Investigation of MHD free convection of power‐law fluids in a sinusoidally heated enclosure using the MRT‐LBM

• Published in: Heat transfer (Hoboken, N.J. Print) N.J. Print), 2022-01, Vol.51 (1), p.355-376
• Main Authors: Afsana, Sadia, Parvin, Afroja, Nag, Preetom, Molla, Md. Mamun
• Format: Article
• Language: English
• Subjects: free convection; heat transfer; magnetic field effect; MRT‐LBM; non‐Newtonian fluid; sinusoidal wall temperature
• ISSN: 2688-4534; 2688-4542
• DOI: 10.1002/htj.22310

Magnetohydrodynamical free convective heat transfer flow of non‐Newtonian power‐law fluids has been analyzed numerically. For numerical simulation, the multiple‐relaxation‐time (MRT) lattice Boltzmann method (LBM) has been employed based on graphics process unit (GPU) computing. The computational domain is a two‐dimensional square cavity with thermally adiabatic upper and base walls, uniformly heated left wall, and sinusoidal heat distribution on the right wall. There is no research on non‐Newtonian fluid using MRT‐LBM using this configuration. Hence it is a new study in this field and novel results have been achieved with the magnetic field effect and sinusoidal wall temperature. The numerical simulations are carried out for different vital parameters such as thermal Rayleigh number ( R a ), Hartmann number ( H a ), and power‐law index ( n) to study the characteristics of heat transport along with the flow physics inside the square enclosure. The streamlines and isotherms elucidate the distribution of fluid flow and energy within the cavity. The energy transfer phenomena are interpreted as the local Nusselt number ( N u ) distribution and the average Nusselt number ( N u ¯ ) along the heated wall. Computational results show that the rate of energy transfer is attenuated due to the augmentation of the magnetic field. However, ( N u ¯ ) exhibits direct correspondence with the Rayleigh number and an inverse relation with the power‐law index ( n ). The elevation of Hartmann number ( H a ) results in the diminution of N u and N u ¯ for pseudoplastic fluid ( n < 1) by 82.65% and 86.04%, respectively. Moreover, the temperature distribution ( θ) of R a = 1 0 5 amplifies by 95.83% compared to R a = 1 0 4 as the fluid transitions from pseudoplastic to dilation behavior. For GPU computing, the NVIDIA CUDA C programming platform is used in the present study.