Profile tube wall temperature

If the degree of superheat is large, it will be necessary to divide the temperature profile into sections and determine the mean temperature difference and heat-transfer coefficient separately for each section. If the tube wall temperature is below the dew point of the vapour, liquid will condense directly from the vapour on to the tubes. In these circumstances it has been found that the heat-transfer coefficient in the superheating section is close to the value for condensation and can be taken as the same. So, where the amount of superheating is not too excessive, say less than 25 per cent of the latent heat load, and the outlet coolant temperature is well below the vapour dew point, the sensible heat load for desuperheating can be lumped with the latent heat load. The total heat-transfer area required can then be calculated using a mean temperature difference based on the saturation temperature (not the superheat temperature) and the estimated condensate film heat-transfer coefficient. 

A 2.5-cm-diameter tube has circumferential fins of rectangular profile spaced at 9.5-mm increments along its length. The fins are constructed of aluminum and are 0.8 mm thick and 12.5 mm long. The tube wall temperature is maintained at 200°C, and the environment temperature is 93°C. The heat-transfer coefficient is 110 W/m2 - °C. Calculate the heat loss from the tube per meter of length. 

A circumferential fin of rectangular profile is constructed of aluminum and surrounds a 3-cm-diameter tube. The fin is 2 cm long and I mm thick. The tube wall temperature is 200°C, and the fin is exposed to a fluid at 20°C with a convection heat-transfer coefficient of 80 W/m2 °C. Calculate the heat loss from the fin. 

Figure 37. Tube wall temperature and heat dux profiles for (op-fired and side-fired configurations.

Schematic temperature and heat flux profiles for a top-fired and a sidewall-fired reformer for identical process outlet conditions are seen in Figure 3.5 below. The top-fired furnace has a high heat flux at the inlet, whereas the sidewall-fired furnace has a more equally distributed heat flux profile. The top-fired furnace has an almost flat tube temperature profile, whereas in a sidewall-fired furnace the tube-wall temperatures increase down the reformer. The terrace-wall fired reformer has profiles similar to the sidewall-fired reformer, whereas the bottom-fired reformer has a larger heat flux in the lower part of the reformer.

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. 

Combustion in a channel is represented by a heat flux profile, and iterations must be carried out until convergence of the heat flux and temperature profiles by use of the boundary condition at the wall. Equation (3.18). If the heat flux is given in one reactor part, the resulting tube-wall temperature may be used in the other reactor part to calculate a new heat flux profile. The solution method is successive iteration with controlled step sizes. 

Recorded temperature profiles from the monotube pilot plant in Figure 3.6 are shown in Figure 3.8 [393]. The simulation uses the two-dimensional homogeneous model using the outer tube-wall temperature... 

A proper optimisation of a steam reformer must always be based on a furnace model, since the delivered heat flux profile is bounded by the furnace configuration and the flexibility of the burners. Seen from an exeigy point of view outer tube-wall temperature and heat flux profiles may decrease the exergy losses [335], but it should be checked if they can be provided by a furnace. 

Simulation of tubular steam reformers and a comparison with industrial data are shown in many references, such as [250], In most cases the simulations are based on measured outer tube-wall temperatures. In [181] a basic furnace model is used, whereas in [525] a radiation model similar to the one in Section 3.3.6 is used. In both cases catalyst effectiveness factor profiles are shown. Similar simulations using the combined two-dimensional fixed-bed reactor, and the furnace and catalyst particle models described in the previous chapters are shown below using the operating conditions and geometry for the simple steam reforming furnace in the hydrogen plant. Examples 1.3, 2.1 and 3.2. Similar to [181] and [525], the intrinsic kinetic expressions used are the Xu and Froment expressions [525] from Section 3.5.2, but with the parameters from [541]. 

The desulfurized natural gas feed is mixed with steam and preheated to 500 °C before entering the reformer tubes. The heat for the reforming reaction is supplied by combustion of fuel in the furnace, which may contain up to 500 tubes with a length of 10 m and a diameter of 10 cm. Figure 6.2.31 shows axial profiles of the tube wall temperature and the heat flux. 

External tube wall temperature or heat flux profiles. 

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). 

It is evident from the above and also from eq. (12) that lack of catalyst activity will cause high temperature both in the gas and in the tube. The advantage of high catalyst activity (and the disadvantage of an unsuitable flux profile) is illustrated in Figure 8 which shows calculated tube wall temperatures in a top fired reformer for various relative catalyst activities in the upper half of the reformer tube. It is seen that loss of activity in the upper part of the tube may lead to significant overheating of the tube. 

Fig. 3. Typical tube-wall-temperature and heat-flux profiles (hydrogen).

For the range of conditions covered herein, an exponential equation was developed for hydrogen which describes the tube-wall-temperature profile in the film-boiling region. This equation applies only to an electrically heated tube having the same temperature—resistance characteristic, orientation, and dimensions as the one used in the present study. Analysis showed that, as a first approximation, the prime variables affecting the shape and absolute values of the temperature profile included flow rate, maximum nucleate flux, and distance downstream of the burnout point. The resultant equation for hydrogen is ... 

Fig.7.Typical tube-wall-temperature profiles. operation at maximum nucleate heat flux (hydrogen).

Surface-temperature profiles associated with minimum film flux for hydrogen showed a humped shape beginning just downstream of the burnout point, as shown by two tjrpical tube-wall-temperature profiles in Fig. 8. The previous temperature equation does not describe the humped profile. Additive terms, believed to be primarily functions of fluid quality and flow rate for a given fluid, are required. It is not known whether or not a humped wall-temperature profile is always associated with a minimum film flux or may also occur with a maximum nucleate heat-flux condition for certain combinations of flow, fluid quality, and heat flux. 

A temperature profile of vapor condensing in the presence of a noncondensable gas on a tube wall, as shown in Figure 16 indicates the resistance to heat flow. Heat is transferred in two ways from the vapor to the interface. The sensible heat is removed in cooling the vapor from t to t, at the convection gas cooling rate. The latent heat is removed only after the condensable vapor has been able to diffuse through the noncondensable part to reach the tube wall. This means the latent heat transfer is governed by mass transfer laws. 

Figure 16. Temperature profile showing effect of vapor condensation on a tube wall in the presence of a noncondensable gas.

Figure 10-28. Tube wall conditions affecting overall heat transfer and associated temperature profile.

Here a steady-state formulation of heat transfer is considered (Pollard, 1978). A hot fluid flows with linear velocity v, through a tube of length L, and diameter D, such that heat is lost via the tube wall to the surrounding atmosphere. It is required to find the steady-state temperature profile along the tube length. 

Fig. 9 shows comparisons of CFD results with experimental data at a Reynolds number of 986 at three of the different bed depths at which experiments were conducted. The profiles are plotted as dimensionless temperature versus dimensionless radial position. The open symbols represent points from CFD simulation the closed symbols represent the points obtained from experiment. It can be seen that the CFD simulation reproduces the magnitude and trend of the experimental data very well. There is some under-prediction in the center of the bed however, the shapes of the profiles and the temperature drops in the vicinity of the wall are very similar to the experimental case. More extensive comparisons at different Reynolds numbers may be found in the original reference. This comparison gives confidence in interstitial CFD as a tool for studying heat transfer in packed tubes. 

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