Application of Response Surface Methodology in the Optimization of Magneto-Hydrodynamic Flow Around and Through a Porous Circular Cylinder

Abstract

In this study MHD flow around and through porous cylinder is numerically investigated. The governing equations are developed in polar coordinate arrangement in both porous and non-porous media on the basis of single-domain technique. The equations are solved numerically based on finite volume method over staggered grid structure. Nusselt number and drag coefficient are selected as two key parameters describing performance of this system. By applying response surface methodology the sensitivity of these parameters to main factors of the problem, including Stuart number, Darcy number and Reynolds number are quantified. RSM is also utilized to perform an optimization process to find the best condition in which the lowest drag force and highest heat transfer rate occur simultaneously. The CFD analysis is carried out for variant Reynolds numbers (10 ≤ Re ≤ 40), Darcy numbers (10-6 ≤ Da ≤ 10-2) and Stuart numbers (2 ≤ N ≤ 10). Streamlines and isotherms are presented to indicate the impacts of such parameters on heat and fluid flow. It can be seen that, Drag coefficient and Nusselt number increase by augmenting magnetic field strength. Beside, Darcy number and Reynolds numbers have a direct and inverse effect on Nuave and Cd, respectively. Results of optimization process show that Nuave and Cd are more sensitive to Reynolds and Stuart numbers, respectively, while they less sensitive to Darcy number. Moreover, it is revealed that the optimum condition occurs at Da = 10-2, Re = 38.1 and N = 4.49.

Optimal characteristics and heat transfer efficiency of SiO 2 /water nanofluid for application of energy devices: A comprehensive study

“…85 As reported in Tables 7 and 8, these values are 519.86, for the viscosity, and 6083.785, for the thermal conductivity, regression models. A large F value implies that the model has a low error.…”

“…85 In the current study, the viscosity and the thermal conductivity are two responses, while the nanofluid concentration and the temperature are the two controllable factors. 85 In the current study, the viscosity and the thermal conductivity are two responses, while the nanofluid concentration and the temperature are the two controllable factors.…”

“…RSM is a mixed mathematical and statistical approach, which can be utilized to establish the relationship between effective parameters and one or more responses. 85 In the current study, the viscosity and the thermal conductivity are two responses, while the nanofluid concentration and the temperature are the two controllable factors. The general cubic form is as follows:…”

“…85 ANOVA comprises many statistical indicators to find out how effective at prediction a model will be. Establishing models and evaluating their fitting accuracy was performed using the analysis of variance (ANOVA) procedure.…”

“…85 The actual data versus the predicted data have been drawn in Figure 11. The proximity of these values to unity indicates that the viscosity and the thermal conductivity of a water-based SiO 2 nanofluid are well modeled.…”