Abstract:

Incorporating novel and advanced teaching tools must be considered one of the important pillars of education in all fields preparing students with a wide spectrum of actualized knowledge. In this sense, response surface methodology (RSM) is proposed as a useful educational tool in Sciences Physics, in general, and practical training in thermodynamics laboratory, in particular, for graduated and under-graduated students.

When trainings, the students generally follow the traditional method of experimentation, in which the effect(s) of an operation variable on the response(s) of a given system is investigated keeping the other variables fixed. Following this conventional or classic method, many experimental tests have to be performed taking a lot of time. Moreover, this classical approach ignores the effects of interactions that may exist between the operating variables of the system. RSM is a collection of mathematical and statistical techniques dealing with design of experiments (DoE) and development of models that characterize the response(s) of the system under study and its subsequent optimization. In this methodology, all factors are simultaneously varied between minimum and maximum values. Furthermore, RSM allows the study of the main effects of parameters and their interactions on the system response(s). In addition, the process optimization involves the determination of the optimal operating variables using a minimum number of experiments.

The main objective of the present study is to propose RSM and DoE as a useful tool for practical trainings of a group of students in all fields of sciences. An example is given in this communication for practical training of 16 students in the Thermodynamics Laboratory using the membrane separation process forward osmosis (FO). The considered statistical experimental design (DoE) is the orthogonal central composite design (CCD) using 3 operating parameters of an FO system. In this case a total of 16 experiments must be carried out [1,2]. Each student performs an experiment taken randomly from the DoE table (i.e. CCD). Then, the students share and discuss the obtained response of the FO system (Y). The students are then divided into groups of 4 to determine the empirical model, which relates Y with the operating parameters. The goodness of the model is then validated statistically by the analysis of variance (ANOVA). Finally, after verifying the accuracy of the developed RSM model, the effects of the interaction between parameters on the response Y are analyzed and figures are plotted as a function of the 3 studied parameters [3]. Optimization step can be finally done by the students. The obtained optimum operating parameters are confirmed experimentally and a report is presented by each student.

This training methodology allows students to work in groups putting into practice the knowledge acquired not only in Thermodynamics but also in Statistics and data analysis, management software like Matlab and/or Matcad, etc.

Acknowledgements:
The authors acknowledge the support of the UCM and Banco Santander (GR3/14) and Abengoa Water (Projects:85/2013;259/2014).

References:
[1] D.C. Montgomery, Design, Analysis of Experiments, John Wiley&Sons, New York,2001.
[2] R.H. Myers, D.C. Montgomery, Response Surface Methodology: Process and Product Optimization Using Designed Experiments, John Wiley&Sons, New York,2002.
[3] M. Khayet et al., Desalination,261(2010)284-292.

Keywords:

Practical training, Thermodynamics laboratory, Response surface methodology, Statistical experimental design, Forward osmosis.