Eur. Phys. J. Plus (2022) 137: 781
https://doi.org/10.1140/epjp/s13360-022-03009-7

Regular Article

Constructional design and mixed convection heat transfer inside lid-driven semicircular cavity

¹ School of Mathematics and Statistics, Nanjing University of Information Science and Technology, 210044, Nanjing, People’s Republic of China
² Department of Basic Sciences and Related Studies, Quaid-e-Awam University of Engineering, Science and Technology, Larkana, Pakistan
³ Department of Mechanics and Engineering Science, Fudan University, 200433, Shanghai, People’s Republic of China
⁴ Department of BS&H, National University of Science and Technology, Islamabad, Pakistan
⁵ Department of Electrical Engineering, Bahria University, Islamabad, Pakistan

^b mhamid@pku.edu.cn, mhamid@fudan.edu.cn, mhamid@nuist.edu.cn

Received: 20 January 2022
Accepted: 4 May 2022
Published online: 6 July 2022

Abstract

In this article, a constructional design-based numerical study is carried out to analyze magnetohydrodynamical (MHD) mixed convection heat transfer inside a water-filled semicircular cavity having cylindrical obstacles inside. The temperature of the upper flat wall is kept at a comparatively greater temperature $T_h$ compared to a circular bottom wall $T_c$. The top wall moves at constant velocity along the positive x-axis, while other cavity walls velocities are considered zero. The heat transfer takes place due to both temperature gradients change and upper flat wall motion. The flow and heat transfer phenomena inside the cavity are governed by the conservation of mass, momentum, and energy, which are formulated as nonlinear partial differential equations with associated boundary conditions. Physical parameters, such as Reynolds number, Richardson number, and Hartmann number, arise upon transformation into non-dimensional form. A well-known finite element method (FEM) is adopted to perform numerical simulation. A triangular mesh is created to discretize the space domain. Galerkin's approach is implemented to choose the test functions. Flow and temperature fields are demonstrated by streamlines and isotherms plots, respectively. The heat transfer rate is presented using the Nusselt number. It is observed that increasing the Richardson number decreases the heat transfer rate. Moreover, the heat transfer rate tends to enhance due to augmentation in the Hartmann number.