Conductive heat flow

The conductive heat flow to the pipeline from the surrounding solid is ... 

Within such objects, conductive heat flow can be solved as well. This is sometimes called conjugate heat transfer in the literature. 

To reduce heat transfer by conduction, an insulant should have a small ratio of solid volume to void. Additionally, a thin-wall matrix, a discontinuous matrix or a matrix of elements with minimum point contacts are all beneficial in reducing conducted heat flow. A reduction in the conduction across the voids can be achieved by the use of inert gases rather than still air. 

Referring again to Fig. 4.3, consider the energy balance from the point of view of a cylindrical control volume. The conductive heat flow dQ/dt crossing the control surfaces into... 

Conductive heat flow (Q), or duty, of a heat exchanger can be calculated from the following equations (where process temperature changes but does not change state) ... 

As indicated in Table 7.10, only in the last decade have models considered all three phenomena of heat transfer, fluid flow, and hydrate dissociation kinetics. The rightmost column in Table 7.10 indicates whether the model has an exact solution (analytical) or an approximate (numerical) solution. Analytic models can be used to show the mechanisms for dissociation. For example, a thorough analytical study (Hong and Pooladi-Danish, 2005) suggested that (1) convective heat transfer was not important, (2) in order for kinetics to be important, the kinetic rate constant would have to be reduced by more than 2-3 orders of magnitude, and (3) fluid flow will almost never control hydrate dissociation rates. Instead conductive heat flow controls hydrate dissociation. 

An extremely fine localization of primordial 3He injection, on a 10-m scale, has also been observed. It has been suggested that lower-than-expected conductive heat flow at oceanic ridges could be due to significant heat transport by hydrothermal circulation (e.g., Talwani, Windisch Langseth, 1971), in which recently emplaced hot rock drives convection of local sea water. On the basis of temperature-salinity relationships, Weiss et al. (1977) made the first identification of hydrothermal circulation in the open ocean, observing several plumes (temperature differential <0.2°C)... 

More detailed examination and sampling allows association of hydrothermal circulation with specific vent fields. In such waters samples in the Galapagos Rift by the Alvin deep submersible, Jenkins, Edmond, and Corliss (1978) report juvenile He enrichments which dwarf the normal saturation concentrations by factors up to 11 for 4He and 60 for 3He (Figure 4.6). A particularly significant feature of this report is that added He occurs roughly in proportion to added heat AT up to 12°C in sampled water), corresponding to about 7.6 x 10 xcal/atom of 3He (Figure 4.7). Jenkins et al. note that if this value is representative, hydrothermal circulation may indeed account for the depression of conductive heat flow relative to models for total heat flux. As... 

This equation is valid for steady-state one-dimensional conductive heat flow. 

Heat flow (in mW from the ocean floor as a function of sediment age (in millions of years, which is proportional to distance from the ridge crest, where age = 0). The dashed line is the predicted heat flow from a crustal cooling model and the solid line is the observed conductive heat flow based on sediment thermal gradients and the heat conduction equation. From Elderfield and Schultz (1995). 

The entropy (denoted by the symbol S) is a state function. In a system in which there are flows of both heat by conduction (Q) and work [W andP dV/dt)] across the system boundaries, the conductive heat flow, but not the workflow, causes a change in the entropy of the system this rate of entropy change is Q/T, where T is the absolute thermodynamic temperature of the system at the point of the heat flow. If, in addition, there are mass flows across the system boundaries, the total entropy of the system will also change due to this... 

G. K. Lewis, Shape Factors in Conduction Heat Flow for Circular Bars and Slabs with Internal Geometries, Int. J. Heat Mass Transfer, Vol. 11, pp. 985-992,1968. 

Lonsdale P, Becker K (1985) Hydrothermal plumes, hot springs, and conductive heat flow in the Southern Trough of Guaymas Basin. Earth Planet Sci Lett 73 211-225 Massoth GJ, Butterfield DA, Lupton JE, McDuff RE, Lilley MD, Jonasson IR (1989) Submarine venting of phase-separated hydrothermal fluids at Axial Volcano, Juan de Fuca Ridge. Nature 340 702-705 McKenzie DP, Davies D, Molnar P (1970) Plate tectonics of the Red Sea and east Africa. Nature 226 243-248... 

The plate is placed in a climatic chamber with a defined temperature (20 °C) and covered by the fabric to be tested. In a steady-state condition, the heating power needed to maintain the plate at 35 °C is equal to the heat flux through the fabric. Thus, by measuring this heating power, the thermal resistance can be calculated. In this method, the intrinsic resistance of the fabric is measured in conjunction with a transition resistance firom fabric to air. This transition resistance is dependent on the radiant and convective heat transfer between the fabric and the environment. For the assessment of the thermal resistance of undergarments, like the base layer or the mid layers, this method is less appropriate, as these layers usually lay between the skin and an outer layer or two fabric layers. In this case, thermal conduction is the main heat transfer mechanism, and, therefore, the thermal resistance has to be calculated from the thermal conductivity of the fabrics. For this purpose, the method described in ISO 5085-1 (1989) and 5085-2 (1989) is used the fabric is placed between two plates with different temperature and the conductive heat flow is assessed. 

Conduction. Heat flow by conduction is a result of transfer of kinetic and/or internal energy between molecules in a fluid or solid. The basic equation of conductive heat transfer is Fourier s law... 

In the electrical analogue the thermal conductance, heat flow and temperature are equivalent to the electrical conductance, current and voltage respectively. 

Two large, flat, porous horizontal plates are separated by a small distance B. The upper plate at y = B is at Tg, while the lower plate at y = 0 is to be kept at To- In order to reduce the heat to be removed from the lower plate, a cooling gas is passed upward through both plates. Find the temperature distribution in the space B and determine the conduction heat flow to the lower plate. 

Many problems in science and engineering can be solved by inspection of the units that the answer will take, that is, by a logical arrangement of the given data. Dimensional analysis is a simple method used to solve many problems by looking at the units of the given information or of a conversion factor and the required units of the desired answer, the method of solution becomes obvious. For example, the equation for conductive heat flow is ... 

Heat flow to the environment through conduction Heat flow to the environment through radiation Heat flow to the environment through convection Totai heat flow that dissipates into the environment... 

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