Forced convection heat transfer profiles

Figure 9-12. The self-similar temperature profile given by Eq. (9-240) for forced convection heat transfer from a heated (or cooled) solid sphere in a uniform velocity field at small Re and large Pe. The function g( i]) represents the dependence of the thermal boundary-layer thickness on // and is given by (9-237).

B.3 Forced Convection Heat Transfer in Tubes-Short Contact Times. A polymeric fluid whose viscosity function is described by the Ellis model is flowing through the tube as shown in Figure 5.26. Determine the temperature profile and the wall heat flux for the... 

The foregoing analysis of free-convection heat transfer on a vertical flat plate is the simplest case that may be treated mathematically, and it has served to introduce the new dimensionless variable, the Grashof number, which is important in all free-convection problems. But as in some forced-convection problems, experimental measurements must be relied upon to obtain relations for heat transfer in other circumstances. These circumstances are usually those in which it is difficult to predict temperature and velocity profiles analytically. Turbulent free convection is an important example, just as is turbulent forced convection, of a problem area in which experimental data are necessary however, the problem is more acute with free-convection flow systems than with forced-convection systems because the velocities are usually so small that they are very difficult to measure. Despite the experimental difficulties, velocity measurements have been performed using hydrogen-bubble techniques [26], hot-wire anemometry [28], and quartz-fiber anemometers. Temperature field measurements have been obtained through the use of the Zehnder-Mach interferometer. The laser anemometer [29] is particularly useful for free-convection measurements because it does not disturb the flow field. 

Jiji, L. M.,andJ. A. Clark, 1964, Bubble Boundary Layer and Temperature Profiles for Forced Convection Boiling in Channel Flow, Trans. ASME, J. Heat Transfer 56 50 58. (4)... 

The heat transfer immediately downstream of the location where heating begins will be dominated by forced convection and will depend on the velocity profile. For a parabolic inlet profile, the forced convection Nusselt number can be approximated by [249] ... 

An important heat-transfer system occurring in process engineering is that in which heat is being transferred from a hot vertical plate to a gas or liquid adjacent to it by natural convection. The fluid is not moving by forced convection but only by natural or free convection. In Fig. 4.7-1 the vertical flat plate is heated and the free-convection boundary layer is formed. The velocity profile differs from that in a forced-convection system in that the velocity at the wall is zero and also is zero at the other edge of the boundary layer since the free-stream velocity is zero for natural convection. The boundary layer initially is laminar as shown, but at some distance from the leading edge it starts to become turbulent. The wall temperature is T K and the bulk temperature T. ... 

Figures 2.5 and 2.6 reveal that deterioration is caused by a different mechanism at low flow rates. The calculation results at G = 39 kg m s and 7 = T, which gives the Reynolds number 10,000, are rearranged in terms of the Grashof number and the Nusselt number in Fig. 2.8. Nu has a minimum value at Gr = 2 x 10. Nu is constant when Gr is lower than it, which means forced convection is dominant. On the other hand, Nu increases linearly when Gr is larger than the minimum point, which implies that natural convection is dominant. The minimum point emerges at the boundary between the two convection modes. Flow velocity and turbulence energy profiles are depicted in Fig. 2.9. When the heat flux is enhanced, the flow velocity increases near the wall and the profile becomes flat. Since turbulence energy is produced by the derivative of flow velocity, it is reduced. Hence, heat transfer is deteriorated. When the heat flux is enhanced above the minimum point, the flow velocity profile is more distorted and turbulent heat transfer is then enhanced. This type of heat transfer deterioration is attributed to acceleration as well as buoyancy. In the present analysis, buoyancy force is dominant. The computational results without the buoyancy force term in the Navier-Stokes equations are...

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