Analysis of Mixed Forced and Free Convection About a Sphere
An analysis is performed to study the flow- and heat-transfer characteristics of laminar mixed forced and free convection about a sphere. The transformed conservation equations of the nonsimilar boundary layers are solved by a finite difference method. Numerical results for gases having a Prandtl number of 0.7 are presented for buoyancy parameters which cover the entire regime of mixed convection, ranging from pure forced convection to pure free convection. In general, it is found that both the local-friction factor and the local Nusselt number increase with increasing buoyancy force for aiding flow and decrease with increasing buoyancy force for opposing flow. The effects of the variation of the local free stream velocities on the wall shear and surface heat-transfer results are also examined. With respect to the heat-transfer results, the buoyancy force effects on forced convection become significant for Gr/Re2 > 1.67 and < -1.33, respectively for aiding and opposing flows. The inertia force effects on free convection are found to be significant for Re2/Gr > 0.01. The buoyancy-affected velocity profiles exhibit an overshoot beyond the local free stream velocity for aiding flow and an S-shape for opposing flow.
T. S. Chen and A. Mucoglu, "Analysis of Mixed Forced and Free Convection About a Sphere," International Journal of Heat and Mass Transfer, Elsevier, Jan 1977.
The definitive version is available at https://doi.org/10.1016/0017-9310(77)90116-8
Mechanical and Aerospace Engineering
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© 1977 Elsevier, All rights reserved.