Constructal tree-shaped microchannel networks for maximizing the saturated critical heat flux

Abstract

A constructal tree-shaped microchannel network for maximizing the saturated critical heat flux in a disc-shaped planar body has been investigated. n 0 radial channels touch the center and n p channels touch the periphery. Designs with no pairing level ( n 0 = n p ), one pairing level ( 2 n 0 = n p ) and two pairing levels ( 4 n 0 = n p ) have been studied. The fluid simulated is R-134a at a saturation temperature of T sat = 30 °C with no inlet subcooling. The flow enters at the center and exits at the periphery. The theoretical CHF model of Revellin and Thome [R. Revellin, J.R. Thome, A theoretical model for the prediction of the critical heat flux in heated microchannels, Int. J. Heat Mass Transfer 51 (2008) 1216–1225], specially developed for micro and minichannels, has been modified and used for predicting the wall CHF of low pressure refrigerants flowing in microchannels. The constraints are the disc radius R and the total volume of ducts V. The degrees of freedom are n 0 , n p and the mass flow rate m ˙ . In each case, the minimum global fluid flow resistance design has been adopted as proposed by Wechsatol et al. [W. Wechsatol, S. Lorente, A. Bejan, Optimal tree-shaped networks for fluid flow in a disc-shaped body, Int. J. Heat Mass Transfer 45 (2002) 4911–4924]. Maximizing the base CHF means increasing the number of central tubes for a given complexity. Furthermore, it is better to use a simple radial structure (with no pairing level) and 2 n 0 central tubes than a design with one pairing level and n 0 central tubes. On one hand, simplified structures seem to be roughly better for maximizing the base CHF. On the other hand, coupling the base CHF and the pumping power leads to different conclusions. There exists an optimal n 0 and n p to maximize the base CHF for each range of pumping power. For instance, for low pumping power, using radial ducts without pairing level is the best solution for dissipating high base CHF whereas for higher pumping power, a more complex design is beneficial with greater n p . In conclusion, the recommended complexity is modest (not maximal), and high complexity is not necessarily the best solution.