Heat transfer in pipe flow

According to Sieder and Tate [505] the following relationship applies for the heat transfer in an empty pipe for the laminar flow (Re 2.300)  

The effect of the parameter L/D makes itself apparent only up to L/D 200. 

It should be remembered, that Sieder and Tate [505] used the viscosity term to correlate heat transfer for cooling and heating, which makes little sense. In each case the boundary layer is completely different also with identical fluids. With the viscosity term the effect of the different /z(T) behavior of the fluid should be separately taken into account for either heat transfer direction, see Section 7.4. 

Heat Tranrfer in Pipes With Static Mixers 

In the creeping flow range, radial liquid exchange is completely absent in the pipe cross-section, thus static mixers should bring about a considerable improvement in heat transfer. 

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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... 

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). 

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 ... 

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 ... 

EFF OF NATURAL CONVECTION IN LAMINAR-FLOW HEAT TRANSFER In laminar flow at low velocities, in large pipes, and at large temperature drops, natural convection may occur to such an extent that the usual equations for laminar-flow heat transfer must be modified. The effect of natural convection in tubes is found almost entirely in laminar flow, as the higher velocities characteristic of flow in the transition and turbulent regimes overcome the relatively gentle currents of natural convection. 

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. 

In the course of the fast growing development of microfluidic devices like Lab-on-a-Chip, microreactors, and micro heat pipes, it is essential to develop effective systems for measuring the temperature distribution in the microscale. For example, for observing the heat transfer in microchannel flows, it is a matter of particular interest to know both the temperature distribution along the wall and the temperature distributirHi in the fluid flow. Conventional methods for temperature measurements are based on thermocouples and resistance thermometers which have a minimum size of about 10 pm and which always interfere with the system to be measured. Contactless methods for measuring temperature, e.g., infrared thermography, have many... 

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. 

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. 

For the heat transfer for fluids flowing in non-circular ducts, such as rectangular ventilating ducts, the equations developed for turbulent flow inside a circular pipe may be used if an equivalent diameter, such as the hydraulic mean diameter de discussed previously, is used in place of d. 

Calame JP, Myers RE, Binari SC, Wood FN, Garven M (2007) Experimental investigation of micro-channel coolers for the high heat flux thermal management of GaN-on-SiC semiconductor devices. Int J Heat Mass Transfer 50 4767-4779 Celata GP, Cumo M, Zummo G (2004) Thermal-hydraulic characteristics of single- phase flow in capillary pipes. Exp Thermal Fluid Sci 28 87-95 Celata GP (2004). Heat transfer and fluid flow in micro-channels. Begell House, N.Y. 

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... 

The first example pertains to forced convection in pipe flow. It is found that the rate of heat transfer between the pipe wall and a fluid flowing (turbulent flow) through the pipe depends on the following factors the average fluid velocity (u) the pipe diameter (d) the... 

All pipe-line work to date has dealt with fluids which are not thixotropic and rheopectic. To an extent this may be justified because the limiting conditions (at startup—for thixotropic materials, and after long times of shear for rheopectic fluids) in pipe flow and some mixing problems are of primary importance. Design for these conditions would be similar to the techniques discussed herein for other fluids. This is not true of problems in heat transfer, however, and inception of work on the laminar flow of thixotropic fluids in round pipes would appear to be in order as a prerequisite to an understanding of such more complex nonisothermal problems. 

Grigull (G8), 1942 Treatment of heat transfer in condensate film on vertical surface, assuming applicability of Prandtl pipe-flow relationships. Comparison with experimental data,... 

Now, if the longitudinal heat transfer in the fluid is neglected, the energy equation for fully developed constant fluid property turbulent pipe flow can be written as ... 

Whitaker, S., Forced Convection Heat-Transfer Correlations for Flow in Pipes, Past Flat Plated, Single Cylinders, Single Spheres, and Flow in Packed Beds and Tube Bundles , AIChE J.. Vol. 18, pp. 361-371.1972. 

Consider the double-pipe heat exchanger shown in Fig. 10-2. The fluids may flow in either parallel flow or counterflow, and the temperature profiles for these two cases are indicated in Fig. 10-7. We propose to calculate the heat transfer in this double-pipe arrangement with... 

There are many well-known dimensionless groups that are used in transport phenomena. Earlier, the Reynolds number was used to correlate data on pressure drop in pipe flow. For correlating data on heat transfer, often the dimensionless groups Nus-selt (Nu), Reynolds (Re), Prandtl (Pr), and Grashof (Gr) are used. They are defined as ... 

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