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Heat Transfer Handbook part 116. The Heat Transfer Handbook provides succinct hard data, formulas, and specifications for the critical aspects of heat transfer, offering a reliable, hands-on resource for solving day-to-day issues across a variety of applications. | EXTERNAL NATURAL CONVECTION 1147 asymptotes an optimal spacing pore size where the hot-spot temperature is minimal when the heat generation rate and volume are fixed is found. The same spacing represents the design with maximal heat generation rate and fixed hot-spot temperature and volume. Analytical and numerical results have been developed for optimal spacings in applications with solid components shaped as parallel plates Bejan 1995 . Optimal spacings for cylinders in crossflow were determined analytically and experimentally in Stanescu et al. 1996 . The spacings of heat sinks with square pin fins and impinging flow were optimized numerically and experimentally in Ledezma et al. 1996 . All the dimensionless results developed for optimal spacings Vopt have the form L Be- 15.58 where L is the dimension of file given volume in the flow direction and BeL is a new dimensionless group the Bejan number that serves as the forced-convection analog of the Ray I eig h number of natural coriecci.oni Bhattccharjee and Gros handler 1988 Petrescu 1994 AP L2 Bil ---------- 15.59 Pf df In this definition AP is the pressure difference maintained across the fixed volume. For example the exponent n in eq. 15.58 is equal to 4 in the case of tami-nar flow through stacks of paraljel-ptaje la i els and is n j ll to 1 in other configurations. The frequency of pulsating flows through microchannels in parallel can be optimized for global system performance subject to total volume and void space constraints. The fundamentals of this optimization opportunity are outlined in Bejan 2000 and Bejan et al. 2004 . 15.5 EXTERNAL NATURAL CONVECTION 15.5.1 Vertical Walls In natural convection the body force is due to internal density differences that are induced by heating or cooling effects. The equations of motion reviewed in Section 15.2.2 are complemented by the assumption that density and temperature changes are sufficiently small so that the linear approximation is valid. This is known as the
