Low-density heat transfer

The percent reduction in heat transfer is obtained by comparing these last two numbers  

The mass flow of coolant air at the wall is calculated from 

We are assuming a constant-properties analysis evaluated at the reference temperature of 398.5 K, so 

A number of practical situations involve heat transfer between a solid surface and a low-density gas. In employing the term low density, we shall mean those circumstances where the mean free path of the gas molecules is no longer small in comparison with a characteristic dimension of the heat-transfer surface. The mean free path is the distance a molecule travels, on the average, between collisions. The larger this distance becomes, the greater the distance required to communicate the temperature of a hot surface to a gas in contact with it. This means that we shall not necessarily be able to assume that a gas in the immediate neighborhood of the surface will have the same temperature as the heated surface, as was done in the boundary-layer analyses of Chap. 5. Because the mean free path is also related to momentum transport between molecules, we shall also be forced to abandon our assumption of zero fluid velocity near a stationary surface for those cases where the mean free path is not negligible in comparison with the surface dimensions. 

Three general flow regimes may be anticipated for the flow over a flat plate shown in Fig. 12 12. First, the continuum flow region is encountered when the mean free path A is very small in comparison with a characteristic body dimension. This is the convection heat-transfer situation analyzed in preceding chapters. At lo wer gas pressures, when A L, the flow seems to slip along the surface and u 4= 0 at y = 0. This situation is appropriately called slip flow. At still lower densities, all momentum and energy exchange is the result of 

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As a first example of low-density heat transfer let us consider the two parallel infinite plates shown in Fig. 12-14. The plates are maintained at different temperatures and separated by a gaseous medium. Let us neglect natural-convection effects. If the gas density is sufficiently high so that A — 0, a linear temperature profile through the gas will be experienced as shown for the case of A. As the gas density is lowered, the larger mean free paths require a greater distance from the heat-transfer surfaces in order for the gas to accommodate to the surface temperatures. The anticipated temperature profiles are shown in... 

A summary of low-density heat transfer is given by Springer [13]. 

The variation in total thermal conductivity with density has the same general nature for ah. cellular polymers (143,189). The increase in at low densities is owing to an increased radiant heat transfer the rise at high densities to an increasing contribution of k. ... 

Sodium is used as a heat-transfer medium in primary and secondary cooling loops of Hquid-metal fast-breeder power reactors (5,155—157). Low neutron cross section, short half-life of the radioisotopes produced, low corrosiveness, low density, low viscosity, low melting point, high boiling point, high thermal conductivity, and low pressure make sodium systems attractive for this appHcation (40). 

By using the simple Reynolds Analogy, obtain the relation between the heat transfer coefficient and the mass transfer coefficient for the gas phase for the absorption of a soluble component from a mixture of gases. If the heat transfer coefficient is 100 W/m2 K, what will the mass transfer coefficient be for a gas of specific heat capacity Cp of 1.5 kJ/kg K and density 1.5 kg/m- The concentration of the gas is sufficiently low for hulk flow effects to be negligible. 

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