Eur. Phys. J. Spec. Top. (2022) 231: 2683-2694
https://doi.org/10.1140/epjs/s11734-022-00587-6

Regular Article

Thermal treatment inside a partially heated triangular cavity filled with casson fluid with an inner cylindrical obstacle via FEM approach

¹ State Key Laboratory of Hydraulics and Mountain River Engineering, College of Water Resource and Hydropower, Sichuan University, 610065, Chengdu, People’s Republic of China
² Department of Mathematics, National University of Modern Languages (NUML), Islamabad, Pakistan
³ Department of Mechanical Engineering, College of Engineering, Prince Mohammad Bin Fahd University, PO Box 1664, 31952, Al Khobar, Kingdom of Saudi Arabia
⁴ School of Mathematics and Statistics, Nanjing University of Information Science and Technology, 210044, Nanjing, People’s Republic of China
⁵ Department of Mechanics and Engineering Science, Fudan University, 200433, Shanghai, People’s Republic of China
⁶ Department of Electrical Engineering, Bahria University, 44000, Islamabad, Pakistan

^d mhamid@pku.edu.cn, mhamid@fudan.edu.cn

Received: 3 December 2021
Accepted: 3 May 2022
Published online: 17 May 2022

Abstract

A comprehensive numerical study is presented for the hydromagnetic flow and heat transfer of Casson fluid in an enclosed partially heated triangular cavity. A cylindrical obstacle is placed with different thermal boundary conditions inside the cavity. The governing partial differential equations are converted to a non-dimensional form via suitable similarity variables. Well-known finite element method (FEM) is employed to solve the governing equations and investigate the impact of various physical parameters like the length of the heating element, Casson and radiation parameters, and the Hartmann number on the streamlines, isotherms, and local Nusselt numbers. Simulations are performed for the three selected (cold, adiabatic, and heated) conditions of an inner cylindrical obstacle. It is demonstrated that the maximum Nusselt number ensues near the edges of the heating element and the Casson parameter tends to reduce the Nusselt number. It is also found that the length of the heating element has substantial effects on the heat transfer in the cavity. The new results of this study may help to study the thermal control and non-Newtonian fluids inside closed enclosures.