Heat transfer coefficient pseudo

A pseudo-convective heat-transfer operation is one in which the heating gas (generally air) is passed over a bed of solids. Its nse is almost exchisively limited to drying operations (see Sec. 12, tray and shelf dryers). The operation, sometimes termed direct, is more aldu to the coudnctive mechanism. For this operation, Tsao and Wheelock [Chem. Eng., 74(13), 201 (1967)] predict the heat-transfer coefficient when radiative and conductive effects are absent by... 

The One-Dimensional Pseudo Homogeneous Model of Fixed Bed Reactors. The design of tubular fixed bed catalytic reactors has generally been based on a one-dimensional model that assumes that species concentrations and fluid temperature vary only in the axial direction. Heat transfer between the reacting fluid and the reactor walls is considered by presuming that all of the resistance is contained within a very thin boundary layer next to the wall and by using a heat transfer coefficient based on the temperature difference between the fluid and the wall. Per unit area of the tube... 

The first type of model considers the heat transfer surface to be contacted alternately by gas bubbles and packets of closely packed particles. This leads to a surface renewal process whereby heat transfer occurs primarily by transient conduction between the heat transfer surface and the particle packets during their time of residence at the surface. Mickley and Fairbanks (1955) provided the first analysis of this renewal mechanism. Treating the particle packet as a pseudo-homogeneous medium with solid volume fraction, e, and thermal conductivity (kpa), they solved the transient conduction equation to obtain the following expression for the average heat transfer coefficient due to particle packets,... 

Control of an evaporator requires more than proper instrumentation. Operator logs should reflect changes in basic characteristics, as by use of pseudo heat-transfer coefficients, which can detect obstructions to heat flow, hence to capacity. These are merely the ratio of any convenient measure of heat flow to the temperature drop across each effect. Dilution by wash and seal water should be monitored since it absorbs evaporative capacity. Detailed tests, routine measurements, and operating problems are covered more fully in Testing Procedure for Evaporators (loc. cit.) and by Standiford [Chem. Eng. Prog., 58(11), 80 (1962)]. 

Heat transfer in bubble column slurry reactors was studied by Kolbel and coworkers (75-77) and Deckwer et al. (13). The addition of solids increases the wall-to--suspension heat transfer coefficient. However, this increase is only due to changes in the physico-chemical properties and represents no independent contribution of the particles. Therefore, the heat transfer model, i.e. eqn. (17), developed by Deckwer (<53) for two-phase BCR also applies to slurry reactors as was proved for particle sizes up to 120 yum. This confirms that solids and liquid in the slurry can be regarded as a pseudo-homogeneous phase provided the gas velocity is large enough to provide for complete fluidization of the particles. 

The choice of a model to describe heat transfer in packed beds is one which has often been dictated by the requirement that the resulting model equations should be relatively easy to solve for the bed temperature profile. This consideration has led to the widespread use of the pseudo-homogeneous two-dimensional model, in which the tubular bed is modelled as though it consisted of one phase only. This phase is assumed to move in plug-flow, with superimposed axial and radial effective thermal conductivities, which are usually taken to be independent of the axial and radial spatial coordinates. In non-adiabatic beds, heat transfer from the wall is governed by an apparent wall heat transfer coefficient. ... 

A significant shift of the reference temperature to higher values, as it is represented by the heat removal line , results in operating conditions which may be called pseudo adiabatic. Each operating point shows runaway behaviour. A comparable situation is obtained if the reference temperature is kept constant but the heat transfer coefficient or area is reduced significantly. Both changes to lower values reduce the slope of the heat removal line with the consequence of an elimination of all intersections. 

Androver, Lopez, Borio, and Pedemera (2009) used a one-dimensional pseudo-homogeneous model for the WGS reaction in an MR with the scope of simulating the steady-state operation by neglecting dispersion effects. Different variables such as temperarnre, the heat transfer coefficient, and the countercurrent mode of sweep... 

Fix-bed reactor is a typical reactor in FTS process, which is firsdy applied in industrial FTS process. As early as 1979, Atwood and Bennett (Albal et al., 1984) have built a 0.25 bilHon c.f/d syngas management FT tubular reactor one-dimensional pseudo homogeneous piston flow model, based on dynamic model of molten iron catalysts as shown in Eqs. (9) and (10), in which dx is the occupancy of CO, dt is the diameter of the tank, r is the reaction rate, F is the inlet amount of the gas, Cp is the specific heat capacity of the system, hu, is the heat transfer coefficient, and 2 is the axial coordination of the tank. 

Quasi-continuum models Of these, the quasi-continuum model is the most common. Here, the solid-fluid system is considered as a single pseudo-homogeneous phase with properties of its own. These properties, for example, diffusivity, thermal conductivity, and heat transfer coefficient, are not true thermodynamic properties but are termed as effective properties that depend on the properties of the gas and solid components of the pseudo-phase. Unlike in simple homogeneous systems, these properties are anisotropic, that is, they have different values in the radial and axial directions. KuUcami and Doraiswamy (1980) have compiled all the equations for predicting these effective properties. Both radial and axial gradients can be accounted for in this model, as well as the fact that the system is really heterogeneous and hence involves transport effects both within the particles and between the particles and the flowing fluid. 

The bed and the fluid are considered as a pseudo-homogeneous medium, and the heat transfer in the bed up to the internal side of the wall is represented by two parameters, the radial effective conductivity snd the internal wall heat transfer coefiident aw,int- The introduction of aw.mt allows us to take into account a weaker heat transfer (smaller effective radial heat transfer coefficient X ad) close to the wall due to less mixing and a higher void fraction of the bed (Figure 4.10.64). Thus, combines the interplay of convective flow at the wall and of conduction by contact between the bed and the heat exchange surface (internal wall), and assumes a jump in temperature direcily at the wall. For relative simple modeling, the consequence of the introduction of mt is also that we use a constant value of within the bed. 

Equation (6.11.43) considers the bed and the fluid as a pseudo-homogeneous medium, and the heat transfer within the bed up to the wall is represented by the radial effective thermal conductivity and the internal wall heat transfer coefficient aw.int- The model assumes a jump in temperature directly at the wall from Tw.int.i to The values of X ad and aw.im were calculated by... 

Heat Balance. The heat transferred per unit time and unit volume of catalyst, H, is proportional to the heat transfer coefficient, U, and the difference between the outer tube wall temperature, T, and the catalyst temperature, T. This term can also be obtained from a onedimensional pseudo-homogeneous model as ... 

Heat transfer experiments and material research studies have been carried out at Kyushu University, IAEA, the University of Tokyo and elsewhere. Comparison of heat transfer coefficients predicted by different correlations is shown in Fig. 1.60. Accuracy above 500°C is important for the calculation of MCST. Calculated MCSTs with different correlations are compared in Table 1.16 [122]. The largest difference is 44°C. Current heat transfer correlations were developed based on experiments using smooth circular tubes. Experiments on fuel bundle geometry are necessary. The effect of grid spacers on the heat transfer correlation should be included in the prediction of MCST. The correlation of downward flow is necessary for the design. Downward flow is adopted in the low temperature region below the pseudo-critical temperature. 

In pseudo-homogeneous models, the process gas and catalyst are assumed to be at the same temperature and to be almost in contact. The pseudo-homogeneous assumption simplifies mass-transfer modelling, since external and internal diffusion are not considered explicitly. An effectiveness factor is applied to reaction rates to model the lower concentration of reactants at the catalyst sites. Since the process gas and catalyst are assumed to be at the same temperature, an overall heat-transfer coefficient can be used to describe heat transfer from the inner tube wall to the catalyst and process gas. 

Heat and mass transfer coefficients can be used to interrogate the importance of external transport phenomena and how to choose reactor size. The latter controls (i) pressure drop, (ii) residence time and thus reactant conversion or flow rate and thus power generated, (iri) the effective reaction rate and thus the process efficiency, (iv) the temperature and (v) whether a system is kinetically controlled and thus ideal for extraction of catalytic kinetics. Another application of Nu and Sh is that a 2D or 3D problem can be reduced to a computationally tractable problem by approximating the transverse transport phenomena using overall transport correlations. Such pseudo-2 D models (also called heterogeneous ID models for catalytic systems) have been used to explore the stability and performance of microbumers with a significantly lower computational effort than CFD models (e.g. [23-25]). 

Radial heat transport may usually be represented by a pseudo-homogeneous model with two parameters (Specchia and Baldi [81], Specchia et al. [82], Specchia and Sicardi [83]). The catalytic bed is assumed to be a pseudo-homogeneous system characterized by an effective thermal conductivity k - and by a heat transfer resistance located at the wall of the reactor. The corresponding coefficient is h. In any point in the reactor the three phases (gas, liquid, solid) are supposed to be at the same temperature. 

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