Heat transfer axisymmetric bodies

Dhir, V.K. and Lienhard, J.H., Laminar Film Condensation on Plane and Axisymmetric Bodies in Non-uniform Gravity, J, Heat Transfer, Vol. 93, p. 97, 1971. 

Unfortunately, however, there are a large number of different types of flow conditions for which the boundary-layer form of the heat transfer correlation (9-255) is not applicable. This applies, basically, to any flow configuration in which the body is completely surrounded by a region of closed streamlines (or pathlines, if the flow is not 2D or axisymmetric). We will discuss high-Peclet-number heat transfer in such cases in Section L. Here, we consider... 

Sehlin, R. C., Forced-Convection Heat and Mass Transfer at Large Peclet Numbers From Axisymmetric Body in Laminar Flow Prolate and Oblate Spheroids, M.S. Thesis (Chem. Eng.), Carnegie Inst. Thechn., Pittsburgh, 1969. 

External transient conduction from an isothermal convex body into a surrounding space has been solved numerically (Yovanovich et al. [149]) for several axisymmetric bodies circular disks, oblate and prolate spheroids, and cuboids such as square disks, cubes, and tall square cuboids (Fig. 3.10). The sphere has a complete analytical solution [11] that is applicable for all dimensionless times Fovr = all A. The dimensionless instantaneous heat transfer rate is QVa = Q AI(kAQn), where k is the thermal conductivity of the surrounding space, A is the total area of the convex body, and 0O = T0 - T, is the temperature excess of the body relative to the initial temperature of the surrounding space. The analytical solution for the sphere is given by... 

W. H. Braun, S. Ostrach, and J. E. Heighway, Free-Convection Similarity Flows About Two-Dimensional and Axisymmetric Bodies With Closed Lower Ends, Int. J. Heat Mass Transfer (2) 121-135,1961. 

F. N. Lin and B. T. Chao, Laminar Free Convection Over Two-Dimensional and Axisymmetric Bodies of Arbitrary Contour, J. Heat Transfer (96) 435-442,1974. 

Dhir and Lienhard [117] extended the Nusselt analysis to include a wide variety of body shapes, including axisymmetric bodies (Fig. 14.18). Their result for the local heat transfer... 

FIGURE 14.18 Condensation on an axisymmetric body [117]. (Reprinted with permission from Trans. ASME, Journal of Heat Transfer.)... 

Numerous workers (B16, F2, F4, H17, J4, K4, K7, L8, M2, S5, and others) estimated the external heat-transfer coefficient in the continuous phase by assuming a velocity profile in the boundary layer and ambient fluid. Except for very low Reynolds numbers, the exact boundary layer solutions only apply to the front part of the drop, up to the separation point. Fortunately, simple assumptions sometimes suffice for extending the derivation to the entire drop, and the relationships obtained are in agreement with experimental data. The limitations of the analytical solutions, as well as their application to nonspherical drops, is concisely demonstrated in Lochiel and Calderbank s (LI8) recent study on mass transfer around axisymmetric bodies of revolutions. 

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