Liquid Desiccant System Research Articles

Thermodynamic optimization of a vacuum multi-effect membrane distillation system for liquid desiccant regeneration

The regenerator is one of the key components in the liquid desiccant air-conditioning system, and improvement of the regenerator performance is key to promoting the overall system energy efficiency. This study entails the investigation of a vacuum multi-effect membrane distillation system (V-MEMD) for liquid desiccant regeneration. The V-MEMD regenerator possesses the merits of high energy efficiency and zero desiccant carry-over. A thermodynamic model has been developed to study the regeneration process based on the principles of heat and mass transfer and heat and mass balances. The model is validated with experimental data, and the discrepancies are observed to be within 10% and 5% for regeneration rate and brine concentration, respectively. Employing the developed and validated model, several V-MEMD configurations have been investigated and the effects of key operating parameters are evaluated. The regenerator performance is observed to degrade at higher feed concentrations, while a higher hot water temperature promotes regeneration rate and thermal efficiency. The proposed configurations expand the operation range of the V-MEMD regenerator to greater than 40 wt% under a heat source temperature of 70 °C. Compared with existing liquid desiccant regeneration systems, the specific energy consumption is reduced by 10–50%.

Dynamic model development of heat and mass transfer for a novel desiccant regeneration system in liquid desiccant dehumidification system

In this paper, from the control point of view, a simplified dynamic model of the Desiccant Regenerations System (DRS) is proposed. The DRS is a serial system of the heat pipe heat exchanger and regenerator whose models are developed by writing the thermal and moisture balance equations, and the heat and mass transfer rates of each subsystem are derived by using the effectiveness-NTU and hybrid modeling approach. The unknown Model parameters are identified through the nonlinear least squares method and unscented Kalman filter algorithm with commissioning information. The dynamic model of the whole system is obtained by integrating the subsystem models to predicts the system performance. Compared with the existing DRS models, the presented model not requires iterative computations and also can be easily transformed into a state-space model. The proposed model accurately reflects the transient and steady state performance of the DRS over the wide operating condition in the experimental validation and is expected to work well for intelligent dynamic control and optimization applications.

Investigation of falling-film plate wettability characteristics under dehumidification and regeneration conditions using LiCl-H2O

Liquid desiccant air conditioning system has unique advantages and prospects in both humidity control and low-grade heat driven cooling. The liquid film wettability is one of the significant factors governing the efficiency of dehumidification/regeneration processes in the system. In this paper, the effect of the LiCl solution properties on falling-film plate wettability characteristic is studied using a VOF method. This paper analyzes the dehumidification and regeneration processes respectively and gets the recommended amount of spray, which was 0.619 m3/(m·h) for dehumidification and 0.662 m3/(m·h) for regeneration. The recommended amount of spray can not only ensure the full-film flow, but also avoid the excessive solution flow rate which may increase the possibility of droplets entrainment. Since the wettability is determined by the coupled effects of the solution density, viscosity and surface tension, the effects of dynamic properties of liquid desiccant on the wettability are studied to explain the influence of the solution temperature and concentration on the wettability. Finally, least squares method is used to fit a formula to describe the effect of solution properties on falling-film plate wettability, which can guide the control of the amount of spray in actual operation.

Interfacial heat and mass transfer analysis in solar-powered, packed-bed adiabatic liquid desiccant regeneration for air conditioning

In this article, a hybrid photovoltaic–thermal (PV/T) module generating both electrical and thermal energy simultaneously has been used in a closed-cycle system to provide regeneration heat via a dynamic solar radiation model as well as electrical power relative to location, time of the day and day of the month. Electrical power generated drives the air fan, water and solution pumps, while the thermal component is used for desiccant’s regeneration. This combination enhances energy efficiency of the air conditioning system. A simplified analytical model of the complex occurrence of coupled heat and mass transmission phenomenon in liquid desiccant regeneration system powered by a hybrid PV/T module is developed. The interfacial air–desiccant interaction in a structured packing vertical column using lithium bromide solution and Mellapak was analysed. The resulting differential equations are solved simultaneously using separative evaluation and step-by-step iterative procedure. The system’s performance was projected with regeneration effectiveness, subject to varying temperatures of air and desiccant solution, moisture content and mass flow rate. It was established that subject to the prevailing local weather conditions, the PV/T module significantly raised desiccant temperature to a high of 67.22°C good enough for the regeneration process. The regeneration rate and effectiveness improved with upsurge in mass flow rate but reduces with a rise in humidity ratio. The optimum flow mix for effective regeneration was therefore established to be 0.847 and 0.00331 kg/min for air and desiccant solution, respectively, for maximum effectiveness of 69.3%. The liquid desiccant solution concentration increased by 30% during when solar radiation peak hours. The obtained theoretical outcomes matched with experimental results from the available literature show a permissible discrepancy of within ±20%, largely due to the fact that the simulation parameters were not the same as the prevailing experimental conditions.

Model-based investigation of a heat pump driven, internally cooled liquid desiccant dehumidification system

Liquid desiccant dehumidification system is regarded as a promising and energy-saving solution for dehumidification. A heat pump driven internally cooled desiccant dehumidification system is investigated in this paper. Dehumidifier and regenerator are both internally cooled/heated types compared to previous adiabatic ones, and heating and cooling capacities of a heat pump cycle are utilized for regeneration and dehumidification respectively. System model is established and validated to investigate system performance and effects of different influencing parameters. It's indicated that two main issues, which are restricting the system performance, are encountered, i.e. mismatching property among the three fluids inside the dehumidifier/regenerator and heat offset due to solutions circulating between dehumidifier and regenerator. Heat transfer mismatching ratio (xt) and mass transfer mismatching ratio (xω) are defined to indicate the degree of mismatching property. A lower solution flow rate and a solution-solution heat exchanger with a better recovery efficiency are highly recommended to obtain a better system performance. Further, an improved system with external pre-cooler and pre-heater was proposed to improve the matching property among the three fluids, and COPsys is found to be increased from 5.96 to 6.68 with an increasing ratio of 12%. xt is found to be reduced from 0.357 to 0.168, and xω from 0.282 to 0.127.

Experimental investigation of a polymer hollow fibre integrated liquid desiccant dehumidification system with aqueous potassium formate solution

Hollow fibres have been studied as the substitute for metallic materials due to the advantages such as light weight, corrosion resistant and low cost in heat and mass transfer applications. A novel polymer hollow fibre liquid desiccant dehumidification system, in which a cross-flow hollow fibre module (fibre inside diameter = 1.4 mm) serves as the dehumidifier, is presented in this paper. This novel hollow fibre integrated liquid desiccant dehumidification system can be used in an air conditioning system to provide a comfortable indoor environment for hot and humid area. Compared with other conventional liquid desiccant dehumidifier, the polymer hollow fibre has a very small diameter which leads to significantly increased surface area. Moreover, the porous feature of the hollow fibre module can help to eliminate any liquid desiccant droplets carryover into the process air. As a less corrosive and more environmental friendly working fluid, aqueous potassium formate (KCOOH) solution has been selected. The dehumidification performance of the proposed system were analysed experimentally under the conditions of incoming air temperature in the range of 30–45 °C. The variations of dehumidification sensible and latent effectiveness, moisture removal rates were studied by varying the incoming air velocity from 0.65 m/s to 4.5 m/s. With the various values of incoming air relative humidity in the range of 55–75% and the solution concentrations between 36% and 62%, the experimental obtained latent effectiveness are in the range of 0.25–0.43 and the sensible effectiveness are in the range of 0.31–0.52, which is in a satisfactory agreement with the empirical correlation of effectiveness-NTU in the literature.

Performance analysis of a hybrid photovoltaic/thermal and liquid desiccant system

Air dehumidification is widely applied in the civilian and industrial use, however, conventional vapor compression air-conditioning system consumes substantial power. Using renewable energy in the air handling process has potential to further reduce the power consumption, meanwhile ease the carbon emission. This paper proposes a novel liquid desiccant system integrated with a photovoltaic/thermal collector for deep dehumidification. The generated electric power drives a vapor compression chiller for cooling the desiccant solution for a two-stage dehumidification, and the releasing heat from the collector is used for the desiccant regeneration. Simulation studies indicated the proposed system has a superior power saving ability of 55.65% comparing with the conventional one, besides the equivalent power generation efficiency reaches 8.7%.

Model-based optimization for a heat pump driven and hollow fiber membrane hybrid two-stage liquid desiccant air dehumidification system

Heat pump driven liquid desiccant dehumidification systems using hollow fiber membrane contactors have emerged as a promising and energy-efficient approach to air dehumidification. This paper reports on an optimization strategy for a two-stage system, which based on a set of heat and mass transfer models. The optimization problem was solved by a genetic algorithm to minimize the energy consumption. An experimental rig was built and experimental data were collected to validate the model-based operating strategy. The strategy implies that an hourly optimal regulation is proposed to control inlet temperatures on the inlet of membrane modules can be hourly regulated under hot and humid weather conditions. It appears that energy consumption is reduced by more than 20% to satisfy the indoor air humidity demand and the energy saving potential is more significant for the high moisture load. Slight variations of optimal energy input can stabilize electric power supply. Energy consumption of the compressor dominates the overall energy consumption and has the greatest potential to improve energy efficiency due to small differences between evaporating and condensing temperatures. The presented optimization strategy can be widely used as a real-time operation guide to monitor and control the systems under hot and humid weather conditions.

A new hybrid photovoltaic/thermal and liquid desiccant system for trigeneration application

Conventional combined cooling, heating and power (CCHP) systems based on fossil fuels, with an acceptable energy performance, however, intensify the greenhouse effect worldwide. Using solar energy in distributed energy systems has the potential to further reduce fossil fuels consumption, and ease carbon emissions. This paper proposes a novel CCHP system by combining concentrated photovoltaic/thermal (PV/T) technology with an advanced air-handling process that realizes independent control of temperature and humidity. The heat produced from a PV/T collector is for desiccant regeneration in a two-stage liquid desiccant cycle in summer, and can be directly supplied to nearby users in winter. An office building under typical climate conditions of Beijing in 2002 was adopted to determine its various energy demands. Due to the efficient use of solar energy, annual energy saving ratio and CO2 emissions reduction ratio are predicted to be 73.28% and 74.55%, respectively. Two extreme conditions determining whether the excess heat from the PV/T collector is used were compared to demonstrate the top and bottom limitations of economic performance. The integrated performance, considering energy, environment and economic factors, reaches 37.48% when no excess heat from PV/T collector is used, and it can be further improved by thermal storage or recovering the excess heat to produce other products. This study provides a new solar utilization technology for trigeneration with advanced integrated performance.

NTUm-based optimization of heat or heat pump driven liquid desiccant dehumidification systems regenerated by fresh air or return air

Liquid desiccant (LD) dehumidification systems have received significant attention in recent years owing to their effectiveness in humidity control and great potential for energy saving in buildings. The optimization of these systems, considering the relevant influencing factors, is thus an important research purpose. This paper focuses on the optimization pf area distribution among the packing towers, under a fixed total area, in the liquid desiccant dehumidification systems. Two typical LD dehumidification systems are analyzed and optimized. One system is regenerated by fresh air and the other system is regenerated by return air, with total heat recovery and the dehumidification modules. The input heat for the heat driven pattern and the input work for the heat pump driven pattern are adopted as the optimizing indexes. It is indicated that for the first system, the square ratio of the optimum NTUm of the dehumidifier to that of the regenerator is equal to the ratio of the enthalpy difference between the fresh air and supply air to that between the fresh air and exhaust air. For the second system, the optimum NTUm of the total heat recovery module accounts for about 30% of the total NTUm. The heat-cold offset takes a great proportion of the input heat, and the NTUm distribution development based on the optimum input work with the heat pump driven pattern is consistent with that based on the optimum input heat with the heat driven pattern. Therefore the optimization of input heat is important for LD systems and can be the representative criterion for their NTUm-based optimization.

Theoretical investigation on energy storage characteristics of a solar liquid desiccant air conditioning system in Egypt

This work presents theoretical study of a standalone outdoor liquid desiccant air conditioning (LDAC) system assisted by solar energy. The liquid desiccant dehumidification cycle was integrated with a double indirect evaporative air cooler and a regenerative air heat recovery. The double indirect evaporative air cooler was used to recover heat from the return air, while air-air heat exchanger was used to recover heat from air leaving the regenerator. A water-in-glass evacuated tube solar collector was used to supply the system with solar heat. The remaining required heat is provided by natural gas fired boiler. The system was simulated by transient model under thermal energy storage, thermochemical energy storage and combined thermal and thermochemical energy storage modes.The theoretical results show that the mean daily thermal coefficient of performance (TCOP) is a strong function of the difference between absolute humidity ratio of outdoor air and saturated air. Results also show that, each tube of solar collector can deliver 30-Watt to operate the LDAC system under thermal energy storage mode for 16 h daily. While in the LDAC system under thermochemical energy storage mode, each tube would deliver 38.5-Watt for 16 h operation.It has been found that, to rise the solar fraction from 90% to 100% in the thermal energy storage mode, the required size of tubes array will be increased by 20%. Also, an analysis was carried out on the TCOP and required storage volume of the different energy storage modes. It shows that the combined energy storage method is the most energy efficient method.Finally, life cycle cost analysis (LCCA) was carried out for the LDAC system using various types of energy storage modes. The comparison indicated that 90% solar fraction LDAC system is the most economic system related to unit prices of solar collector and gas prices in Egypt. The total annual cost for the 90% solar assisted LDAC system is found to be lower than that of a vapor compression cycle (VCC) by about 50.5%. At the second order, the thermal energy storage mode by 49%. On the other side, the thermochemical energy storage mode is the least cost saving energy storage mode.

Performance evaluation of a high-influx, bubble dehumidifier

In hot humid climates, a major portion of air conditioning energy is used for dehumidification. In traditional centralized air conditioning systems, air is cooled below the dew point to remove the moisture. This process is energy intensive. Liquid desiccant dehumidification systems (LDDS) provide a promising alternative as they use low grade or free energy like solar energy. Majority of the existing direct-contact liquid desiccant dehumidification modules adopt the concept of low influx rates which ensures high residence time resulting in improved dehumidifier performance. There is limited knowledge with respect to high influx rates which is the topic of this paper. The overall objective of this study is to evaluate the performance of a high-influx, bubble dehumidifier. A prototype dehumidifier employing aqueous Lithium Chloride (LiCl) as desiccant that could accommodate high-influx rates was developed and experiments were conducted to evaluate its performance. Results of the experiments are analyzed in terms of performance parameters namely moisture removal rate (MRR) and dehumidifier effectiveness. The apparatus could achieve a maximum MRR of 0.28 g/s resulting in 66% dehumidifier effectiveness. Empirical equations to predict the MRR were developed through linear regression using experimental data. The input variables used in regression are the inlet depth, the inlet air vapor pressure, the desiccant solution vapor pressure and the diffusion coefficient of water in LiCl solution, along with the design parameters. The diffusion coefficient parameter which was ignored in other dehumidifier models was found to be imperative in this research. The developed empirical equations were validated by comparing the predicted and measured values on a new set of experiments, the data for which were not used for regression. It is found that the time-dependent nonlinear response of the system is predicted accurately by the empirical model. The root mean square errors of the observed and predicted values are less than 8%.

A novel finite difference model coupled with recursive algorithm for analyzing heat and mass transfer processes in a cross flow dehumidifier/regenerator

Maintaining the relative humidity within the desired level in hospitals, research laboratories and pharmaceutical industries is very crucial. Among the various techniques reported over the last three decades, liquid desiccant dehumidification has been found promising. Dehumidifier and regenerator are the key components in the liquid desiccant dehumidification system. In this paper, the coupled heat and mass transfer analyses in a cross flow liquid desiccant dehumidifier and regenerator are presented. A novel finite difference based thermodynamic model is developed using the governing equations of mass, momentum and energy and a recursive algorithm is proposed for solving the developed model. The simulated results obtained from the developed model are validated with the experimental data reported in the literature and a good agreement is observed between them. The contour plots for the distribution of air and desiccant enthalpies, air specific humidity and solution concentration along the longitudinal and the transverse directions of the packed tower are represented. Also, the contour plots for the desiccant concentration at different Lewis numbers are presented. Further, the influence of Lewis number on operating and performance parameters are also discussed in detail.

Experimental and theoretical research on the electrical conductivity of a liquid desiccant for the liquid desiccant air-conditioning system: LiCl aqueous solution

At present, the energy consumption in buildings occupies a large proportion of total energy use, and air-conditionings cost a large proportion of energy in the buildings. The liquid desiccant air-conditioning system has a good energy saving potential and the electrodialysis (ED) regeneration is a reliable choice for the liquid desiccant regeneration. In order to establish the energy consumption model and the performance coefficient model of liquid desiccant air-conditioning system based on ED regeneration using LiCl, experimental and theoretical research on the electrical conductivity of LiCl aqueous solution with a lot of concentrations and temperatures was conducted in this paper. The results show that when polynomial degrees of the mass concentration and the temperature of the LiCl aqueous solution are both 3, the electrical conductivity model for the LiCl aqueous solution is most suitable as its simplicity and high accuracy. Moreover, when the concentration is 36% and the temperature is 22 °C, the liquid desiccant cooling system has the maximum COP of about 5. Finally, a case study of a small office room was conducted, and the result shows that the liquid desiccant cooling system based on electrodialysis regeneration has a good energy-saving potential.

Performance evaluation of a membrane-based flat-plate heat and mass exchanger used for liquid desiccant regeneration

Liquid desiccant dehumidification system has gained much progress recently for its considerable energy saving potential without liquid water condensation. Within the system, regeneration is of great importance since diluted desiccant solution after dehumidification needs to be re-concentrated. The operational characteristics of a membrane-based flat-plate heat and mass exchanger used for liquid desiccant regeneration are investigated in this study. The liquid desiccant and air are in a cross-flow arrangement, and separated by semi-permeable membranes to avoid carry-over problem. The regeneration performance is examined by numerical simulation and experimental test. Solution side effectiveness, temperature decrease rate (TDR) and moisture flux rate (MFR) are applied to evaluate heat and mass transfer in the regenerator. Effects of main operating parameters are assessed, which include dimensionless parameters (i.e. number of heat transfer units NTU and solution to air mass flow rate ratio m∗), solution inlet properties (i.e. temperature Tsol,in and concentration Csol,in) and air inlet conditions (i.e. temperature Tair,in and humidity ratio Wair,in). It is found that m∗ and NTU are two of the most important parameters and their effects on the regeneration performance are interacted with each other. There is hardly benefit to the performance improvement by increasing NTU at low m∗ or increasing m∗ at low NTU. Even though the regeneration performance can be improved by increasing m∗ and NTU, its improvement gradient is limited when m∗ and NTU exceed 2 and 4 respectively. It is also found that increasing solution inlet temperature is an effective approach to enhance the regeneration performance, while air inlet temperature and humidity ratio have negligible effects on it.

Studying the heat and mass transfer process of liquid desiccant for dehumidification and cooling

Desiccant-based dehumidification has gained significant attention in recent years to develop the energy efficient hybrid air-conditioning systems particularly for the tropical climate. Thus far, complex and tedious theoretical models have been developed to analyze the heat and mass transfer phenomena involved in liquid desiccant dehumidification processes. In the present study, a simple theoretical model has been presented to quantify the heat and mass transfer rates of the water-cooled liquid desiccant dehumidification and cooling processes for air-conditioning applications. Seven coupled ordinary differential equations have been developed to describe the complex heat and mass transfer processes. As far as the solution approach and practical application are concerned, the governing equations are solved simultaneously using the numerically stable 4th order Runge-Kutta scheme while preserving its accuracy to 6% in construct to full-scale model simulation. The developed model is rationally modified to study the performance of adiabatic dehumidifiers. The dehumidification and cooling performances of the adiabatic and water-cooled dehumidifiers are analyzed over a wide range of operating conditions. Finally, the energy performance enhancement potentials of the hybrid liquid desiccant air-conditioning system have been demonstrated. By analyzing the dehumidification and cooling performance, an energy saving of up to 25% can be achieved using the hybrid air-conditioning systems.

Feasibility of a hybrid photovoltaic/thermal and liquid desiccant system for deep dehumidification

Air dehumidification is widely applied in the civilian and industrial use, however, conventional vapor compression air-conditioning system consumes substantial power. Using renewable energy in the air handling process has potential to further reduce the power consumption, meanwhile ease the carbon emission. This paper proposes a novel liquid desiccant system integrated with a concentrated photovoltaic/thermal collector for deep dehumidification. The generated electric power drives a vapor compression chiller for cooling the desiccant solution for a two-stage dehumidification, and the released heat from the collector is used for the desiccant regeneration. Simulation studies indicated the proposed system has a superior power saving ability of 55.65% comparing with the conventional one, besides the equivalent power generation efficiency reaches 8.7% in the base design condition. A comparative driven force analysis showed the two-stage dehumidification has a better match of driven force compared with the single-stage liquid desiccant dehumidification, thus leading to a reduced irreversible loss of 65.43%. Sensitivity analysis indicated that the dehumidification temperature has a decisive effect on the system performance. The exergy efficiency has a maximum value of 13% as the dehumidification temperature is 22.3 °C. The economic studies showed that the investment on the concentrated photovoltaic/thermal collector account for the largest share of the total initial investment, and has a significant effect on the payback period. The payback period would be reduced further if the benefit of the clean development mechanism (CDM) is considered.

Experimental investigation of the wetting characteristics of an aqueous ionic liquid solution on an aluminum fin-tube substrate

In falling film liquid desiccant systems, finding a suitable pair of liquid desiccant and contact surface is of primary engineering interest. This requires knowledge on the wetting characteristics of the liquid on the solid substrate, which consequently requires intensive experimental investigation. In this study, the wetting characteristics of a new ionic liquid aqueous solution in an aluminum fin-tube substrate were experimentally investigated. Then, a simple method for estimating the wetted area on the substrate through image processing was developed. Visual analysis of the surface wetting was also conducted, and three types of wetting patterns are discussed. Experimental results on the static contact angle and contact angle hysteresis suggest that the ionic liquid solution is mostly wetting, and the aluminum surface is slightly to moderately rough. It was found that the wettability of the ionic liquid solution increases as the ionic liquid mass fraction increases. The wetting hysteresis phenomenon and the factors contributing to its occurrence were also clarified. The results from this study would be useful for the development of a new model or improvement of existing wetting models, which can help improve the prediction and control of the heat and mass transfer performance in internally cooled/heated fin-tube contactors.

Energy saving potential of thermoelectric modules integrated into liquid desiccant system for solution heating and cooling

The main objective of this research was to investigate the impact thermoelectric modules (TEMs) integrated into a liquid desiccant (LD) system have on the heating and cooling of the desiccant solution, and to evaluate the energy saving potential of the proposed system. Two TEM-integrated LD systems were considered; in the first case (i.e., Case A), the TEMs accommodated the solution heating load at the regenerator and a portion of the solution cooling load at the absorber. The remaining solution cooling load was met by an auxiliary chiller. In the second case (i.e., Case B), the TEMs accommodated both the solution cooling and heating loads before the absorber and the regenerator, while extra heat released from the hot side of the TEMs was reclaimed and used to heat the scavenger air entering the regenerator. The conventional LD system, with a boiler and a chiller for heating and cooling the desiccant solution, was also considered as a reference case, to evaluate the energy saving potential of both TEM-integrated LD systems. Hourly energy consumption and temperature variation in the desiccant solution in each system case were predicted via detailed energy simulation with existing mathematical and empirical models for each system component, such as the absorber, regenerator of LD, and TEMs. An approach for determining the required number of TEMs and the optimum temperature difference between the hot side and the cold side of the TEMs is also suggested, based on the coefficient of performance (COP) of the TEMs. It was found that a primary energy saving of about 2% could be expected in Case A compared with the reference case, whereas 55% more primary energy was consumed in Case B. Consequently, based on detailed energy simulations for the TEM-integrated LD system, it was found that the TEMs should be sized to accommodate the regeneration heating load of the desiccant solution before the solution enters the regenerator. In this case, the cooling capacity of the TEMs would be insufficient for cooling the strong solution before the solution enters the absorber, and an auxiliary cooling device would be required.

Dynamic model for a novel liquid desiccant regeneration system operating in vacuum condition

This paper presents the development of a dynamic model for a newly proposed Absorption-based Liquid Desiccant Regeneration (ALDR) system operating in vacuum condition which can reduce the regeneration temperature to around 20–35 °C. The dynamic model is developed based on the internal and external enthalpy balances and mass balances in the components and it accounts for the dynamic behavior due to the heat and mass transfer process in the components. This approach is simpler as detailed enthalpy at each state point can be avoided. The developed dynamic model is verified using the data obtained from the experimental platform constructed in the laboratory. The dynamic response of the simulation results is in good agreement with the experimental data. This model can predict the relevant parameters such as the temperature, concentration and mass flow of the desiccant solution and temperature of the heating and cooling sources when a step change of inlet water temperature is applied to system. The developed model will be useful for the elaboration of control system in the future.