Transient External Conduction from Isothermal Convex Bodies

The three solutions corresponding to the three boundary conditions can be used to obtain approximate solutions for other convex bodies, such as a cube, for which there are no analytical solutions available. The dimensionless parameters Bi and Fo are defined with respect to the equivalent sphere radius, which is obtained by setting the surface area of the sphere equal to the surface area of the given body, i.e., a = Vi4/(4tt). This will be considered in the following section, which covers transient external conduction from isothermal convex bodies. 

Transient External Conduction From Isothermal Convex Bodies... 

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... 

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