Author(s)

Muhammad Sajjad Hossain^1*, Md. Abdul Alim², Laek Sazzad Andallah³

¹Department of Arts and Sciences, Ahsanullah University of Science & Technology (AUST), Dhaka, Bangladesh.
²Department of Mathematics, Bangladesh University of Engineering & Technology (BUET), Dhaka, Bangladesh.
³Department of Mathematics, Jahangirnagar University, Dhaka, Bangladesh.

A numerical research on magnetohydrodynamic mixed convection flow in a lid-driven trapezoidal enclosure at non-uniform heating of bottom wall has been studied numerically. The enclosure consists of insulated top wall and cold side walls, too. It also contains a heated triangular block (Rot = 0° - 90°) located somewhere inside the enclosure. The boundary top wall of the enclosure is moving through uniform speed U₀. The geometry of the model has been represented mathematically by coupled governing equations in accordance with proper boundary conditions and then a two-dimensional Galerkin finite element based numerical approach has been adopted to solve this paper. The numerical computations have been carried out for the wide range of parameters Prandtl number (0.5 ≤ Pr ≤ 2), Reynolds number (60 ≤ Re ≤ 120), Rayleigh number (Ra = 10³) and Hartmann number (Ha = 20) taking with different rotations of heated triangular block. The results have been shown in the form of streamlines, temperature patterns or isotherms, average Nusselt number and average bulk temperature of the fluid in the enclosure at non-uniform heating of bottom wall. It is also indicated that both the streamlines, isotherm patterns strongly depend on the aforesaid governing parameters and location of the triangular block but the thermal conductivity of the triangular block has a noteworthy role on the isotherm pattern lines. Moreover, the variation of Nu_av of hot bottom wall and θ_av in the enclosure is demonstrated here to show the characteristics of heat transfer in the enclosure.

Mixed Convection, Magentohydrodynamic, Finite Element Method, Trapezoidal Enclosure, Triangular Block, Non-Uniform Heating

Hossain, M.S., Alim, Md.A. and Andallah, L.S. (2020) Finite Element Analysis of Magnetohydrodynamic Mixed Convection in a Lid-Driven Trapezoidal Enclosure Having Heated Triangular Block. American Journal of Computational Mathematics, 10, 441-459. doi: 10.4236/ajcm.2020.103025.