Thermal Convection in a Heated-Block Duct with Periodic Boundary Conditions by Element-by-Element Treatment

The periodic nature of stream-wise flow occurs in a cooling channel so frequently due to the multiple heat sources in electronic equipment, demanding the creation of an effective technique to improve the heat-cooling convection. This work explores thermal convection enhancement in a heated-block duct for periodic boundary conditions using the element-by-element (EBE) treatment in a semi-implicit projection finite element method (FEM) through a preconditioned conjugate gradient (PCG) solver. The effects of changing the Reynolds numbers (100, 175, and 250) on rectangular cylinders installed in the channel under periodic boundary conditions were studied using time-mean Nusselt number enhancement, friction factor enhancement, and thermal performance coefficient. The results show that the rectangular cylinders installed stream-wise above an upstream block promote thermal convection in the heated-block duct due to modifying the flow of no cylinders. However, increasing the number of rectangular cylinders increases the friction factor enhancement. As a result, the case for periodic boundary conditions with a rectangular cylinder above every two blocks has the best thermal performance coefficient.