Heat per unit volume

Note that the temperature profile differs from the total heat profile because the heat per unit volume depends not only on the local temperature but also on the local density of the flame gas. In the preheat zone the profile of conducted heat coincides with the profile of total heat, whereas in the reaction zone the conducted heat gradually drops to zero. The difference between total heat and conducted heat represents the heat gained by chemical reaction. The volume integral of the total heat is approximately H, and the volume integral of the conducted heat is approximately H"... 

One of the assumptions made in solving the flow in the fully developed region of the capillary was that of constant fluid temperature throughout the flow region. This is not a valid assumption for the flow of very viscous fluids at high rates of shear in which a nonuniform temperature field is created. As we have already mentioned in connection with the thermal-energy balance (Section 2.2), the rate of viscous heating per unit volume ev is... 

A second area in our combustion work is in direct-combustion. Large industrial combustors are too costly to use for experimentation. However, we have a unique 500 lb/hr. pulverized coal/oil furnace which closely simulates the performance, in other words, the value of the heat per unit volume of commercial unit. Our main thrust in using this is that of resolving applied problems. With this combustor, we ve studied the handling, pulverizing, combustion, and fouling characteristics of SRC-I fuel and operated it on these fuels first during October, 1974. 

If too low a proportion of combustible gas is present, only a small quantity of heat per unit volume of mixture is liberated when the layer surrounding the initial source of heat is inflamed, and the products of combustion have to impart heat to a considerable volume of inert gases. The number of collisions between molecules of combustible gas and of oxygen that are chemically fruitful is therefore small. Such collisions, resulting in combination, will occur only in the neighbourhood of the initial source of heat, around which an aureole or cap will form of a size dependent on the nature and quantity of the combustible gas present. 

Loss factor. As used in dielectric measurements, a factor proportional to conductance per cycle, and hence a measure of the total energy dissipated as heat per unit volume of the dielectric. 

The development of a maximum in tan 5 or ihe loss modulus at the glass-to-rubber transition is explained as follows. At temperatures below Tg the polymer behaves elastically, and there is little or no flow to convert the applied energy into internal work in the material. Now It, the energy dissipated as heat per unit volume of material per unit time because of flow in shear deformation, is... 

This is Poynting s theorem in the frequency domain (Stratton, 1941). It says that the energy flow outside the domain V] is formed by the balance between the energy dissipated in heat per unit volume per second, and the energy introduced through tlie extraneous currents j. ... 

The difficulty of understanding heat largely arose from its confusion with the concept of temperature. Early scientists tended to believe that objects came to thermal equilibrium when they each contained an equal amount of heat per unit volume. Black, whose work was published after his death in 1799, did much to clarify the position. He showed that different substances have different heat capacities. Thermal equilibrium is established between two bodies when their temperatures become equal. Heat will flow until temperature gradients disappear. Thus temperature difference provides the driving force for the flow of heat. The relation between the amount of heat transferred to a body, and the ensuing change in its temperature, depends on its heat capacity ... 

A is the thermal conductivity, and Q is transition heat per unit volume. Introducing the differential temperature, AT, and multiplying both sides by dt and integrating over a time interval large enough to make all the transient terms negligible, the following expression is obtained ... 

Latent heat per unit votume of melt. bLatcni heat per unit volume of solid. 

The thermohydraulic features of lead-bismuth and lead coolants are high boiling temperatures and the relative inertness compared with sodium. The melting and boiling points of sodium are respectively 98°C and 883 C. For lead-bismuth eutectic the respective figures are 123.5°C and 1670°C and for lead 327 C and 1740°C at atmospheric pressure. The boiling points are well above cladding failure temperatures. The specific heats per unit volume of lead-bismuth and lead are similar to those of sodium but the conductivities are about a factor of 4 smaller. 

O = quality factor, characterizing the coil stress S( ) = specific heat per unit volume V = quench voltage... 

The heating in the light field can be estimated as STzzaPTt/Cp, where a is the absorption coefficient in cm", T, [j] is the relaxation time, and [erg/cm -deg] is the specific heat per unit volume. If the width of the beam is greater than the cell width L then r, js (L /tt) V t where [cmVs] is the thermal diffusivity. 

C = specific heat per unit volume of the crystal V = speed of heat-transporting acoustic wave (phonon)... 

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