Model Designed to Acquire an Optimized Performance Implementing L27 Orthogonal Array for the Prandtl Fluid Flow Maneuvering Grey Relational Theory

Abstract

To design a resourceful model, the optimization technique is executed in the present analysis which helps in attaining a theoretical framework of high productivity which assists in minimising the cost and time. The novelty lies in optimising the responses of surface drag and enhanced heat and mass transfer which is so far not reported in the literature. The stretched geometry is contemplated as replicating a polymer sheet, which endorses substantial application in industries with the effects of linear radiation, thermo-diffusion, and diffusion-thermo impacts. The L27 orthogonal array is explained using the Taguchi optimization method to record the signal-to-noise ratio for the response of heat and mass transfer rate individually. Multi-response optimization is carried out using grey relational analysis, producing grey relational grades and respective ranks. Numerical solutions are retained using the Runge-Kutta Fehlberg method. Parametric results revealed that intense radiation contributes to amplifying the rate of heat transfer and having a strong impact on the diffusion-thermo effect. Elevated mass transmission rate can be procured for higher thermophoresis parameters and Soret numbers. On the other hand, the lowest transfer rate of mass is received at a higher value of the Schmidt number. Outcomes of the work showcase that the 22nd experimental run with the curvature parameter at 3.5, Prandtl number at 7.1, Elastic parameter at 3, radiation parameter at 1.6, and thermophoresis parameter at 0.4 is an optimized level for Nusselt number and Sherwood number. Analysis of variance on grey relational grade reveals that curvature parameter has the largest contribution on grey relational grade of about 41.16%, followed by radiation parameter with 38.96% contribution. The least contribution, as stipulated by Prandtl number, is about 2.07%.

Keywords

• Grey relational analysis
• multiple response optimization
• Taguchi method, Prandtl nanofluid, Soret-Dufour effect, curved stretching sheet