Mathematical modeling of evaporative cooling of moisture bearing epoxy composite plates

Abstract

Research is performed to assess the potential of surface moisture evaporative cooling from composite plates as a means of reducing the external temperature of military aircraft. To assess the feasibility of evaporative cooling for this application, a simplified theoretical model of the phenomenon is formulated. The model consists of a flat composite plate at an initial uniform temperature, T0. The plate also possesses an initial moisture (molecular water) content, M0. The plate is oriented vertically and at t=0 s, one surface is exposed to a free stream of air at an elevated temperature. The other surface is exposed to stagnant air at the same temperature as the plate’s initial temperature. The equations associated with energy and mass transport for the model are developed from the conservation laws per the continuum mechanics hypothesis. Constitutive equations and assumptions are introduced to express the two nonlinear partial differential equations in terms of the temperature, T, and the partial density of molecular water, ρw. These equations are approximated using a weak form Galerkin finite element formulation and the α–family of time approximation. An algorithm and accompanying computer program written in the Matlab programming language are presented for solving the nonlinear algebraic equations at successive time steps. The Matlab program is used to generate results for plates possessing a variety of initial moisture concentrations, M0, and diffusion coefficients, D. Surface temperature profiles, over time, of moisture bearing specimens are compared with the temperature profiles of dry composite plates. It is evident from the results that M0 and D affect the surface temperature of a moist plate. Surface temperature profiles are shown to decrease with increasing M0 and/or D. In particular, dry and moist specimens are shown to differ in final temperatures by as much as 30°C over a 900 s interval when M0 = 30% and D is on the order of 10–8m2/s (T0 = 25°C, h = 60 W/m2°C, T∞ = 90°C).