Lattice Boltzmann simulation of natural convection flow around a horizontal cylinder located beneath an insulation plate

In this paper, two-dimensional heat transfer solution of natural convection around an isothermal cylinder located beneath an insulation wall is studied. The effects of distance ratio of the cylinder to the wall as well as the impact of the dimensionless Rayleigh number in the flow and heat transfer are taken into account. Solving the flow equations for $ L/D$ ratio with values 0.5, 0.7, and 1.5 and the Rayleigh number ranging from 1000 to 40000 is carried out. The results are compared with the experimental data which present a good agreement. The results indicate that the effect of weakened natural convection flow in the cylinder commences when decreasing $ L/D$ ratio from the value 1.5 to 0.5 leading to a decline in heat transfer and the Nusselt number. This process occurs in all values of the Rayleigh number. For the ratio number greater than 1.5, the impact of adiabatic wall is neglected, and there is no significant influence on the natural convection flow. Increasing the angle from $0^\circ $to$180^\circ $results in a fall in the Nusselt number which is as a consequence of growth in the distances of isothermal lines.