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General guides to support the refurbishment design indicate separately the solutions to common problems such as thermal loss, interstitial condensation, sound transmission, fire safety etc. This paper deals with combined solutions that take into account simultaneously two of these aspects, aiming both at reducing thermal losses and at avoiding or limiting problems related to moisture transfer and condensation, jointly with an indispensable cost analysis. Improving the energy performance of buildings should start from the evaluation of the building's envelope energysaving options. The subject of the research is oriented to typical buildings, often critical from the energy standpoint, which are represented by social housings. The refurbishment target should be the NZEB model, even if it is very difficult to find suitable general solutions. As the renovation design process depends also on the sustainability of costs, an evaluation procedure, previously proposed, is widened to take into account this aspect, by considering characteristics and constraints, and assuring reasonable costs for the most suitable solutions. The methodology has been applied to a case study represented by a common building unit. The insulation improvement is made through a choice of the most suitable combination of material and thickness, with the aim not only of the energy saving, but also of the reduction of the risk of vapour condensation that depends, among other things, on the position of the insulating materials within the wall's structure. Some combined refurbishment solutions for the building envelope are examined and the corresponding costs are evaluated. Moreover, to show the importance of the problem in mild and continental climates, a comparison of the results in different climatic conditions is presented.

Steady combined forced and free convection is investigated in a vertical channel having a wall at rest and a moving wall subjected to a prescribed shear stress. The moving wall is thermally insulated, while the wall at rest is kept at a uniform temperature. The analysis deals with the fully-developed parallel flow regime. The governing equations yield a boundary value problem, that is solved analytically by employing a power series expansion of the velocity field with respect to the transverse coordinate. It is shown that the nonlinear interplay between buoyancy and viscous dissipation may determine the existence of dual solutions of the boundary value problem corresponding to fixed values of the applied shear stress on the moving wall and of the hydrodynamic pressure gradient. It is shown that a nontrivial fully separated flow may occur such that the hydrodynamic pressure gradient is zero and the shear stress vanishes on both walls. (2000). 76R10, 80A20, 76D05, 34B15. Mathematics Subject Classification

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