Heat flow density

The heat flow density q of a material depends on the local temperature gradient, according to Fourier s law ... 

Thin boundary layers provide the highest values of heat flow density. Because the boundary layer gradually develops upstream from the inlet point, the heat flow density is highest at the inlet point. Heat flow density-decreases and achieves its final value in the region of fully developed flow. The correction is noted in the equations by means of the quotients d/.L and d/x. 

Haenel, R., Stegena, L., Rybach, (eds.) Handbook of Terrestrial Heat-Flow Density Determination, Kluwer Academic Publishers, Dordrecht, Netherlands, 87 (1988). 

The kinetic theory leads to the definitions of the temperature, pressure, internal energy, heat flow density, diffusion flows, entropy flow, and entropy source in terms of definite integrals of the distribution function with respect to the molecular velocities. The classical phenomenological expressions for the entropy flow and entropy source (the product of flows and forces) follow from the approximate solution of the Boltzmann kinetic equation. This corresponds to the linear nonequilibrium thermodynamics approach of irreversible processes, and to Onsager s symmetry relations with the assumption of local equilibrium. 

Rybach L. (1988) Determination of heat production rate. In Handbook of Terrestrial Heat-flow Density Determination (eds. R. Haenel, L. Rybach, and L. Stegena). Kluwer, pp. 125-142. 

Correia, A., Jones, F.W. Fricker, A. (1990) Terrestrial heat flow density estimates for the Jeanne d Arc Basin offshore eastern Canada. Geophysics 59, 1625-1633. 

The nucleate boiling superheat AT has been described as a function of the heat flow-density complex equations. There exist essentially tw o kinds of boiling correlations the transport equations valid for a special configuration and equations closely related to the equilibrium thermodynamics of quasi-static systems. The transport equations determine the details of the heat transport mechanism with consideration of the force field and special conditions of each particular system, but they are so complex that it is difficult to arrive at satisfactory equations which will be valid in the entire range of pressures from the triple to the critical point. 

The experimental data plotted in Figs. 1 through 6 represent the highest values reported and show the broad superheat range typical of nucleate boiling, which is often due to different nucleation conditions. For comparison, the heat flow density (the peak flux of natural convection pool boiling on a horizontal plate as given by Kutateladze)... 

Because of the pipe wall of vertical U-tube is very thin (4 mm), could neglect the influence of pipe side, consider that the heat of concrete transferred form the pipe equal to the heat that circulating solution inside the pipe spread to the bury tube. So the change heat of per unit area underground tube and concrete, also as heat flow density q is ... 

From this equation, the original Fourier s equation is retrieved by substituting the entropic flow density Js times the temperature Tby the heat flow density. 

The local temperature distribution and the change of the temperature on the surface of a roller with time, can be viewed as the overlaying of a stationary temperature field with a field resulting from a temperature oscillation. The illustration shows the local heat-flow density in a roller as a function of the number of revolutions (see Fig. 3.19). 

The critical heat flow density at the dry out point of the tube surface strongly depends on the pressure range (57). 

Thermal conductivity characterizes the heat flow density <7 as a result of a temperature gradient (Fourier s law) ... 

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