Thermal optimization of MHD nanofluid over a wedge by using response surface methodology: Sensitivity analysis

Ahmed Zeeshan ^a,*, Dilawar Hussain ^a,b, Zaheer Asghar ^c,d, Muhammad Mubashir Bhatti ^e, Faisal Z. Duraihem ^f

a. Department of Mathematics & Statistics, FBAS, International Islamic University Islamabad, H-10, Islamabad 44000, Pakistan
         b. Department of Mathematics, Faculty of Natural and Health Sciences, University of Baltistan, Skardu 16100, Pakistan
         c. Centre for Mathematical Sciences, Pakistan Institute of Engineering and Applied Sciences, Nilore, Islamabad 45650, Pakistan
         d. Centre for Physics and Applied Mathematics, Pakistan Institute of Engineering and Applied Sciences, Nilore, Islamabad 45650, Pakistan.
         e. Department of Mathematics and System Sciences, Shandong University of Science and Technology, Shandong, China
         f. Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

Abstract: It is well documented that heat transfer is enhanced with addition of nanosized particles in fluid. But, in a mechanical system there are variety of factors influences the heat transfer. Some factors are significant while others are not. In this paper, authors will discuss sensitivity of different input parameters such as Le, Nt and Nb on output responses Nu_x and Sh_x. To achieve this goal, the problem is modeled using basic conservation laws. The formulated model is a set of PDEs, which are converted to set of non-linear ODEs by using similarity transformation. Then these ODEs are solved numerically by using MATLAB built in package bvp4c and compared the numerical results with existing work and found good results. Sensitivity analysis is performed by employing RSM to determine the relationship between the input parameters such that 0.1≤Le≤1, 0.1≤Nt≤1 and 0.1≤Nb≤1 and the output responses (Nu_x and Sh_x. ANOVA tables are generated by using RSM. By using the ANOVA tables the correlations between input parameters and output response are developed. To check the validity of correlated equations, the residuals are plotted graphically and show best correlations between input parameters and output responses. The high values of R²=98.65 and Adj R²=97.43 for Nu_x and R²=97.83 and Adj R²=95.88 for Sh_x demonstrates the high validity of ANOVA results to perform sensitivity analysis. Finally, we have conducted a sensitivity analysis of the responses and came to the important results that Nt and Nb is most sensitive to Nusselt number and Sherwood number respectively.

Keywords: Sensitivity analysis; Nusselt number; Sherwood number; Response surface methodology (RSM), Analysis of variance (ANOVA); Nano fluid

https://doi.org/10.1016/j.jppr.2023.10.003