Unsteady heat transfer behavior

The model based on the concept of pure limiting film resistance involves the steady-state concept of the heat transfer process and omits the essential unsteady nature of the heat transfer phenomena observed in many gas-solid suspension systems. To take into account the unsteady heat transfer behavior and particle convection in fluidized beds, a surface renewal model can be used. The model accounts for the film resistance adjacent to the heat transfer... 

An accurate design of unsteady-state catalytic processes requires knowledge about the catalyst behavior and reaction kinetics under unsteady-state conditions, unsteady-state mass and heat transfer processes in the catalyst particle and along the catalyst bed, and dynamic phenomena in the catalytic reactor. New approaches for reactor modeling and optimization become necessary. Together, these topics form a wide area of research that has been continuously developed since the 1960s. 

Arrays of Cylinders. The heat transfer behavior of a tube in a bank differs considerably from that of a single tube immersed in a flow of infinite extent. The presence of adjacent tubes in an array and the turbulence and unsteadiness generated by upstream tubes generally tend to increase the overall heat transfer from a particular tube. After the flow has passed through several rows of tubes, however, the heat transfer from individual tubes becomes independent of their location and just a function of the Reynolds number with a parametric dependence on the array geometry. Average and local heat transfer data for tube banks have been summarized by Zukauskas [67],... 

Free-Stream Turbulence and Unsteadiness. It was shown in Fig. 6.27 that the free-stream turbulence level significantly affects local and overall heat transfer from single cylinders in cross flow. This is caused primarily by early transition of the laminar boundary layer on the forward portion of the cylinder and subsequently by delayed separation of the turbulent boundary layer from the surface of the cylinder. Free-stream turbulence and unsteadiness also affect, to varying degrees, the heat transfer behavior of a turbulent boundary layer in the absence of transition-point shift and separation. 

In general, it can be concluded that substantial progresses have been made in the experimental and theoretical analysis of trickle-bed reactors under unsteady-state conditions. But until now these results are not sufficient for a priori design and scale-up of a periodically operated trickle-bed reactor. The mathematical reactor models, which are now available are not detailed enough to simulate all of the main transient behavior observed. For solving this problem specific correlations for specific model parameters (e.g. Hquid holdup, mass transfer gas-solid and liquid-solid, intrinsic chemical kinetic, etc.) determined under dynamic conditions are required. The available correlations for important hydrodynamic, mass-and heat-transfer parameters for periodically operated trickle-bed reactors leave a lot to be desired. Indeed, work for unsteady-state conditions on a larger scale may also be necessary. 

In the theoretical treatment, the heat- and mass-transfer processes shown in Fig. 6 were considered. Simultaneous solution of the equations describing the behavior of the unsteady-state reaction system permits the temperature history of the propellant surface to be calculated from the instant of oxidizer propellant contact to the runaway reaction stage. 

As a rule, mathematical models of unsteady-state processes cannot be formulated by simple addition of time derivatives to the equations describing the steady-state behavior of the reaction system. They relate both to the reaction kinetics as well as to the heat and mass transfer processes. For example, modeling of unsteady-state processes in a fixed bed reactor requires accounting for the processes of heat and mass transfer between the catalyst surface and the bulk of gas phase, although for steady-state operation these factors can be neglected. 

A wide class of forced unsteady-state processes have already been realized on the commercial scale using specific dynamic phenomenon, that takes place during performance of an exothermic reaction in a fixed bed of catalyst. This phenomenon is referred to in the literature as wrong-way behavior of a fixed bed reactor [20]. Substantial differences in characteristic times of heat and mass transfer in a packed bed reactor result in a surprising rise of temperature inside the reactor after... 

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