Statistical analysis and mathematical modeling of modified single slope solar still

ABSTRACT

Conventional single slope solar still integrated with a parabolic trough collector in addition to packaged glass ball layer was used in water desalination. Experimental work carried and data obtained were used in modeling the influential parameters affecting water desalination using principal component analysis to reduce parameters’ numbers. These parameters were then applied in constructing a Response Surface Model (RSM). System’s Performance has been predicted in terms of temperatures; saline water temperatures (T_w), glass cover temperatures (T_g), dry bulb temperature (T_db), and wet bulb temperature (T_wb) inside the conventional solar still. Along with the above temperatures, ambient air temperature (T_a), Oil inlet temperature (T_oi) and solar intensity (I). The impact of these parameters can highly effect the water desalination yield. The RSM is developed to predict the impact of these parameters. Principal Component Analysis (PCA) reduced and categorized the number of effective parameters to three components containing the parameters (T_w, T_wb, and T_db), (I, T_a, and T_g) and (T_a, T_oi, and I) respectively. These combinations were then tested using the two different RSM optimized models; Modified Reduced Quadratic and Two-Factor Interaction (2FI) model. These models were tested by monitoring nine statistical indices namely: RMSE, P-value, F-value, R², R²_adj, R²_pred, BIC, PRESS, and AICc. Results obtained for this model showed minimum RMSE value and higher values of R², R²_adj and R²_pred as well as lowest values for BIC and AICc. Concluding supremacy of (I, T_a, and T_g) Modified Reduced 2FI model over the others.

KEYWORD:

• RSM
• PCA
• solar still desalination
• design improvements
• design of experiment
• box Bencham

Nomenclature

AICcAkaike’s Information Criterion

ANNArtificial Neural network

BICBayesian Information Criterion

F-valueFisher–Snedecor distribution

Isolar intensity

PCAPrincipal Component Analysis

PRESSPredicted Residual Error Sum of Squares

P^Taccompanying loading matrix

P-valueprobability value

R²Coefficient of determination

R²_adjAdjusted Coefficient of determination

R²_predPredicated Coefficient of determination

RMSERoot Mean Square Error

SSESum Square Error

SSTTotal Sum Square.

Tscore matrix

T_aambient air temperature

T_dbdry bulb temperature

T_gglass cover temperature

T_oiOil inlet temperature

T_wsaline water temperature

T_wbwet bulb temperature

Xindependent variable

λ_iEigenvalue associated with the eigenvector p_i

Acknowledgments

The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University for funding this work through Research Group Program under grant number (R.G.P.1/132/40).

Additional information

Funding

The authors are grateful for the funding and assistance received by the Deanship of Science Studies, King Khalid University, Abha-Asir, Saudi Arabia, with a grant number [R.G.P.1/132/40] under Research Group Program to complete the research work.

Notes on contributors

Osman Haitham

Haitham Osman is an Assistant Professor at King Khalid university, graduated from Newcastle University (UK). His research interests included but not limited to process modeling and optimization, advance process control, separation processes, and machine learning. He has published papers in journals and conferences in the area of process statistical modeling, numerical analysis, optimization, and artificial intelligence.

Madiouli Jamel

Jamel Madiouli is an Assistant Professor at Kairouan university. Graduated from Monastir University (Tunisia) in collaboration with RAPSODEE in EMAC, France, he undertook number of posts within Gafsa university, King Khalid University and finally Kairouan university.Dr Madiouli works in different areas within the Mechanical engineering arena, among them but not limited to drying, sintering, solar energy, desalination and shrinkage measurement during thermal processes

Shigidi Ihab

Ihab Shigidi is an Assistant Professor at King Khalid University, Graduated from Loughborough University, he undertook  number of posts within King Khalid University.Dr Shigidi works in different areas within the Chemical engineering arena, among them but not limited to separation processes, desalination, transport phenomena and mathematical modelling.