A comprehensive analysis of conduction-controlled rewetting by the Heat Balance Integral Method

A two region conduction-controlled rewetting model of hot vertical surfaces with a constant wet side heat transfer coefficient and negligible heat transfer from dry side is solved by the Heat Balance Integral Method (HBIM). The HBIM yields a simple closed form solution for rewetting velocity and temperature distribution in both dry and wet regions for given Biot numbers. Using this method it has been possible to derive a unified relationship for one-dimensional object and two-dimensional slab and rod. The effect of convection is expressed by an effective Biot number whose exact value depends on the geometry and process parameters. The solutions are found to be exactly the same as reported by Duffey and Porthouse [R.B. Duffey, D.T.C Porthouse, The physics of rewetting in water reactor emergency core cooling, Nucl. Eng. Des. 25 (1973) 379–394], Thompson [T.S. Thompson, An analysis of the wet-side heat transfer coefficient during rewetting of a hot dry patch, Nucl. Eng. Des. 22 (1972) 212–224] and Sun et al. [K.H. Sun, G.E. Dix, C.L. Tien, Cooling of a very hot vertical surface by falling liquid film, ASME J. Heat Transfer 96 (1974) 126–131; K.H. Sun, G.E. Dix, C.L. Tien, Effect of precursory cooling on falling-film rewetting, ASME J. Heat Transfer 97 (1974) 360–365]. Good agreement with experimental results is also observed.