a b s t r a c tThis paper describes the implementation of an integrated cost optimality and environmental assessment involving alternative energy efficiency retrofit packages for a building that dates from the beginning of the 20th century. A building typical of the building stock in the centre of Coimbra (located in the central region of Portugal and recently classified as a UNESCO World Heritage Site) was used to illustrate the methodology presented. The results were also analysed for the same building in two other locations. A life-cycle (LC) model was implemented to assess different energy efficiency measures for an apartment. The economic assessment complied with European Directive 2010/31/EU. The results show that the lowest life-cycle environmental impacts were obtained for insulation thicknesses between 50 and 120 mm, which are also cost-optimal. It is also shown that insulation thicknesses of more than 80 mm do not improve energy efficiency or global cost reduction. This paper shows that, even though historic buildings in Portugal do not have to comply with building energy codes, significant energy savings can be achieved for them without changing their historic character. It was also concluded that economic and environmental costs can both be minimised by choosing the most suitable energy efficiency retrofit measures.

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a b s t r a c tEuropean Union (EU) regulations aim to ensure that the energy performance of buildings meets the cost-optimality criteria for energy efficiency measures. The methodological framework proposed in EU Delegated Regulation 244 is addressed to national authorities (not investors); the optimal cost level is calculated to develop regulations applicable at domestic level. Despite the complexity and the large number of possible combinations of economically viable efficiency measures, the real options for improving energy performance available to decision makers in building retrofit can be established. Our study considers a multi-objective optimization approach to identify the minimum global cost and primary energy needs of 154,000 combinations of energy efficiency measures. The proposed model is solved by the NSGA-II multi-objective evolutionary algorithm. As a result, the cost-optimal levels and a return on investment approach are compared for a set of suitable solutions for a reference building. Eighteen combinations of retrofit measures are selected and an analysis of the influence of real options on investments is proposed. We show that a sound methodological approach to determining the advantages of this type of investment should be offered so that Member States can provide valuable information and ensure that the minimum requirements are profitable to most investors.

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This paper presents analytical Green's functions for the transient heat transfer phenomena by conduction, for an unbounded medium, halfspace, slab and layered formation when subjected to a point heat source. The transient heat responses generated by a spherical heat source are computed as Bessel integrals, following the transformations proposed by Sommerfeld [Sommerfeld A. Mechanics of deformable bodies. New York: Academic Press; 1950; Ewing WM, Jardetzky WS, Press F. Elastic waves in layered media. New York: McGraw-Hill;1957]. The integrals can be modelled as discrete summations, assuming a set of sources equally spaced along the vertical direction. The expressions presented here allow the heat field inside a layered formation to be computed without fully discretizing the interior domain or boundary interfaces.The final Green's functions describe the conduction phenomenon throughout the domain, for a half-space and a slab. They can be expressed as the sum of the heat source and the surface terms. The surface terms need to satisfy the boundary conditions at the surfaces, which can be of two types: null normal fluxes or null temperatures. The Green's functions for a layered formation are obtained by adding the heat source terms and a set of surface terms, generated within each solid layer and at each interface. These surface terms are defined so as to guarantee the required boundary conditions, which are: continuity of temperatures and normal heat fluxes between layers. This formulation is verified by comparing the frequency responses obtained from the proposed approach with those where a double-space Fourier transformation along the horizontal directions [Tadeu A, António J, Simões N. 2.5D Green's functions in the frequency domain for heat conduction problems in unbounded, half-space, slab and layered media. CMES: Computer Model Eng Sci 2004;6(1):43-58] is used. In addition, time domain solutions were compared with the analytical solutions that are known for the case of an unbounded medium, a half-space and a slab. q

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Analytical Green's functions in the frequency domain are presented for the three-dimensional diffusion equation in an unbounded, halfspace, slab and layered media. These proposed expressions take into account the conduction and convection phenomena, assuming that the system is subjected to spatially sinusoidal harmonic heat line sources and do not require any type of discretization of the space domain. The application of time and spatial Fourier transforms along the two horizontal directions allows the solution of the three-dimensional time convection-diffusion equation for a heat point source to be obtained as a summation of one-dimensional responses. The problem is recast in the time domain by means of inverse Fourier transforms using complex frequencies in order to avoid aliasing phenomenon. Further, no restriction is placed on the source time dependence, since the static response is obtained by limiting the frequency to zero and the high frequency contribution to the response is small.The proposed functions have been verified against analytical time domain solutions, known for the case of an unbounded medium, and the Boundary Element Method solutions for the case of the half-space, slab and layered media. q