Heat transfer in pipes

Heat Transfer in Pipes Solve the problem of conductive heat transfer across an infinitely long tube of inside and outside radii of / , and Ra. Consider the following two physical situations (a) the surface temperatures at If and Ra are maintained at 7) and T0 (b) both the inside and outside tube surfaces are exposed to heat transfer fluids of constant temperatures Ta and Tb and heat-transfer coefficients ht and h0. 

The inclusion of the viscosity number, Vis = Pw/p, in the process equation for heat transfer in pipes goes back to Sieder and Tate [29]. These researchers succeded to correlate experimental data obtained in pipe flow with the term (pw/p)-0 14. In this manner, the differences between the cooling and heating process were considered, these manifesting themselves by the differences in the thickness of the boundary layers. In heating, practically no boundary layer is present as compared to cooling. The heat transfer characteristics read ... 

Compute the process-side heat-transfer coefficient. The correlations for inside (process-side) heat-transfer coefficient in an agitated tank are similar to those for heat transfer in pipe flow, except that the impeller Reynolds number and geometric factors associated with the tank and impeller are used and the coefficients and exponents are different. A typical correlation for the agitated heat-transfer Nusselt number (ANu = htT/k) of a jacketed tank is expressed as... 

The temperature dependence of the viscosity of the liquid and thereby the boundary layer thickness upon cooling and heating is taken into consideration with the viscosity term Vis = Following the suggestion of Sieder and Tate [505], that experimental data for heat transfer in pipes upon heating and cooling correlated upon inclusion of Vis , this expression was also accepted in most research studies over heat transfer in mixing. 

R. Oskay and S. Kakac, Effect of viscosity variations on forced convection heat transfer in pipe flow, METU Journal of Pure and Applied Sciences 6, 211-230 (1973). 

MORE ACCURATE ANALOGY EQUATIONS. A number of more elaborate analogy equations connecting friction and heat transfer in pipes, along flat plates, and in annular spaces have been published. They cover wider ranges of Reynolds and Prandtl numbers than Eq. (12.52) and are of the general form... 

Levich [32] solved eqn. (1) for a channel electrode by invoking an approximation originally introduced in 1928 by Leveque in his theory of heat transfer in pipes [33]. In the present context, this simplification can be written as... 

J. W. Ou, and K. C. Cheng, Viscous Dissipation Effects on Thermal Entrance Region Heat Transfer in Pipes with Uniform Wall Heat Flux, Appl. Sci. Res., (28) 289-301,1973. 

The Reynolds analogy, defined as the ratio of the Stanton number to the local skin friction coefficient St/(c//2) is a function of the Prandtl number and is extremely useful for estimating heat transfer. Pressure drop can be used to predict heat transfer in pipes, and the skin friction can be used to predict Stanton number for external flows. 

Temperature obviously affects the physical properties of the fluids, thus indirectly affecting the transfer coefficients. As in the case of heat transfer in pipes, equations involving viscosity corrections for temperature differences between bulk and interface have been suggested (Eq. 11-14, Table II) and are especially applicable for viscous continuous phases. No correction is needed for water, for instance, especially at > 50. At lower (A Re)c. natural convection is pronounced, especially in liquid systems with low kinematic viscosity. Since the transfer coefficient for natural convection is a function of the Grashof number, one may expect some effects of the temperature gradient. Steinberger and Treybal s equation (Eq. 6) allows for these effects. 

Wigner s style is best illustrated by the recipe sheets he would distribute to his group. Whether the matter at issue was computation of the multiplication constant, or heat transfer in pipes, or elastic deformation, he would prepare a one-page recipe sheet on which he summarized the relevant formulae including appropriate constants. (His heat transfer sheet has enabled me to hold my own in arguments about heat transfer for more than 40 years )... 

Hughmark employed this u to derive a correlation for Son and Hanratty (1967) and Hughmark (1971,1974) correlated wall to fluid heat transfer in pipe flow based on the relatively simple and well-established boundary layer theory. In the case of pipe flow, momentum transfer is solely by skin friction because of the geometry involved. Nonetheless, this approach was extended to particle-fluid mass transfer in turbulent flow. The correlation proposed was of the following form ... 

Several wick stmctures are in common use. First is a fine-pore (0.14—0.25 mm (100-60 mesh) wire spacing) woven screen which is roUed into an annular stmcture consisting of one or more wraps inserted into the heat pipe bore. The mesh wick is a satisfactory compromise, in many cases, between cost and performance. Where high heat transfer in a given diameter is of paramount importance, a fine-pore screen is placed over longitudinal slots in the vessel wall. Such a composite stmcture provides low viscous drag for Hquid flow in the channels and a small pore size in the screen for maximum pumping pressure. 

Heat transfer in static mixers is intensified by turbulence causing inserts. For the Kenics mixer, the heat-transfer coefficient b is two to three times greater, whereas for Sulzer mixers it is five times greater, and for polymer appHcations it is 15 times greater than the coefficient for low viscosity flow in an open pipe. The heat-transfer coefficient is expressed in the form of Nusselt number Nu = hD /k as a function of system properties and flow conditions. 

Convection is the heat transfer in the fluid from or to a surface (Fig. 11.28) or within the fluid itself. Convective heat transport from a solid is combined with a conductive heat transfer in the solid itself. We distinguish between free and forced convection. If the fluid flow is generated internally by density differences (buoyancy forces), the heat transfer is termed free convection. Typical examples are the cold down-draft along a cold wall or the thermal plume upward along a warm vertical surface. Forced convection takes place when fluid movement is produced by applied pressure differences due to external means such as a pump. A typical example is the flow in a duct or a pipe. 

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. 

In many of the applications of heat transfer in process plants, one or more of the mechanisms of heat transfer may be involved. In the majority of heat exchangers heat passes through a series of different intervening layers before reaching the second fluid (Figure 9.1). These layers may be of different thicknesses and of different thermal conductivities. The problem of transferring heat to crude oil in the primary furnace before it enters the first distillation column may be considered as an example. The heat from the flames passes by radiation and convection to the pipes in the furnace, by conduction through the... 

For the common problem of heat transfer between a fluid and a tube wall, the boundary layers are limited in thickness to the radius of the pipe and, furthermore, the effective area for heat flow decreases with distance from the surface. The problem can conveniently be divided into two parts. Firstly, heat transfer in the entry length in which the boundary layers are developing, and, secondly, heat transfer under conditions of fully developed flow. Boundary layer flow is discussed in Chapter 11. 

Neglect any resistance to heat transfer in the pipe walls. 

The micro-channels utilized in engineering systems are frequently connected with inlet and outlet manifolds. In this case the thermal boundary condition at the inlet and outlet of the tube is not adiabatic. Heat transfer in a micro-tube under these conditions was studied by Hetsroni et al. (2004). They measured heat transfer to water flowing in a pipe of inner diameter 1.07 mm, outer diameter 1.5 mm, and 0.600 m in length, as shown in Fig. 4.2b. The pipe was divided into two sections. The development section of Lj = 0.245 m was used to obtain fully developed flow and thermal fields. The test section proper, of heating length Lh = 0.335 m, was used for collecting the experimental data. 

For conventional size pipes the flow regimes depend on orientation. Two-phase air-water flow and heat transfer in a 25 mm internal diameter horizontal pipe were investigated experimentally by Zimmerman et al. (2006). Figure 5.38 shows the flow... 

Direct measurements of turbulent heat transfer in smooth pipes led to the correlation known as the Dittus-Boelter equation... 

ESDU 78031 (2001) Internal forced convective heat transfer in coiled pipes. 

Kool, J. Trans. Inst. Chem Eng. 36 (1958) 253-8. Heat transfer in scraped vessels and pipes handling viscous materials. 

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