## 1 Introduction  
The work in this paper is conducted to continue the research work submitted for applied science [1], for the modeling and simulation of a two-stage adsorption chiller with heat recovery.  
Since the 1980s, due to projected energy shortages, many researchers have investigated the performance and operation of adsorption in air conditioning, freezing and heat pump applications for solar energy because of the near coincidence of peak of cooling load and available solar load [2; 3; 4; 5; 6; 7; 8; 9]. The subject was handled experimentally and mathematically from basic fundamentals, number of stages, working pairs, mass and heat recovery and cycle time optimization, in addition to many parametric studies for chiller components, such as adsorption bed and heat exchangers [10]. Dynamic modeling for optimizing the half-cycle time of adsorption at a different solar intensity was presented and showed remarkable improvements in cooling capacity [11]. Two of the pioneering researchers were ([PERSON], 1983) who carried out many fundamental experiments on the solar-powered adsorption cooling system. A simple model that takes into account both adsorption properties and apparatus characteristics was used to interpret experimental results. The heat and mass transfer were also interpreted by this model. They studied quantitatively the effect of regeneration temperature on the cooling performance ([PERSON] et al., 2012). Parametric analysis studied a two-stage adsorption chiller using reheat demonstrating the effect of the overall thermal conductance and adsorbent mass on system performance ([PERSON] et al., 2012; [PERSON] et al., 2013; [PERSON] et al., 2014). Bed and heat exchanger configurations to reduce heat-transfer resistance and improve performance were reviewed for a single-stage and a multistage adsorption chiller ([PERSON] et al., 2013; [PERSON] et al., 2014). Finally, [PERSON], [PERSON] and [PERSON] studied, using MATLAB, the performance of a silica gel adsorption chiller at different operating and physical conditions ([PERSON] et al., 2013). A parametric study of the influence of many system parameters on the performance is accomplished and discussed ([PERSON] et al., 2013). Many studies showed that system performance (cooling capacity and COP) is strongly affected by the number of transfer units of an adsorber/desorber, and the number of transfer units of a condenser is the least sensitive parameter ([PERSON] et al., 2013; [PERSON] et al., 2014). Some researchers studied the effect of particle diameter and adsorbent bed thickness on bed thermal conductivity and how this lead to a dramatic improvement in specific cooling power (SCP) ([PERSON] et al., 2014). The performance of three different solar cooling systems is examined by a solar electrical, a solar thermal and a hybrid solar electrical-thermal cooling system for different regional climates ([PERSON] et al., 2014; [PERSON] et al., 2014). The performance of silica gel/water adsorption chiller for the Jordan climate was evaluated experimentally and theoretically against ambient temperature, global solar radiation, relative humidity, wind speed and temperatures of the solar adsorption system at different locations of the experimental setup ([PERSON] et al., 2014; [PERSON] et al., 2014).  
The novelty of this work includes the enhancement of the performance of a transient models' medium capacity for an air-cooled adsorption chiller that could work at near-ambient temperature and a humidity higher than any other chillers ever built (up to 50 \({}^{\circ}\)C) by applying mass and heat recovery and optimizing for operating conditions and cyclic time. The results of the models will be used for predicting the cooling capacity of larger sizes and different operating conditions.