Heat time constant

The numerator has a positive and a negative term. After a step change in the load, initially s is large, resulting in a negative response which varies linearly with the relative temperature difference and the heating time constant. Finally the vapor flow will become equal to the inlet flow. 

Balakrishnan and Edgar (2000) evaluated gain-scheduled control of a commercial RTF reactor. They determined that a FID controller based on a semi-empirical model of the heating process provided effective temperature control of the reactor. Derivation of a fundamental heat transfer model based on an unsteady-state energy balance yielded an approximate second-order transfer function with wafer heating time constant T and heating lamp time constant << t, ). 

For constant energy simulations without temperature regulation, use heating steps of about 0.5 ps and a healing time of 20-30 ps. In gen eral, short h eating tim es and large temperature steps perturb th e initial system m ore than Ion gcr heating times and small tern -perature steps. 

If the heating time t or cooling time t are non-zero, or if the run time tj. is non-zero and constant temperature is selected, velocities are adjusted (rescaled) during the molecular dynamics run to change the temperature of the system. 

The time constants characterizing heat transfer in convection or radiation dominated rotary kilns are readily developed using less general heat-transfer models than that presented herein. These time constants define simple scaling laws which can be used to estimate the effects of fill fraction, kiln diameter, moisture, and rotation rate on the temperatures of the soHds. Criteria can also be estabHshed for estimating the relative importance of radiation and convection. In the following analysis, the kiln wall temperature, and the kiln gas temperature, T, are considered constant. Separate analyses are conducted for dry and wet conditions. 

FIG. 8-48 Temperature leaving a heat exchanger responds as a distributed lag, the gain and time constant of which vary inversely with flow. 

Time constants. Where there is a capacity and a throughput, the measurement device will exhibit a time constant. For example, any temperature measurement device has a thermal capacity (mass times heat capacity) and a heat flow term (heat transfer coefficient and area). Both the temperature measurement device and its associated thermowell will exhibit behavior typical of time constants. 

The period after which this can be repeated will depend upon the heating curve and the thermal time constant of the motor, i.e. the time the motor will take to reach thermal equilibrium after repeated starts (See Chapter 3). 

I = time of heating or tripping time of the relay (hours) r = heating or thermal time constant (hours). The larger the machine, the higher this will be and it will vary from one design to another. It may fall to a low of 0.7-0.8 hour. 

Nole In both the above case.s. which are almost similar, so far as the sw itching heats of the stator or the rotor are concertied, the overcurrent protection (noted at serial no. 4) is redundant, as its time constant is much higher (of the order of several minutes) compared to the temperature rise, particularly of the rotor, which is linear and much more rapid under such conditions. Therefore, such protection saves the machine from excessive thermal stresses. 

Overcurrent protection. To provide a thermal replica protection, the relay is set according to motor s heating and cooling (/ - 1) curves supplied by the motor manufacturer. If these curves are not available, they can be established with the help of motor heating and cooling time constants, as in equations (3.2) and (3.4). A brief procedure to establish the motor thermal curves when they are not available is explained in Section 3.6. 

In the case of a temperature probe, the capacity is a heat capacity C == me, where m is the mass and c the material heat capacity, and the resistance is a thermal resistance R = l/(hA), where h is the heat transfer coefficient and A is the sensor surface area. Thus the time constant of a temperature probe is T = mc/ hA). Note that the time constant depends not only on the probe, but also on the environment in which the probe is located. According to the same principle, the time constant, for example, of the flow cell of a gas analyzer is r = Vwhere V is the volume of the cell and the sample flow rate. 

Whereas heat capacity is a measure of energy, thermal diffusivity is a measure of the rate at which energy is transmitted through a given plastic. It relates directly to processability. In contrast, metals have values hundreds of times larger than those of plastics. Thermal diffusivity determines plastics rate of change with time. Although this function depends on thermal conductivity, specific heat at constant pressure, and density, all of which vary with temperature, thermal diffusivity is relatively constant. 

Response time constant 403 Rkster. S. 6-13,655 Return bends, heat exchanger 505 Reversed flow 668 Reversibility, isothermal flow 143 Reversible adiabatic, isentropic flow 148... 

The numerical experiment started at a steady-state value of 200 C for both temperature nodes with an output of 16.89% for both heaters output number 1 was then stepped to 19.00%. If both outputs had been stepped to 19%, then both nodes would have gone to 220 C. The temperature of node 5 does not go as high, and the temperature of node 55 goes too high. In the reduced order model, the time constant x represents the effect of radial heat conduction, while the time constant X2 represents the effect of axial heat conduction. SimuSolv estimates these two parameters of the dynamic model as ... 

However, even with the most advanced measuring and simulation tools, the most efficient methods are simple calculations that give an order-of-magnitude estimation of the influence of a phenomenon. Time constants for diffusion, heat conduction, and acceleration are very useful. For example, the time constant for diffusion Td = f/D is the time it takes to fill a cube of size I by diffusion, and the time for a particle to accelerate from zero velocity to approximately two-third of the velocity of the surrounding fluids is 118/j, where p[Pg.331]

For a thermometer to react rapidly to changes in the surrounding temperature, the magnitude of the time constant should be small. This involves a high surface area to liquid mass ratio, a high heat transfer coefficient and a low specific heat capacity for the bulb liquid. With a large time constant, the instrument will respond slowly and may result in a dynamic measurement error. 

The temperature response of the measurement element shown in Fig. 2.13 is strictly determined by four time constants, describing a) the response of the bulk liquid, b) the response of the thermometer pocket, c) the response of the heat conducting liquid between the wall of the bulb and the wall of the pocket and d) the response of the wall material of the actual thermometer bulb. The time constants c) and d) are usually very small and can be neglected. A realistic model should, however, take into account the thermal capacity of the pocket, which can sometimes be significant. 

Heat tranfer processs time constants are formulated as... 

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