Adsorption cooler design, modeling, and dynamics and performance analyses

This paper presents an adsorption cooler (AC) driven by the surplus heat of a solar thermal domestic hot water system to provide cooling to residential buildings. A cylindrical tube adsorber using granular silica gel as adsorbent and water as adsorbate is considered. The AC is modelled using a two-dimensional distributed parameter model that was implemented in previous adsorption heating and cooling studies. The performance coefficients of the resultant thermally driven colling system are obtained for a broad range of working conditions. The thermally driven AC has a coefficient of performance (COP) of 0.5 and a specific cooling power (SCP) of 44 W.kg--1, considering condenser, evaporator, and regeneration temperatures of 15 oC, 18 oC, and 70 oC, respectively. Moreover, results show that the AC can be used for refrigeration purposes at temperatures as low as 2 oC, and that it can also operate during hotter days under temperatures of 42 oC.This work was supported by the grant SFRH/BD/145124/2019 and the projects UIDB/00481/2020 and UIDP/00481/2020 - FCT - Fundação para a Ciência e a Tecnologia; and CENTRO-01-0145-FEDER-022083 - Centro Portugal Regional Operational Programme (Centro2020), under the PORTUGAL 2020 Partnership Agreement, through the European Regional Development Fund. The present study was developed in the scope of the Smart Green Homes Project [POCI-01- 0247-FEDER- 007678], a co-promotion between Bosch Termotecnologia S.A. and the University of Aveiro. It is financed by Portugal 2020 under the Competitiveness and Internationalization Operational Program, and by the European Regional Development Fund

Multidimensional continued fractions, dynamical renormalization and KAM theory

The disadvantage of `traditional' multidimensional continued fraction algorithms is that it is not known whether they provide simultaneous rational approximations for generic vectors. Following ideas of Dani, Lagarias and Kleinbock-Margulis we describe a simple algorithm based on the dynamics of flows on the homogeneous space SL(2,Z)\SL(2,R) (the space of lattices of covolume one) that indeed yields best possible approximations to any irrational vector. The algorithm is ideally suited for a number of dynamical applications that involve small divisor problems. We explicitely construct renormalization schemes for (a) the linearization of vector fields on tori of arbitrary dimension and (b) the construction of invariant tori for Hamiltonian systems.Comment: 51 page