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Summa~An inert compressible gas confined between infinite parallel planar walls is subjected to significant heat addition at the boundaries. The wall temperature is increased during an interval which is scaled by the acoustic time of the container, defined as the passage time of an acoustic wave across the slab. On this time scale heat transfer to the gas occurs in thin conductive boundary layers adjacent to the walls. Temperature increases in these layers cause the gas to expand such that a finite velocity exists at the boundary-layer edge. This mechanical effect, which is like a time-varying piston motion, induces a planar linear acoustic field in the basically adiabatic core of the slab. A spatially homogeneous pressure rise and a bulk velocity field evolve in the core as the result of repeated passage of weak compression waves through the gas. Eventually the thickness of the conduction boundary layers is a significant fraction of the slab width. This occurs on the condition time scale of the slab which is typically a factor of 106 larger than the acoustic time. The further evolution of the thermomechanical response of the gas is dominated by a conductive-convective balance throughout the slab. The evolving spatially-dependent temperature distribution is affected by the homogeneous pressure rise (compressive heating) and by the deformation process occurring in the confined gas. Superimposed on this relatively slowly-varying conduction-dominated field is an acoustic field which is the descendent of that generated on the shorter time scale. The short-time-scale acoustic waves are distorted as !hey propagate through a slowly-varying inhomogeneous gas in a finite space. Solutions are developed in terms of asymptotic expansions valid when the ratio of the acoustic to conduction time scales is small. The results provide an explicit expression for the piston analogy of boundary heat addition.

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Laminar falling film condensations over a vertical plate with an accelerating vapor flow is analyzed in this work in the presence of condensate suction or slip effects at the plate surface. The following assumptions are made: (i) laminar condensate flow having constant properties, (ii) pure vapor with a uniform saturation temperature in the vapor region, and (iii) the shear stress at the liquid/vapor interface is negligible. The appropriate fundamental governing partial differential equations for the condensate and vapor flows (continuity, momentum, and energy equations) for the above case are identified, nondimensionalized, and transformed using nonsimilarity transformation. The transformed equations were solved using numerical, iterative, and implicit finite-difference methods. It is shown that the freestream striking angle has insignificant influence on the condensation mass and heat transfer rates, except when slip condition is present and at relatively small Grl/Re2 values. Moreover, it is shown that increasing the values of the dimensionless suction parameter (VS) results to an increase in dimensionless mass of condensate (Γ(L)/(μl Re)) and Nusselt number (Nu(L)/Re1/2). Thus, it results in an increase in condensation mass and heat transfer rates. Finally, it is found that the condensation and heat transfer rates increase as Jakob number, slip parameter, and saturation temperature increase. Finally, the results of this work not only enrich the literature of condensation but also provide additional methods for saving thermal energy.

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