Taguchi Method and Numerical Simulation for Variable Viscosity and Non-Linear Boussinesq Effects on Natural Convection over a Vertical Truncated Cone in Porous Media

Ken Ming Tu,Kuo Ann Yih,Jyh Horng Chou,Fu I Chou

doi:10.3390/en13020504

Abstract

This study uses an optimization approach representation and numerical solution for the variable viscosity and non-linear Boussinesq effects on the free convection over a vertical truncated cone in porous media. The surface of the vertical truncated cone is maintained at uniform wall temperature and uniform wall concentration (UWT/UWC). The viscosity of the fluid varies inversely to a linear function of the temperature. The partial differential equation is transformed into a non-similar equation and solved by Keller box method (KBM). Compared with previously published articles, the results are considered to be very consistent. Numerical results for the local Nusselt number and local Sherwood number with the six parameters (1) dimensionless streamwise coordinate ξ, (2) buoyancy ratio N, (3) Lewis number Le, (4) viscosity-variation parameter θ r , (5) non-linear temperature parameter δ 1 , and (6) non-linear concentration parameter δ 2 are expressed in figures and tables. The Taguchi method was used to predict the best point of the maxima of the local Nusselt (Sherwood) number of 3.8636 (5.1156), resulting in ξ (4), N (10), Le (0.5), θ r (−2), δ 1 (2), δ 2 (2) and ξ (4), N (10), Le (2), θ r (−2), δ 1 (2), δ 2 (2), respectively.

Highlights

The coupled heat and mass transfer of free convection in saturated porous media have many important applications in nature and engineering
The numerical results are presented for the dimensionless streamwise coordinate ξ ranging from 0 to 4, the buoyancy ratio N ranging from 1 to 10, the Lewis number Le ranging from 0.5 to 2, the viscosity-variation parameter θr ranging from −2 to 2, the non-linear temperature parameter δ1 ranging from 0.5 to 2, the non-linear concentration parameter δ2 ranging from 0.5 to 2
(2), 1 (2), 2 (2), the results show that the local Sherwood number is 5.1156 for the case of ξ (4), N

Summary

Introduction

The coupled heat and mass transfer of free convection in saturated porous media have many important applications in nature and engineering. Cheng et al [1] analyzed natural convection of a Darcian fluid about a cone. With respect to the study on heat and mass transfer, the coupled heat and mass transfer by free convection over a truncated cone in porous media, variable wall temperature and variable wall concentration (VWT/VWC) or variable heat flux and variable mass flux (VHF/VMF) was solved by Yih [2]. Energies 2020, 13, 504 integral approach for heat and mass transfer by natural convection from truncated cones in porous media with variable wall temperature and concentration. Cheng [4] extended the work of Yih [2] and

Methods

Results

Conclusion