Heat loss assumptions

Liquified gases are sometimes stored in well-insulated spherical containers that are vented to the atmosphere. Examples in the industry are the storage of liquid oxygen and liquid ammonia in spheres. If the radii of the inner and outer walls are r, and r, and the temperatures at these sections are T, and T, an expression for the steady-state heat loss from the walls of the container may be obtained. A key assumption is that the thermal conductivity of the insulation varies linearly with the temperature according to the relation ... 

Air containing 0.005 kg water vapour per kg of dry air is heated to 325 K in a dryer and passed to the lower shelves. It leaves these shelves at 60 per cent humidity and is reheated to 325 K and passed over another set of shelves, again leaving at 60 per cent humidity. This is again repeated for the third and fourth sets of shelves, after which the air leaves the dryer. On the assumption that the material on each shelf has reached the wet-bulb temperature and that heat losses from the dryer may he neglected, determine ... 

However, a number of theories on flame quenching were also developed. Some of these were based on arbitrary assumptions concerning the conditions for quenching [7,11]. Another group of theories were based on the energy conservation equation for the flame, including heat loss [19-21]. 

The profile shown in Figure 15.21 represents the furnace efficiency, if the casing heat losses are neglected. Making this assumption, the process duty plus the stack loss represents the heat released by the fuel. 

B The assumptions include no heat loss to the surroundings or to the calorimeter, a solution density of 1.00 g/mL, a specific heat of 4.18 J g 1 °C 1, and that the initial and final solution volumes are the same. The equation for the reaction that occurs is NaOH(aq) + HCl(aq) - NaCl(aq) + H20(l). Since the two reactants combine in a one to one mole ratio, the limiting reactant is the one present in smaller amount. 

The simplifying assumptions of constant molar heat of vaporisation, no heat losses, and no heat of mixing, lead to a constant molar vapour flow and a constant molar reflux flow in any section of the column, that is Vn = Vn+1, Ln = Ln+1, and so on. Using these simplifications, the two enrichment equations are obtained ... 

This treatment, which is due to Semenov, includes two assumptions, a uniform reactant temperature and heat loss by convection. While these may be reasonable approximations for some situations, e.g. a well-stirred liquid, they may be unsatisfactory in others. In Frank-Kamenetskii s theory, heat transfer takes place by conduction through the reacting mixture whose temperature is highest at the centre of the vessel and falls towards the walls. The mathematics of the Frank-Kamenetskii theory are considerably more complicated than those of the simple Semenov treatment, but it can be shown that the pre-explosion temperature rise at the centre of the vessel is given by an expression which differs from that already obtained by a numerical factor, the value of which depends on the geometry of the system (Table 7). 

The relationships developed from field measurements have been made dimensionless with the assumptions that v = 1.33 x 10 m /s and AijO = 2.6 x 10 m /s to facilitate comparisons between relations and avoid dimensional problems. They are given in Table 9.2. The early measurements were to investigate the loss of water from the reservoirs of the Colorado River in the United States, and the later measurements were designed to investigate heat loss from heated water bodies. A revelation occurred in 1969, when Shulyakovskyi brought in buoyancy forces as related to natural convection to explain the heat loss from heated water at low wind velocities. This was picked up by Ryan and Harleman (1973), who realized that natural convection could explain the need for a constant term in front of the relationship for gas film coefficient, as had been found by Brady et al. (1969), Kohler (1954), Rymsha and Dochenko (1958), and Shulyakovskyi (1969). Finally, Adams et al. (1990) rectified... 

An assumption involving heat losses from the reactor is made in most treatments. The effect of heat transfer on the maximum reaction rates of a homogeneous reactor has been treated by DeZubay and Woodward (14). It was found that a lowering of the reactor surface temperature appreciably lowered the chemical reaction rates. Longwell and Weiss (43) found, for example, a loss equal to 5% of the maximum adiabatic heat liberated reduces the maximum heat release rate by more than 30%, while a 20% heat loss reduces the rate about 85%. One should not assume an adiabatic system without some definite knowledge of the magnitude of the heat losses. 

In this balance, the assumption is made that the molar heat capacities and the latent heals of vaporization of all components arc identical. It is also assumed that heat losses from the column and heals of mixing are negligible. With these assumptions, the upward vapor flow and the... 

Results pertinent to the theory of critical diameter are contained for the most part in earlier works by English authors. Despite his erroneous assumptions, Holm obtained the correct relation between the critical diameter and the flame velocity (1.4.6). The remarkable work by Daniell on the theory of flame propagation contains an analysis of the influence of heat losses. The losses enter directly into the equation describing the temperature distribution in the flame zone. A solution exists only for heat losses which do not exceed a certain limit, and under critical conditions (at the limit of propagation), the flame velocity drops to a certain fraction (40-50%) of the theoretical flame velocity. Daniell was also the first to indicate definitely that the flame velocity cannot be constructed from thermal quantities alone and by dimensional considerations must be proportional to the square root of the reaction rate. 

This similarity was established in [2] by consideration of the second-order differential equations of diffusion and heat conduction. Under the assumptions made about the coefficient of diffusion and thermal diffusivity, similarity of the fields, and therefore constant enthalpy, in the case of gas combustion occur throughout the space this is the case not only in the steady problem, but in any non-steady problem as well. It is only necessary that there not be any heat loss by radiation or heat transfer to the vessel walls and that there be no additional (other than the chemical reaction) sources of energy. These conditions relate to the combustion of powders and EM as well, and were tacitly accounted for by us when we wrote the equations where the corresponding terms were absent. 

The temperature computed on the assumption that there are no heat losses is at any rate the upper limit of the true temperature. In rapidly burn-... 

In the sixth and last step, the system is still considered to be purely conductive, with heat exchange at the wall to the surroundings and the zero-order approximation of the kinetics is replaced by a more realistic kinetic model. This technique is very powerful in autocatalytic reaction, since a zero-order approximation leads to the very conservative assumption that the maximum heat release rate is realized at the beginning of the exposure and maintained at this level, respectively increasing with temperature, during the whole time period. In reality, the maximum heat release rate is delayed, and only achieved later on. Thus, heat losses may lead to a decreasing temperature during the induction time of the autocatalytic reaction. 

Under the assumption of sufficiently high laser excitation energies, the heat loss at peak particle temperature is dominated by sublimation. Hence, the maximal signal is proportional to the particle volume... 

Steam at 403 K is supplied through a pipe of 25 mm outside diameter. Calculate the heat loss per metre to surroundings at 293 K, on the assumption that there is a negligible drop in temperature through the wall of the pipe. The heat transfer coefficient h from the outside of the pipe of the surroundings is given by ... 

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