Numerical simulation of flow and heat transfer in a pipe with nail-shaped hurdles

We investigate fluid flow and heat transfer in a channel obstructed by nail-shaped hurdles under forced convection using the Finite Difference Method. Due to the absence of an analytical solution, numerical techniques are employed. The channel is geometrically transformed into a rectangular configuration using curvilinear coordinates. Elliptic grid generation is used to discretize the domain. The Navier-Stokes equations are reformulated through the vorticity stream function formulation, and the Finite Difference Method incorporates a coordinate transformation approach. Effects of Reynolds numbers between (20 <= Re <= 600), Prandtl numbers (0.71,17.1), and nail spans (0.1 <= h <= 0.7) on velocity, temperature profiles is studied. Local and Average Nusselt numbers on Nail-shaped hurdle are also calculated. The observed maximum Nusselt numbers are 13.49, 27.83, and 11.86 at Ra = 600, Pr = 7.1, and h = 0.1, respectively Results show that higher Reynolds and Prandtl numbers increase Nusselt numbers, enhancing heat transfer. Narrower nail spans improve heat transfer efficiency.