Flow heated laminar tube

Flow systems in use may be classified as heated laminar tubes, or plug flow tube reactors, (PFTR) and burners, or heated turbulent flow reactors and well-stirred reactors, or continuous stirred-tank reactors, (CSTR). 

The inside film coefficient represents the resistance to heat flow caused by the change in flow regime from turbulent flow in the center of the tube to laminar flow at the tube surface. The inside film coefficient can be calculated from ... 

In this section the influence of the pressure in the capillary and the heat flux fluctuations on the stability of laminar flow in a heated capillary tube is analyzed. All the estimations performed in the framework of the general approach and developed in the previous section are kept also in the present cases. Below we will assume that the single cause for capillary pressure oscillations is fluctuations of the contact angle due to motion of the meniscus, whereas heat flux oscillations are the result of fluid temperature fluctuations only. 

Flow in a Tube. Laminar flow with a flat velocity profile and slip at the walls can occur when a viscous fluid is strongly heated at the walls or is highly non-Newtonian. It is sometimes called toothpaste flow. If you have ever used Stripe toothpaste, you will recognize that toothpaste flow is quite different than piston flow. Although Vflr) = u and z(7) = 1, there is little or no mixing in the radial direction, and what mixing there is occurs by diffusion. In this situation, the centerline is the critical location with respect to stability, and the stability criterion is... 

Much can be learned by analyzing the structure of a flame in more detail. Consider, for example, a flame anchored on top of a single Bunsen burner as shown in Fig. 4.3. Recall that the fuel gas entering the burner induces air into the tube from its surroundings. As the fuel and air flow up the tube, they mix and, before the top of the tube is reached, the mixture is completely homogeneous. The flow velocity in the tube is considered to be laminar and the velocity across the tube is parabolic in nature. Thus the flow velocity near the tube wall is very low. This low flow velocity is a major factor, together with heat losses to the burner rim, in stabilizing the flame at the top. 

Dravid, A.N. Smith, K.A, Merrill, E.W.J and Brian, P.L.T. "The Effect of Secondary Fluid Motion on Laminar Flow Heat Transfer in Helically Colled Tubes", paper presented at 68th National A.I.Ch.E, Meeting, Houston, Texas, 1971... 

The quasi-steady laminar model is now employed to describe the heat transfer near the wall. Note that while the shear stress at the wall can be related easily to the pressure drop for the flow in a tube, it is more difficult to establish a relation between these two quantities for a packed or fluidized bed. However, while for the flow in a tube the dissipated energy is not uniform over the section... 

In the forced convection heat transfer, the heat-transfer coefficient, hy mainly depends on the fluid velocity because the contribution from natural convection is negligibly small. The dependence of the heat-transfer coefficient, hy on fluid velocity, IT, which has been observed empirically (1—3), for laminar flow inside tubes, is h V1//3 for turbulent flow inside tubes, h V3//4 and for flow outside tubes, h V2/73. Flow may be classified as laminar or turbulent. Laminar flow is generally characterized by low velocities and turbulent flow by high velocities. It is customary to use the Reynolds number, Rtf, to identify whether a flow is laminar or turbulent. 

In Ulrichson and Schmit s work on laminar flow heat transfer in the entrance region of circular tubes the following results were obtained. 

In many practical applications, condensation occurs on a column of vertically aligned horizontal tubes. In such a case, as illustrated in Fig. 11.16, the condensate cascades from tube to tube down the column of tubes. If the flow remains laminar, the heat transfer rate from lower tubes will decrease because of the thickening condensate film. 

It turns out that Eq. (5-56) can also be applied to turbulent flow over a flat plate and in a modified way to turbulent flow in a tube. It does not apply to laminar tube flow. In general, a more rigorous treatment of the governing equations is necessary when embarking on new applications of the heat-trans-fer-fluid-friction analogy, and the results do not always take the simple form of Eq. (5-56). The interested reader may consult the references at the end of the chapter for more information on this important subject. At this point, the simple analogy developed above has served to amplify ouf understanding of the physical processes in convection and to reinforce the notion that heat-transfer and viscous-transport processes are related at both the microscopic and macroscopic levels. 

Consider the tube-flow system in Fig. 5-13. We wish to calculate the heat transfer under developed flow conditions when the flow remains laminar. The wall temperature is Tw, the radius of the tube is rc, and the velocity at the center of the tube is u0. It is assumed that the pressure is uniform at any cross section. The velocity distribution may be derived by considering the fluid element shown in Fig. 5-14. The pressure forces are balanced by the viscous-... 

The developed velocity profile for turbulent flow in a tube will appear as shown in Fig. 5-15. A laminar sublayer, or film, occupies the space near the surface, while the central core of the flow is turbulent. To determine the heat transfer analytically for this situation, we require, as usual, a knowledge of the temperature distribution in the flow. To obtain this temperature distribution, the... 

The analysis of Sec. 5-10 has shown how one might analytically attack the problem of heat transfer in fully developed laminar tube flow. The cases of undeveloped laminar flow, flow systems where the fluid properties vary widely with temperature, and turbulent-flow systems are considerably more complicated but are of very important practical interest in the design of heat exchangers and associated heat-transfer equipment. These more complicated problems may sometimes be solved analytically, but the solutions, when possible, are... 

Flfl. 6-3 Influence of heating on velocity profile in laminar tube flow. 

While the engineer may frequently be interested in the heat-transfer characteristics of flow systems inside tubes or over flat plates, equal importance must be placed on the heat transfer which may be achieved by a cylinder in cross flow, as shown in Fig. 6-7. As would be expected, the boundary-layer development on the cylinder determines the heat-transfer characteristics. As long as the boundary layer remains laminar and well behaved, it is possible to compute the heat transfer by a method similar to the boundary-layer analysis of Chap. 5. It is necessary, however, to include the pressure gradient in the analysis because this influences the boundary-layer velocity profile to an appreciable extent. In fact, it is this pressure gradient which causes a separated-flow region to develop on the back side of the cylinder when the free-stream velocity is sufficiently large. 

Bergles, A. E., and R. R. Simonds Combined Forced and Free Convection for Laminar Flow in Horizontal Tubes with Uniform Heat Flux, Int. J. Heat Mass Transfer, vol. 14, p. 1989, 1971. 

In laminar flow in a tube with constant surface temperature, both the friction factor and the heat tranter coefficient remain constant in the fully developed region. 

Tlie friction factor/and the Nusselt number relations are given in Table 8-1 for fully developed laminar flow in tubes of various cross sections. The Reynolds and Nu.sselt numbers for flow in these tubes are based on the hydraulic diameter D/, - 4AJp, where is the cross sectional area of the tube and p is its perimeter. Once the Nusselt number is available, the convection heat transfer coefficient is determined from h = / Nu/D. ... 

Some simple heal transfer equipments consist of two concentric tubes, and are properly called double-tube heat exchangers (Fig. 8-27). In such devices, one fluid flows through the tube while the other flows through the aunular space. The governing differential equations for both flow.s are identical. I herefore, steady laminar flow through an annulus can he studied analytically by using suitable boundary conditions. 

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