through the tube walls). The tube entering from the right contains a thermocouple. The polymer tubes in the foreground surround metal rods. The rods are bare between the tube sheets. An electrical potential applied between them and the water tubes anodically protects the tubes against acid side corrosion.

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,... 

Advantages of three-phase fluidized beds over trickle beds and other fixed bed systems are temperature uniformity, high heat transfer, ability to add and remove catalyst particles continuously, and limited mass transfer resistances (both external to the particles and bubbles, because of turbulence and limited bubble size, and inside the particles owing to relatively small particle diameters). Disadvantages include substantial axial dispersion (of gas, liquid, and particles), causing substantial deviations from plug flow, and lack of predictability because of the complex hydrodynamics. There are two major applications of gas-liquid-solid-fluidized beds biochemical processes and hydrocarbon processing. 

In many industrially important situations, it is impossible to maintain geometric, mechanical (kinematic/hydrodynamic and turbulence similarities), and thermal similarities simultaneously. Consider a stirred tank reactor with heat exchange only through a jacket on its external surface. The jacket heat transfer area to vessel volume ratio is proportional to (l/T). Evidently, with scale-up, this ratio decreases, and it is difficult to maintain the same heat transfer area per unit volume as in the small-scale unit. Additional heat transfer area is required to cater to the extra heat load resulting from increase in reactor volume. This area can be provided in the form of a coil inside the reactor or an external heat exchanger circuit. In both cases, the flow patterns are significantly different than the model contactor used in bench-scale studies and kinematic similarity is violated. This is the classic dilemma of a chemical engineer it is impossible to preserve the different types of similarities simultaneously. 

In the case of airlift reactors, the flow pattern may be similar to that in bubble columns or closer to that two-phase flow in pipes (when the internal circulation is good), in which case the use of suitable correlations developed for pipes may be justified [55]. Blakebrough et al. studied the heat transfer characteristics of systems with microorganisms in an external loop airlift reactor and reported an increase in the rate of heat transfer [56], In an analytical study, Kawase and Kumagai [57] invoked the similarity between gas sparged pneumatic bioreactors and turbulent natural convection to develop a semi-theoretical framework for the prediction of Nusselt number in bubble columns and airlift reactors the predictions were in fair agreement with the limited experimental results [7,58] for polymer solutions and particulate slurries. 

With an effective thermal model of the cells, modules and overall system, an analysis of the performance under different situations and load conditions can be evaluated. This proves to be a very useful tool in the development of the pack as these thermal models can be input into computational fluid dynamic (CFD) models to determine how the cells will heat during operation. A good CFD model can be used to determine flow rates, turbulence, and heat transfer within a pack. In addition, it is possible to use a lumped parameter model to develop a simplified model where the external parameters are basically ignored and the model is designed using fully adjustable parameters to do high-level evaluations of the thermal effectiveness of a system. 

The Sherwood number can be viewed as describing the rabo of convective to diffusive transport and finds its counterpart in heat transfer in the form of the Nusselt number. It is high ( 1) when flow is turbulent or the boundary layer "film" is very thin. The Biot number has the same form as the Sherwood number but refers to two adjacent phases or media. In one of these, which we term internal, transport is usually by diffusion. This can be in a gas bubble, a liquid drop, a porous solid parbcle, or some other enbty. The adjacent ("external") phase is a liquid or a gas in relative motion to the particle and has an attendant "film resistance." Like the Sherwood number, Bi is high ( 1) when the external phase is in turbulent motion (caused, for example, by stirring) or the boxmdary layer is very thin. We will have more to say about it in Illustration 5.1. 

In the present eonfiguration, air inlet boundaries are assumed to be Pressure Inlet while outflow boundaries are assumed Pressure Outlet . Pressure inlet boundary conditions were used to define the total pressure and other scalar quantities at flow inlets. Pressure outlet boundary conditions were used to define the static pressure at flow outlets. At the nozzle inlet, the air pressure was varied. At the nozzle outlet, the pressure was supposed to be the external pressure (one atmosphere). At the wall of the nozzle standard wall function boundary condition was applied. Although the high velocity of air stream was a heat source that will increase the temperature in the nozzle, the nozzle length was very short and the process oecurs in a very short time. For simplification, it was assumed that the process is adiabatic i.e. no heat transfer occurred through walls. The flow model used was viscous, compressible airflow [1, 6-10]. The following series of equations were used to solve a compressible turbulent flow for airflow simulation [1,6-12] ... 

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,... 

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