Transient Heat Transfer Between a Semi-Infinite Hot Plate and a Flowing Cooling Liquid Film

Abstract

Heat transfer between a hot, semi-infinite plate and thin liquid film flowing over its surface is considered. As the plate is semi-infinite, the finite cooled portion of the plate and the temperature at the moving film front are time variable. The heat transfer is transient, as opposed to the usual quasi-steady process that exists when the plate is infinite. To investigate the transient heat transfer, solutions describing the temperature fields of the wet and dry portions of the plate are conjugated at the moving film front. The basic characteristics of transient cooling process are found to be governed by a dimensionless parameter named the Leidenfrost number, which is the ratio of the Biot number and the square of the Peclet number. The plate temperatures at the moving front, the film velocity, and the time required to reach the wetting temperature are calculated.

Unsteady conjugate forced convection heat/mass transfer from a finite flat plate

“…Other solutions of the conjugate heat/mass transfer from a finite/infinite flat plate were obtained analytically or numerically in [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31] (in agreement with the aims of this work, we restricted the citation only to the forced convection analysis in laminar flow). The following observations can be made from the analysis of the mathematical models used in :…”

“…-the boundary layer approximation was widely used to model the transfer in the fluid; -except for Pozzi and coworkers [12,16,24,25,28] (and the references cited herein), Dorfman [27] and Juncu [29], a steady temperature profile in both phases was assumed; Pozzi and co-workers, focused on the unsteady conjugate heat transfer problem from a semi-infinite plate; an integral formulation of the boundary layer equations models the heat transfer in the fluid phase; in the solid, the heat [27] the one dimensional transient conduction equations for the wet and dry portions of the plate, conjugated at the moving film front, were solved; the unsteady forced convection heat transfer from a finite plate with spatially uniform temperature was analysed numerically in [29].…”

The Green’s functions for peridynamic non-local diffusion

“…When the size of electronic devices decreases to less than the mean free path of the phonon of the material, violation of the local theory has been revealed experimentally in these nanostructures [1,2]. Large temperature gradients may appear in emergency cooling [3] and rapid transient heat transfer [4]. In such situations, the heat flux is found to be smaller than that predicted by the local theory [5].…”

Peridynamic Thermal Diffusion

“…The peridynamic results are compared with the two-dimensional predictions in the case of homogeneous plate, 12 k k k  . As observed in Fig.19, there exists a close agreement between the two-and threedimensional models.…”

“…Rewetting in a nuclear reactor is employed to restore temperatures to a safe range following accidental dry out or loss of coolant. Emergency cooling is introduced to the system via an upward moving water front or by spraying from the top of the reactor [11,12]. A moving discontinuity occurs in the heat generating solid at the quench front due to the sudden change in heat transfer condition at the solid surface.…”