Wall temperature, calculation adiabatic

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. 

We first calculate the recovery (adiabatic-wall) temperature. From Fig. 12-10... 

Figure 10.10a shows propane conversion contours obtained from 2D CFD calculations for catalytic propane combustion in a non-adiabatic microchannel for the conditions mentioned in the caption [23]. Unlike the homogeneous combustion case, the preheating and combustion zones in catalytic microburners overlap since catalytic reactions can occur on the hot catalyst surface close to the reactor entrance. Figure 10.10b shows a discontinuity in the Nu profile, similar to the homogeneous combustion problem. In this case, it happens at the boundary between the preheat-ing/combustion zone and the post-combustion zone. At this point, the bulk gas temperature (cup-mixing average) and wall temperatures cross over and the direction... 

An exothermal reaction with an adiabatic temperature rise of 100 K is to be performed in a tubular reactor with internal diameter of 30 mm, wall thickness of 2 mm, and surrounding jacket of thickness 30 mm containing water. Calculate the effective temperature rise that would occur if the reactor suddenly lost the utilities. In this situation, the reactant flow is stopped and there is no water flow in the jacket. 

Note further that the final state of the piston having slammed into the arrest, is not an equilibrium state temporarily the piston, walls, and arrests are at temperatures different from that of the gas at the time of impact the various subsystems are in different states which differ from the final system of the assembly. Heat exchange will now occur between the inside adiabatic walls and arrests and the gas until the equilibrium state develops. For purposes of calculating work performed, one must thus start with the initial equilibration state and end with the final... 

The first situation concerns two stages of a typical commercial adiabatic reactor. The principles of calculating the conversion in an adiabatic reactor were covered earlier and illustrated in Section 8.3, so will not be presented here but as a problem at the end of the chapter. The second case. concerns a reactor with the catalyst in tubes, with the walls cooled byia constant-temperature boiling hquid. Calculations for this system are presented in detail below. 

Adiabatic processes. Ratio of the specific heats. If the gas is contained in st vessel, the walls of which are impermeable to heat or adiabatic so that no interchange of heat with the surroundings is possible, the energy of the gas diminishes by the amount of the work done against the external pressure. On the other hand, if the gas is compressed, its energy increases by the amount of the work done in the compression. In the first case there is a fall, in the second a rise in the temperature of the gas. The magnitude of the change in temperature may be calculated from equation (2) as follows ... 

Example 2.3 A flat wall of thickness <5 has a constant temperature o- At time t = 0 the temperature of the surface x = 6 jumps to s, whilst the other surface x = 0 is adiabatic, Fig. 2.19. Heat flows from the right hand surface into the wall. The temperature rises with time, whereby the temperature of the left hand surface of the wall rises at the slowest rate. The temperature increase at this point, i.e. the temperature (x = 0, t) is to be calculated. 

Example 5.10 The hollow cylinder from Example 5.9 has black radiating walls. The two ends are kept at temperatures T) = 550 K and T2 = 300 K. The body area 3 is adiabatic, Q3 = Qr = 0. Calculate the heat flow Qj and the temperature Ts = Tr of the reradiating body area, if this is taken to be an approximately isothermal area (zone). 

The symmetry of the construction means that it is sufficient to just consider the top half of the oven. It forms the schematically illustrated enclosure in Fig. 5.63b. It is bounded at the top by the heated square 1 with j = 0.85, at the side by the rectangular areas 2 with e2 = 0.70, which release heat to the outside, and below by the metal plate R. It is adiabatic as a result of symmetry, and represents a reradiating wall. We will assign the approximately uniform temperatures T), T2 and Tr to these surfaces, such that the radiative exchange in a hollow enclosure bounded by three zones is to be calculated according to (5.148) or (5.151). 

Develop a mathematical model of an adiabatic wetted wall column. Hint. The model will be similar to that presented in Section 15.2. Use your model to generate composition profiles for the wetted wall column of Modine as discussed in Example 11.5.3. This is a lengthy exercise and will require you to calculate physical properties as a function of temperature, pressure, and composition. Modine s experimental data are most accessible in a paper by Krishna (1981a). 

Based on a co-flow configuration, the effect of various parameters on cell performance has been studied systematically. The study covers the effect of (a) air flow rate, (b) anode thickness, (c) steam to carbon ratio, (d) specific area available for surface reactions, and (e) extend of pre-reforming on cell efficiency and power density. Though the model predicts many variables such as conversion, selectivity, temperature and species distribution, overpotential losses and polarization resistances, they are not discussed in detail here. In all cases calculations are carried for adiabatic as well as isothermal operation, fii calculations modeling adiabatic operation the outer interconnect walls are assumed to be adiabatic. All calculations modeling isothermal operation are carried out for a constant temperature of 800°C. Furthermore, in all cases the cell is assumed to operate at a constant voltage of 0.7 V. 

Except for the limiting case of the irreversible isotherm discussed above the prediction of the temperature and concentration profiles requires the simultaneous solution of the coupled differential heat and mass balance equations which describe the system. The earliest general numerical solutions for a nonisothermal adsorption column appear to have been given almost simultaneously by Carter and by Meyer and Weber. These studies all deal with binary adiabatic or near adiabatic systems with a small concentration of an adsorbable species in an inert carrier. Except for a difference in the form of the equilibrium relationship and the inclusion of intraparticle heat conduction and finite heat loss from the column wall in the work of Meyer and Weber, the mathematical models are similar. In both studies the predictive value of the mathematical model was confirmed by comparing experimental nonisothermal temperature and concentration breakthrough curves with the theoretical curves calculated from the model using the experimental equilibrium... 

Estimation of equivalent ullage and condensed masses for the case where the ullage volume is pressurized may be handled as indicated previously. When transfer occurs, the volume changes and the calculational method must allow for this effect. It is convenient to assume that the volume change is instantaneous at constant pressure. The operation is not adiabatic. Heat flow occurs which will raise the temperature of the newly emerged wall area from the liquid bulk temperature to the saturation temperature of the gas at the system pressure. After this transient effect, the gas to wall heat exchange is as dictated by (11) with the proper boundary conditions. These are discussed below. 

The predicted pressure profile is obviously a direct result of the assumptions made in the calculations. Winter assumed isothermal conditions at the barrel wall and adiabatic conditions at the flight tip. With stock temperature increases in the order of 100°C and more, it is unlikely that the isothermal boundary condition is valid for the barrel. For the same reason, it is unlikely that the adiabatic boundary condition is valid for the flight tip, particularly since the rest of the screw will be at much lower temperature. Unfortunately, it is difficult to measure actual temperature and pressure profiles. Thus, the predicted temperature and pressure profiles have not been compared to experimental results. 

Winter [30] has performed numerical calculations of the developing temperature profile in the flight clearance for power law fluids. He assumed isothermal conditions at the barrel wall and adiabatic conditions at the screw flight surface. These assumptions are considerably more realistic than the purely adiabatic case or the purely isothermal case, although a better boundary condition would probably be a prescribed maximum heat flux. Winter calculates a typical maximum temperature increase of about ISO C. This value is closer to the maximum temperature rise in the adiabatic case than the maximum temperature rise in the isothermal case. These analyses indicate that the temperature rise in the flight clearance can be quite significant and can play a very important role in degradation in extruders. 

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