Wall temperature profile

What does the longitudinal temperature profile look like for given inlet temperatures and/or wall temperature profiles Are the hot spots excessive for reasons of selectivity, catalyst deactivation, etc ... 

For the reformer we assume that the outer wall temperature profile of the reformer tubes decouples the heat-transfer equations of the furnace from those for the reformer tubes themselves. The profile is correct when the heat flux from the furnace to the reformer tube walls equals the heat flux from the tube walls to the reacting mixture. We must carry out sequential approximating iterations to find the outer wall temperature profile Tt,o that converges to the specific conditions by using the difference of fluxes to obtain a new temperature profile T) o for the outer wall and the sequence of calculations is then repeated. In other words, a T) o profile is assumed to be known and the flux Q from the furnace is computed from the equations (7.136) and (7.137), giving rise to a new Tt o-This profile is compared with the old temperature profile. We iterate until the temperature profiles become stationary, i.e., until convergence. 

In this paper, the problem of product non-uniformity is placed in perspective as we consider the simple case of flow between parallel plates with a flat velocity profile accompanied by a first order reaction. The system equations involved are non-dimensionalized and four parameters identified. A systematic attempt is made to explore a host of constrained and unconstrained wall temperature profiles that alleviate the problem of product non-uniformity at the reactor outlet. Work is already underway to study similar problems in complex polymerization systems, and some preliminary results are reported here. 

Figure 2. Typical two-zone wall temperature profile normalized by Tin-...

For the case of continuous wall temperature profiles, a function fitting approach was used. Although there are no end conditions on Tw(z) to be satisfied, for all the cases considered in this paper Tw(z) is expected to be high near the entrance to the reactor and lower near the exit. Thus, with a decreasing optimal wall temperature sequence in mind, a Laguerre expansion (with exponential weighting) of the wall temperature was chosen. The expansion can be represented as... 

Simple methods have been presented to study constrained and free optimization in two-zone reactor systems and in systems with a continuous wall temperature profile. 

A computationally efficient method of function fitting using an orthogonal polynomial expansion is presented for approximating continuous wall temperature profiles. 

Wall temperature profiles are plotted vs. distance down the combustion channel for a number of total flow rates and hexane-to-air ratios in Figure 4. The wall temperature decreases slightly at first, then rises slowly, then rapidly, and finally decreases slowly. As the flow rate is increased, the flame front, as reflected by the rapid rise in wall temperature, moves toward the exit of the tube, and the maximum temperature decreases. Decreasing the hexane-to-air ratio also shifts the flame front toward the exit. 

The measured values of NO, and CO at the exit are plotted in Figure 5 vs. residence time at high temperature. These values of residence time were computed from the gas temperature profile down the tube, which was estimated from the wall temperature profile. The NO, decreases, and the CO increases with decreasing residence time as might be expected from kinetic considerations. These very low values of NO, and moderate values of CO are comparable in magnitude and trend with those of Bem-... 

The close correspondence of the measured wall temperature profiles and exit-gas compositions to those of Bernstein and Churchill (3) for the combustion of premixed propane vapor and air suggests that combustion in a refractory tube is relatively insensitive to the composition and state of the fuel as long as evaporation precedes combustion. 

Stable fiames from atomized fuel droplets and air can be established inside a refractory tube over a range of flow rates, drop sizes, and fuel-to-air ratios. The wall temperature profiles and exit-gas compositions correspond closely to those for premixed fuel gas and air. Very low NO, contents are attainable despite the high flame temperatures. 

Gas and wall temperature profiles and methane conversions obtained by integrating Eqs. (1), (2), and (5) after substituting Eq. (7) in the heat balance Eq. (5) are shown in Fig. 6. As for fully coated monoliths, the washcoat temperature is the highest at the inlet and decreases slightly thereafter, asymptotically merging with the gas temperature. Washcoat temperatures can be calculated from Eq. (8), which is derived by substituting Eqs. (4) and (7) in Eq. (5) and letting kr oo. The half-factor reflects the fact that the gas temperatures in the catalytic and noncatalytic channels are the same. 

This formula agrees very well with the near-wall temperature profile data of Blackwell et al. [99] obtained in air if Prr= 0.7 and Pr, = 0.88. It should be noted that good agreement with the data was achieved here without consideration of near-wall turbulent Prandtl number variations observed by some investigators [100]. 

The actual wall temperature profiles tend to the first of these extremes at low mass fluxes and to the second at high mass fluxes (where the concentration of droplets is sufficient to maintain near-saturation conditions in the vapor). The four-gradient models are remarkably successful in predicting the systematic change from one extreme to the other, the calculated wall temperature profiles agreeing well with those measured. 

A comparison between lumped and distributed models for hybrid reactors for catalytic combustion of methane was more recently investigated by Groppi et a/. The validation of one-dimensional models was made on the basis for different Nusselt correlations and geometrical properties of the monolith channel. In general, the simulations showed a mismatch of the wall temperature profiles predicted with the one-dimensional model. One-dimensional models could show good agreement of the gas exit temperature, which is an important parameter for hybrid reactors as described in the previous section. The catalyst has to ignite in... 

Figure 10.7 (a) Symmetry and channel wall temperature profiles along the reactor length. Solid lines, without radiation dashed lines, with radiation, (b) Heat flux profile alongthe upperchannel wall when accounting for radiation. Heat flux into the channel is positive heat flux out of the channel is negative. 

WALL-TEMPERATURE PROFILES. Figure 2 is a family of inside wall-temperature distributions along the tube for various flow rates and heat fluxes. These represent typical tube-temperature distributions from the 0.375 in. OD... 

The furnace — with the exhaust chirrmey on the top — has radiant wall burners in six levels on two opposite walls to supply the heat of reaction to a single full-size tube located in the centre. Such a configuration is appropriate since it allows simulation of almost any outer tube-wall temperature profile by variation of the burner firing pattern. 

The simulator is used to investigate three important aspects of the model the significance of the endcaps, conductivity in the heat exchanger wall and the adjustable parameter (the heat transfer coeflScient). Model parameters are given in Table 7.4. Simulation shows that the endcaps have little effect on the temperature profiles in the steady-state simulator. The shape of the temperature profiles are very similar and the transition points are within 1 percent of each other. The only significant difference that the addition of the endcaps makes is in the corner in the wall temperature profile because of the discontinuity in the wall thickness. This corner can be seen in Figures 7.19, 7.20, and 7.21 at z = 0.85. 

Figure 3.4 Computed wall temperature profiles for the catalytic channel geometry in Fig. 3.3 and two H2/air stoichiometries =0.3 and 6.9) having the same adiabatic equilibrium temperature Tad. In the fuel-lean =0.3, results are shown for Case 1 which is adiabatic and transport-limited, Case 2 with only catalytic reactions (C), and Case 3 with both catalytic and gas-phase reactions (C-G). In the fuel-rich

Figure 3.23 Computed wall temperature profiles in the catalytic channel of Fig. 3.3 at selected times for a Hj/CO/air mixture (solid lines) with q>=026, vol. ratio 1 1, Tin = 500 K, 0in=4 m/s, and p = 5 bar. Dashed lines are predictions with only CO fuel, having the same exothermicity as the H2/CO mixture. The times marked fjg and fjt denote catalytic ignition and steady state, respectively. Adapted from Zheng et al. (2014) (with permission).

The evolution of the total conversion of methane and of the conversion of methane into CO2 is shown in Fig. 11.9.l.A-4, together with the process gas temperature, total pressure, and wall temperature profiles. The temperature drop... 

In this work, thermal cracking reactors of ethylene plants are investigated dynamically. The main attention is given to the cracking coil. The modelling of the furnace itself is not considered.The tubular reactor is modelled by assuming the external wall temperature profile or heat flux profile of the coil. There is no report on dynamic analysis of this type of reactor in the literature except Jackman and Arises work (12). The literature is mainly interested in the steady state modelling of these reactors and control. 

Heat Transfer to Coilso If the wall temperature profile is... 

The first case corresponds to a case which has not "lit off." We note first that without axial conduction of heat in the wall the solution has to be unique ( ), and there is no hysteresis curve. For an inlet temperature of 600°F the wall temperature profile is shown in Figure 4 for different average velocities. 

Until now the simulation of a thermal cracking coil has generally been uncoupled from that of the fire box by imposing either a tube wall temperature profile or a heat flux profile. It is then checked a posteriori whether or not the fire box permits such profiles to be attained. The fire box calculations generally proceed along the Lobo Evans approach (J ), although more recently zone methods have been applied, thus permitting a temperature distribution in the fire box to be calculated (2, 3, 4, 5). 

The wall temperature profile in a steady-state situation can easily be calculated from Eqns. (14.14) and (14.17) ... 

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