This paper focuses on the natural convection of heat transfer using magnetohydrodynamic (MHD) Bingham nanofluid. Utilizing the multiple-relaxation-time (MRT) lattice Boltzmann method (LBM) within a C -shaped enclosure and the NVIDIA graphics processing unit (GPU)-based compute unified architecture (CUDA) C/C++ platform, the simulation is carried out numerically. Inside the cavity, the base fluid is water and the nanofluid is Al 2 O 3 . Boundary conditions are presented in accordance with the heated, cold, and adiabatic conditions present in the cavity's various walls. Several parameters including Bingham number ( B n = 0 , 0.5 , 1 , 1.5 , 2 ), Rayleigh number ( R a = 10 4 , 10 5 , 10 6 ), Hartmann number ( H a = 0 , 10 , 20 , 30 ), and nanoparticle volume fraction ( ϕ = 0 , 0.01 , 0.02 , 0.03 , 0.04 ). The results of the numerical simulation are shown using streamlines and isotherms, velocity-temperature, Local Nusselt number, and average Nusselt number. From the obtained results it is found that for the variation of Bn , Ha , and ϕ with different Ra the rate of heat transfer decreases along the bottom wall and increases for the left and top walls. The average Nusselt number decreases while Bn , Ha rises. On the other contrary, the average Nu increases as ϕ increases. Response surface methodology (RSM) is added here to have better understanding of the effects of parameter used. RSM includes statistical table for the combination of data set and their graphs to understand the accuracy. Moreover, regression analysis shows how average Nu increases or decreases with the variation of different parameters. The C-shaped geometry provides an excellent option in heat exchanging or electronic cooling equipment the chip designing technology. This study is only for two-dimensional laminar flow.

Competing Interests: The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Md. Mamun Molla reports financial support was provided by 10.13039/501100019782North South University. Md. Mamun Molla reports financial support was provided by Government of the People's Republic of Bangladesh 10.13039/501100008804Ministry of Science and Technology. Md. Mamun Molla reports a relationship with North South University that includes: employment. No conflicts of interest.

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