Application of central composite design (CCD)-response surface methodology (RSM) for optimization of heat transfer in dusty nanofluid flow with velocity slip

Abstract

Background and Purpose

The consequence of thermal radiation is scrutinized on the heat transport of Nano-diamond/silicon oil and silver/silicon oil nanofluids through a stretching endless plate. The single phase (Tiwari and Das) model is employed for nanofluid. The major objective of this study is to optimize the RSM-based Central composite design modeling to optimization of the heat transfer in dusty Oldroyd-B nanofluid across stretching surface. Additionally the velocity slip effect is considered. The dust particle phase is also taken into account. The significance of viscous dissipation, joule heating, inclined magnetic field with convective condition is investigated.

Methodology

The partial differential equations are developed under consideration, then transform to ODE’s by utilizing similarity tools. The transformed model of ODE’s is tackled numerically via bvp4c MATLAB tool with shooting algorithm. The effect of magnetic parameter, fluid interaction parameter, nanoparticle volume fraction, slip parameter and temperature interaction parameter on velocity field and temperature distribution of fluid phase and dust phase is investigated. Furthermore the Nusselt number on the wall is observed for interactive parameters of mass concentration of dust particles, fluid particles interaction parameter for velocity and unsteady parameters utilizing the face-centered Central Composite design (CCD) of the Response Surface Methodology (RSM). Additionally, Analysis of Variance (ANOVA) algorithm and 3D plots are utilized to examine the consequence of experimental design parameters via the response. The recommended model significance has been analyzed in conditions of correlation coefficient ($R^2$), mean square error (MSE), root means square error (RMSE), prediction standard error to acknowledge the most excellent strong.

Results

The difference between the Predicted R² of 0.9467 and the Adjusted R² of 0.9867 is less than 0.2, which is assumed to be a reasonable concurrence. Furthermore results of the current analysis indicate that velocity gradient for nanofluid is diminishes for larger fluid particle interaction parameter for velocity, while the dust phase velocity is improved. The increment in Temperature gradients is observed via increasing values of the nanoparticle fraction and temperature base fluid particle interaction parameter. From the results it is concluded that skin friction coefficient is reduced with larger magnetic parameter for both mono nanofluids. Furthermore the heat transfer rate is increased by increasing the thermal radiation parameter for both mono nanofluids. It is concluded that silver/silicon oil nanofluid play a higher role in heat transportation as compare to Nano-diamond/silicon oil.

Keywords:

• CCD
• dust particle phase
• nanofluids
• Oldroyd-B fluid model
• response surface methodology (RSM)
• viscous dissipation

Disclosure statement

No potential conflict of interest was reported by the author(s).