Multiple-relaxation-time lattice boltzmann simulation of natural convection of ethylene Glycol -Al2O3 power-law Non-newtonian nanofluid in an open enclosure with adiabatic fins

The heat transfer by natural convection of a nanofluid, which is ethylene glycol$-A{l}_2{O}_3$ has been analyzed in an open cavity numerically using the multiple-relaxation-time - lattice Boltzmann method by the graphics processing unit high-performance parallel computing. The right side of the cavity is open, and different boundary conditions have been applied to all the walls. Besides, one adiabatic fin has been installed on each side of the enclosure’s top and bottom sides. Here, the Prandtl number is fixed at 16.6, and the Rayleigh number changes from ${10}^4-{10}^6$ with the nanoparticle volume fraction from $0\%-5\%$ has been used for numerical simulations. Besides, in this work, the power-law index is an important parameter as well, and 0.7, 0.8, 1, 1.2, and 1.4 are the values of this parameter. Results are presented concerning both the average and local Nusselt numbers in the form of streamlines, isotherms, temperature distributions, velocity distributions, heat transfer rate, and entropy production. It is observed when increases, average Nusselt number increases $607.94\%$, and for this reason, the overall heat transfer rate rises because of buoyancy force. In addition, the average Nusselt number falls by $83.28\%$ when the power-law index rises; as a result, the total heat transfer rate falls because fluid viscosity increases with the power-law index. It is also observed that for shear-thickening fluids, the temperature gradient is higher. On the contrary, the temperature started decreasing with the increase of the power-law index. Additionally, the local Nusselt number value rises as power-law index falls. Moreover, the heat transfer rate increases by $7.08\%$ when volume fraction increases. The intensity of buoyancy force reduces with the increase of volume fraction. Besides, the overall entropy generation rises when the Rayleigh number and the volume fraction increase, but it decreases when the power-law index increases. So, when the Rayleigh number is ${10}^6$, the power-law index is 0.7, and the volume fraction is 0.00 then the entropy generation is the highest. This current research has many applications for example heat exchangers, electronic cooling equipment, solar heating systems, aerospace applications, medical devices, and entropy generation-related systems.