Thick-walled tube, conduction through

Thermometer pocket, heat transfer u>. example 544 Tliemiosyphon reboilers 496 Thick-walled tube, conduction through 392 Thiele. E. W. 637.655 Thiele modulus 637... 

Figure 9.8. Conduction through thick-walled tube or spherical shell The heat flow at any radius r is given by ...

Two complex tissues, the xylem and phloem, provide the conducting network or "circulatory system" of plants. In the xylem or woody tissue, most of the cells are dead and the thick-walled tubes (tracheids) serve to transport water and dissolved minerals from the roots to the stems and leaves. The phloem cells provide the principal means of downward conduction of foods from the leaves. Phloem cells are joined end to end by sieve plates, so-called because they are perforated by numerous minute pores through which cytoplasm of adjoining sieve cells appears to be connected by strands 5-9 pm in diameter.154 Mature sieve cells have no nuclei, but each sieve cell is paired with a nucleated "companion" cell. 

A fire tube contains a flame burning inside a piece of pipe which is in turn surrounded by the process fluid. In this situation, there is radiant and convective heat transfer from the flame to the inside surface of the fire tube, conductive heat transfer through the wall thickness of the tube, and convective heat transfer from the outside surface of that tube to the oil being treated. It would be difficult in such a simation to solve for the heat transfer in terms of an overall heat transfer coefficient. Rather, what is most often done is to size the fire tube by using a heat flux rate. The heat flux rate represents the amount of heat that can be transferred from the fire tube to the process per unit area of outside surface of the fire tube. Common heat flux rates are given in Table 2-11. 

With RESS, the heating power Q is supplied by a heat source that is separated from the inner wall of the expansion device by a solid wall of a thickness suitable to contain the applied static pressure. We assume that the heat is uniformly supplied on the outer surface of tubing of length L and outer diameter Do (Figure 4b). The heat flow through the tubing wall by conduction must be equal to the heat flow into the fluid from the inner wall ... 

Sizing of heat exchangers assumes a certain heat-transfer efficiency between the bulk fluid and metal wall. Because biofilms more or less behave like gels on the metal surface, heat transfer can occur only by conduction through the biofilm. The thermal conductivity of biofilms is similar to that of water but much less than that of metals. On the basis of relative thermal conductivities (Table 2.37), a biofilm layer 41 p,m thick offers the same resistance to heat transfer as a titanium tube wall 1000 p,m thick. 

Water at 293 K is heated by passing through a 6.1 m coil of 25 mm internal diameter pipe. The thermal conductivity of the pipe wall is 20 W/m K and the wall thickness is 3.2 mm. The coil is heated by condensing steam at 373 K for which the film coefficient is 8 kW/m2 K. When the water velocity in the pipe is I tn/s, ils outlet temperature is 309 K. What will the outlet temperature be if the velocity is increased to 1.3 m/s, if the coefficient of heat transfer to the water in the tube is proportional to the velocity raised to the 0.8 power ... 

Film-condensation coefficients for vertical surfaces. Film-type condensation on a vertical wall or tube can be analyzed analytically by assuming laminar flow of the condensate film down the wall. The film thickness is zero at the top of the wall or tube and increases in thickness as it flows downward because of condensation. Nusselt (HI, Wl) assumed that the heat transfer from the condensing vapor at 7, K, through this liquid film, and to the wall at 7 K was by conduction. Equating this heat transfer by conduction to that from condensation of the vapor, a final expression can be obtained for the average heat-transfer coefficient over the whole surface. 

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