Numerical simulation of combined convective heat transfer in a sinusoidal cavity with lid-driven cap affected by fractal blocks

Improving the thermal performance of equipment on large and small scales is one of the most important issues in engineering. In this numerical study, the flow and combined convection heat transfer in a two-dimensional (2D) sinusoidal cavity affected by the movement of indirect hot fluid flow are investigated using the finite volume method. By using water/silver nanofluid in volume fractions (φ) of 0 to 0.06 and using fractal surfaces in a 2D cavity with a lid-driven cap in Richardson numbers (Ri) 0 to10, an attempt is made to increase the heat transfer efficiency of the sinusoidal hot surface. The results of this research show that due to the increase in the convective heat transfer coefficient resulted from the strengthening of the fluid velocity, a significant decrease in the temperature of the hot surface is achieved. At Ri = 10, due to the slower movement of the cap and the full compliance of the fluid with the sinusoidal surface, the heat penetration in the fluid layers increases and the temperature graphs become more uniform. The flow circulation between the two hot and cold sources is affected by the density gradients in the cooling fluid and the movement of the cap can create a different temperature distribution. The fluid temperature distribution is also dependent on moving areas in the cavity. The placement of fluid on fractal surfaces is associated with extreme velocity changes. Due to the presence of viscosity and the formation of the velocity boundary layer, this behavior also affects the movement of the fluid layers to the solid surface areas. The highest value of the Nusselt number (Nu) is gained during fluid contact with a cold lid-driven cap on the left side of the cavity. As the fluid moves further on the surfaces of the moving cavity, the hot fluid gradually exchanges its energy with the cavity cover and the fluid cools down. The presence of solid nanoparticles in a higher φ has a significant effect on reducing the temperature of the hot surface, which is due to the increase in the thermal conductivity of the cooling fluid. Compared to the base fluid, this behavior at φ = 0.06 has created a higher thermal efficiency increase of about 15 %. The lowest shear stress is related to the areas of fluid separation on the curved surface. In all investigated cases, the increase of φ can increase the average shear stress between 35 % and 43 % in different Ri.