Heat Transfer in a Pipe

There are three interfaces in this problem, and by writing the energy balance at each interface, there will be three linear equations and three unknown temperatures  

Heat transfer from steam to pipe Heal transfer from pipe to insulation Heat transfer from insulation to air  

Rearranging the above three energy balance equations yields the set of linear algebraic equations, shown below, which can be solved to find the three unknowns T, Tj, and Ty 

Method of Solution The function is written based on Gauss elimination in matrix form. It applies complete pivoting strategy by searching rows and columns for the maximum pivot element. It keeps track of column interchanges, which affect the positions of the unknown variables. The function applies the back-substimtion formula [Eq. (2.110)] to calculate the unknown variables and interchanges their order to correct for column pivoting. 

At the begi nning, the program checks the determinant of the matrix of coefficients to see if the matrix is singular. If it is singular, the program gives the rank of the matrix and terminates calculations. 

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Schleicher, C.A. and Tribus, M., "Heat Transfer in a Pipe with Turbulent Row and Arbitrary Wall-Temperature Distribution , Trans. ASME, vol. 79, pp. 789-797, 1957. 

G A. Sleicher, and M. Tribus, Heat Transfer in a Pipe with Turbulent Flow and Arbitrary Wall-Temperature Distribution, 1956 Heat Transfer and Fluid Mechanics Institute, Stanford University Press, Stanford, pp. 59-78,1956. 

Eroshenko, V.M., Ershov, A.V., Zaichik, L.I., 1986. Effect of variability of physical properties of a gas on turbulent flow and heat transfer in a pipe with permeable walls. J. Eng. Phys. 50, 135-139. 

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 through a pipe wall. A pipeline parr 15m long carries water. Its internal diameter d, is 34 mm and its external diameter is 42 mm. The thermal conductivity of the pipe X is 40 W m K". The pipeline is located outdoors, where the outdoor temperature Oao is -8 C. Determine the minimum flow velocity necessary in the pipe to prevent the pipe from freezing. The heat transfer coefficient inside the pipe is = 1000 W m K and outside the pipe = 5 W m" K aiid = 4 W m -K . The specific heat ca-... 

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... 

Heat Transfer in Insulated Pipes Solve case (b) of Problem 2.22 for a composite tube made of material of thermal conductivity kj for / , < r < Rm and of material of thermal conductivity k0 for Rm < r < R0. 

Another example of heat transfer involving a porous medium is heat transfer from a pipe or cable buried in soil or in a bed of crushed stones which is saturated with around water which is flowing through the soil or stones. This is illustrated in Fig. 10.3. 

Discussion Note that the total rate of heat transfer through a pipe Is constant, but the heat flux q = QI 2nrL) is not since it decreases In the direction of heat transfer v/ith increasing radius,... 

For turbulent heat transfer in long pipes, the individual film coefficient inside a pipe can be... 

G. Yang, Z. F. Dong, and M. A. Ebadian, Convective Heat Transfer in a Helicoidal Pipe Heat Exchanger, J. Heat Transfer, (115) 796—800,1993. 

Y. Mori and W. Nakayama, Forced Convection Heat Transfer in a Straight Pipe Rotating Around a Parallel Axis, Int. J. Heat Mass Transfer (10) 1179-1194,1967. 

V. Vidyanidhi, V. V. S. Suryanarayana, and V. C. Chenchu Raju, An Analysis of Steady Freely Developed Heat Transfer in a Rotating Straight Pipe, J. Heat Transfer (99) 148-150,1977. 

Heat transfer inside a pipe. The Buckingham theorem, given in Section 3.11 states that the function relationship among q quantities or variables whose units may be given in terms of u fundamental units or dimensions may be written as q — u) dimensionless groups. 

The equation holds for N, . of 0.6 to 3000 (G2, LI). Note that theNj,. for gases is in the range 0.5-3 and for liquids is above 100 in general. Equation (7.3-25) for mass transfer and Eq. (4.5-8) for heat transfer inside a pipe are similar to each other. 

The selection of materials for these applications is often a compromise between the requirements of the process flow and the type of water. Associated with such heat exchangers are pumps, pipes, and valves to distribute the water and return it to source. The various metals commonly used in heat exchangers have quite different thermal conductivities (Table 8.9). However, the thermal conductivity of the metal wall is only one component of the resistance to heat transfer in a heat exchanger tube. In a condenser (i.e., where steam is condensing on cold tubes), for example, the resistance to heat transfer through a tube wall is made up of five main components as illustrated in Fig. 8.15 [8]. The tube wall resistance is comparatively small so that changes in thermal conductivity from the use of different metals in not necessarily very significant. 

Solves a set of simultaneous linear algebraic equations that model the heat transfer in a steel pipe using the Gauss Elimination method (Gauss.m). 

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. 

In predicting the time required to cool or heat a process fluid in a full-scale batch reactor for unsteady state heat transfer, consider a batch reactor (Figure 13-2) with an external half-pipe coil jacket and non-isothermal cooling medium (see Chapter 7). From the derivation, the time 6 to heat the batch system is ... 

Heat transfer coefficient between a pipe and a wall. Water flows in a pipe d =15 mm) with a velocity of v = 1.0 m s. The mean temperature of water is 0 , = 15 °C, and the wall temperature 6 = 50 °C. Calculate the heat transfer coefficient away from the pipe inlet. For water the properties are... 

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. 

Compressibility of a gas flowing in a pipe can have significant effect on the relation between flowrate and the pressures at the two ends. Changes in fluid density can arise as a result of changes in either temperature or pressure, or in both, and the flow will be affected by the rate of heat transfer between the pipe and the surroundings. Two limiting cases of particular interest are for isothermal and adiabatic conditions. 

As the pressure in a pipe falls, the kinetic energy of the fluid increases at the expense of the internal energy and the temperature tends to fall. The maintenance of isothermal conditions therefore depends on the transfer of an adequate amount of heat from the surroundings. For a small change in the system, the energy balance is given in Chapter 2 as ... 

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... 

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