Time singularities in conjugated thermo-fluid-dynamic phenomena

Abstract

The thermo-fluid-dynamic field that arises when an infinite thick plate is impulsively accelerated to a constant speed in a laminar regime is studied, taking into account the coupling of the convection and conduction in the fluid with the conduction in the solid. Two significant cases are discussed depending on the boundary condition imposed on the unwetted side of the plate: constant temperature or adiabatic wall. The work is particularly focused on analysing the singularities arising in the field at the initial time. For this purpose an exact analytical solution of the problem governed by the Navier– Stokes equations with constant properties and by the energy equations in the fluid and in the solid is proposed and discussed. The non-dimensional parameter governing the conjugated effects is shown to be the ratio between the thermal effusivities in the fluid and in the solid. The results have also been extended to the analysis of compressible flows by the Stewartson–Dorodnitsin transformation

Conjugated heat transfer in unsteady channel flows

“…As in the case of Rayleigh flow over a thick plate [10], K is the main additional parameter ruling the conjugated effects. K is the thermal activity ratio:…”

“…The temperature at the solid-fluid interface can be obtained substituting the spatial derivatives of equations (7), (10) or (11) in Eq. (12).…”

“…Just in the recent years exact analytical solutions describing conjugated effects have been published. Pozzi and Tognaccini [10] found the solution for the conjugated heat transfer in the case of an impulsively accelerated flow from rest to a constant speed over an infinite plate of finite thickness in the case of imposed temperature and of adiabatic condition on the unwetted side of the plate. Pozzi et al [11] showed that, in the case of plate of infinite thickness the solutions in both the fluid and in the solid are self-similar with very simple analytical expressions.…”

Unsteady conjugate forced convection heat/mass transfer in ensembles of spherical particles with cell models

“…Using the boundary-layer formalism, only the case of fluid spheres with internal circulation at high Peclet numbers was considered. It must be mentioned that the boundary-layer approximation used in [2][3][4] is not entirely similar to that employed for the flat plate [1,[5][6][7][8][9][10]. For fluid spheres with internal circulation at high Pe numbers, thin thermal/concentration boundary layers on both sides of the interface were considered.…”

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 :…”