The numerical results converge to the exact results through refining the mesh. The isotherms are also obtained at different times until a steady-state solution is reached.

After the temperature field is attained, the local Nusselt number is computed for the tubes in the bundle at different times. The outcome is found to be in acceptable concurrence with those from the previous studies. A grid independence study for the energy equation preceded the final mesh. The L2 norm of the error between numerical and exact solutions is also presented for three different hybrid meshes. Weighting the 3-D, transient, convection-diffusion equation for a cube verifies the numerical results.

On the other hand, the finitedifference technique discretizes the derivatives toward the tube axis. The proposed hybrid method employs a 2-D Taylor-Galerkin finite-element method, and the energy equation perpendicular to the tube axis is discretized. An equilateral triangle (ET) tube pattern is considered for the staggered tube bank.

The investigation used Reynolds numbers of 100 and 300, Prandtl number of 0.7, and pitch-to-diameter ratio of 1.5. The approach solves the 3-D unsteady energy equation in nonisothermal fluid flow over a staggered tube bank with five tubes in the flow direction. This article presents a hybrid finite-element=finite-difference approach.

Adina meshfree group