Flow, adiabatic laminar

The temperature counterpart of Q>aVR ccj-F/R and if ccj-F/R is low enough, then the reactor will be adiabatic. Since aj 3>a, the situation of an adiabatic, laminar flow reactor is rare. Should it occur, then T i, will be the same in the small and large reactors, and blind scaleup is possible. More commonly, ari/R wiU be so large that radial diffusion of heat will be significant in the small reactor. The extent of radial diffusion will lessen upon scaleup, leading to the possibility of thermal runaway. If model-based scaleup predicts a reasonable outcome, go for it. Otherwise, consider scaling in series or parallel. 

P 21] The mixing of gaseous methanol and oxygen was simulated. The equations applied for the calculation were based on the Navier-Stokes (pressure and velocity) and the species convection-diffusion equation [57]. As the diffusivity value for the binary gas mixture 2.8 x 10 m2 s 1 was taken. The flow was laminar in all cases adiabatic conditions were applied at the domain boundaries. Compressibility and slip effects were taken into account The inlet temperature was set to 400 K. The total number of cells was —17 000 in all cases. 

Solution This flow is z-axisymmetric. We, thus, select a cylindrical coordinate system, and make the following simplifying assumptions Newtonian and incompressible fluid with constant thermophysical properties no slip at the wall of the orifice die steady-state fully developed laminar flow adiabatic boundaries and negligible of heat conduction. 

At large values of the Zel dovich number, the chemical reaction is confined to a thin sheet in the flow. For all purposes except the analysis of the sheet structure, the sheet may be treated as a surface—for example, G(x, t) = 0—which in terms of the Cartesian coordinates (x, y, z) may be written locally as x = F y, z, t) if the x coordinate is not parallel to the sheet in its local orientation. When analyses are pursued in outer-scale variables, it is convenient to work in a coordinate system that moves with the sheet. For the undisturbed flow, let the x coordinate be normal to the planar flame, with the unburnt gas extending to x = — oo and the burnt gas to x = -1- oo. Employ the steady, adiabatic, laminar flame speed, measured in the burnt gas, = po Vq/p with Vq given by equation (5-78), and the thermal diffu-... 

The temperature counterpart of 3JjR is atjR, and if atjR is low enough, then the reactor will be adiabatic. Since a the situation of an adiabatic laminar flow... 

The pilot reactor is a tube in isothermal or adiabatic laminar flow, and molecular diffusion is negligible. The larger reactor will have the same value for 1 and will remain in laminar flow. The RTD will be unchanged by the scaleup. If diffusion in the small reactor did have an influence, it will lessen upon scaleup, and the RTD will approach that for the diffusion-free case. This will hurt yield and selectivity. 

The problems of micro-hydrodynamics were considered in different contexts (1) drag in micro-channels with a hydraulic diameter from 10 m to 10 m at laminar, transient and turbulent single-phase flows, (2) heat transfer in liquid and gas flows in small channels, and (3) two-phase flow in adiabatic and heated microchannels. The smdies performed in these directions encompass a vast class of problems related to flow of incompressible and compressible fluids in regular and irregular micro-channels under adiabatic conditions, heat transfer, as well as phase change. 

Hetsroni et al. (2005) evaluated the effect of inlet temperature, channel size and fluid properties on energy dissipation in the flow of a viscous fluid. For fully developed laminar flow in circular micro-channels, they obtained an equation for the adiabatic increase of the fluid temperature due to viscous dissipation ... 

Two-dimensional compressible momentum and energy equations were solved by Asako and Toriyama (2005) to obtain the heat transfer characteristics of gaseous flows in parallel-plate micro-channels. The problem is modeled as a parallel-plate channel, as shown in Fig. 4.19, with a chamber at the stagnation temperature Tstg and the stagnation pressure T stg attached to its upstream section. The flow is assumed to be steady, two-dimensional, and laminar. The fluid is assumed to be an ideal gas. The computations were performed to obtain the adiabatic wall temperature and also to obtain the total temperature of channels with the isothermal walls. The governing equations can be expressed as... 

This chapter assumes isothermal operation. The scaleup methods presented here treat relatively simple issues such as pressure drop and in-process inventory. The methods of this chapter are usually adequate if the heat of reaction is negligible or if the pilot unit operates adiabatically. Although included in the examples that follow, laminar flow, even isothermal laminar flow, presents special scaleup problems that are treated in more detail in Chapter 8. The problem of controlling a reaction exotherm upon scaleup is discussed in Chapter 5... 

After the bifurcation behavior is examined, the role of flame-wall thermal interactions in NOj is studied. First, adiabatic operation is considered. Next, the roles of wall quenching and heat exchange in emissions are discussed. Two parameters are studied the inlet fuel composition and the hydrod3mamic strain rate. Results for the stagnation microreactor are contrasted with the PSR to understand the difference between laminar and turbulent flows. 

Clearly, in the absence of a radial temperature or velocity gradient, no radial mass transfer can exist unless, of course, a reaction occurs at the bed wall. When a system is adiabatic, a radial temperature and concentration gradient cannot exist unless a severe radial velocity variation is encountered (Carberry, 1976). Radial variations in fluid velocity can be due to the nature of flow, e.g. in laminar flow, and in the case of radial variations in void fraction. In general, an average radial velocity independent of radial position can be assumed, except from pathological cases such as in very low Reynolds numbers (laminar flow), where a parabolic profile might be anticipated. 

C per 10 MPa. The temperature rise in laminar flow is highly nonuniform, being concentrated near the pipe wall where most ofthe dissipation occurs. This may result in significant viscosity reduction near the wall, and greatly increased flow or reduced pressure drop, and a flattened velocity profile. Compensation should generally be made for the heat effect when AP exceeds 1.4 MPa (203 psi) for adiabatic walls or 3.5 MPa (508 psi) for isothermal walls (Gerard, Steidler, and Appeldoorn, Ind. Eng. Chem. Fundam., 4, 332-339 [1969]). 

The flow patterns, composition profiles, and temperature profiles in a real tubular reactor can often be quite complex. Temperature and composition gradients can exist in both the axial and radial dimensions. Flow can be laminar or turbulent. Axial diffusion and conduction can occur. All of these potential complexities are eliminated when the plug flow assumption is made. A plug flow tubular reactor (PFR) assumes that the process fluid moves with a uniform velocity profile over the entire cross-sectional area of the reactor and no radial gradients exist. This assumption is fairly reasonable for adiabatic reactors. But for nonadiabatic reactors, radial temperature gradients are inherent features. If tube diameters are kept small, the plug flow assumption in more correct. Nevertheless the PFR can be used for many systems, and this idealized tubular reactor will be assumed in the examples considered in this book. We also assume that there is no axial conduction or diffusion. 

Derive an expression for the Nusselt number in fully developed laminar slug flow through an annulus when the inner and outer surfaces of the annulus have diameters of Dj and D0 respectively and when there is a uniform heat flux applied at the inner surface and when the outer surface is adiabatic. 

Consider constant-property, fully developed laminar flow between two large parallel plates, i.e., in a wide plane duct. One plate is adiabatic and the other is isothermal and the velocity is high enough for viscous dissipation effects to be significant. Determine the temperature distribution in the flow. 

We must consider the laminar and turbulent portions of the boundary layer separately because the recovery factors, and hence the adiabatic wall temperatures, used to establish the heat flow will be different for each flow regime. It turns out that the difference is rather small in this problem, but we shall follow a procedure which would be used if the difference were appreciable, so that the general method of solution may be indicated. The free-stream acoustic velocity is calculated from... 

Air at 7 kPa and -40°C flows over a flat plate at Mach 4. The plate temperature is 35°C, and the plate length is 60 cm. Calculate the adiabatic wall temperature for the laminar portion of the boundary layer. 

A wind tunnel is to be constructed to produce flow conditions of Mach 2.8 at Ix = -40°C and p = 0.05 atm. What is the stagnation temperature for these conditions What would be the adiabatic wall temperature for the laminar and turbulent portions of a boundary layer on a flat plate If a flat plate were installed... 

Annular flow is associated with two Nusselt numbers—Nu on the inner tube surface and Nu on the outer tube surface—since it may involve heat transfer on both surfaces. The Nu.sselt numbers for fully developed laminar flow with one surface isothermal and the other adiabatic are given in Table 8-4, When Nusselt numbers are known, the convection coefficients for the inner and the outer surfaces are determined from... 

Nusselt number fer fully developed laminar flow in an annulus v/ith one surface isothermal and the other adiabatic (Kays and Perkins, 1972)... 

We may first divide tubular reactors into those designed for homogeneous reactions, and therefore basically just an empty tube, and those designed for a heterogeneously catalyzed reaction, and hence to be packed with a catalyst. Both types can of course be operated adiabatically, and it was the simplest model of these that we discussed in the last chapter. If the temperature of the reactor is to be controlled this is through the wall, and the associated problems of heat transfer now arise. These include transfer at the wall and subsequent radial diffusion across the flowing reactants. In the empty tubular reactor there may be considerable variations in flow rate across the tube. For example, in the slow laminar flow the fluid... 

---