7 An LES study and ... in-line tube-banks defined a criterion for minimizing the square of the error as In order to obtain a local value, varying in time and space in a fairly wide range, for the model constant C , one takes ∂E ∂C and sets it zero to get A negative C represents the transfer of flow energy from the subgrid-scale eddies to the resolved eddies, which is known as back-scatter and regarded as a desirable attribute of the dynamic model. The Large Eddy Simulation (LES) of turbulent flow over tube-banks is hampered by expensive computational cost incurred when the dynamic and thin near-wall layer is fully resolved. To obviate the computational cost associated with calculating the wall shear stress from the laminar stress- strain relationship that requires the first cell to be put within the range of y + ≈ 1, Werner et al.[37] proposed a simple power-law to replace the law of the wall, in which the velocity profile on a solid wall is given as following, where A = 8 . 3 and B = 1 / 7. An analytical integration of Eq. (21) results in the following relations for the wall shear stress where u$_{p}$ is velocity component parallel to the wall and given by: | u$_{p}$ | = µ 2 ρΔy A 2 1 − B (22) | τ$_{w}$ | =      2 µ | u$_{p}$ | Δy for y + ≤ 11 . 81 ρ$^{[}$ 1 − B 2 A$^{1+}$$^{B}$ 1 − B ( µ ρΔy ) 1+ B + 1+ B A ( µ ρΔy $^{B}$| u$_{p}$ | ) ] 2 1+ B for y + > 11 . 81 (21) u + =      y + for y + ≤ 11 . 81 A ( y $^{+}$) B for y + > 11 . 81 (20) C = 1 2 L$_{ij}$M$_{ij}$ M$_{ij}$M$_{ij}$ (19) E = ( L$_{ij}$ − δ$_{ij}$ 3 L$_{kk}$ − 2 CM$_{ij}$ ) 2 (18) 2.2 The Werner and Wengle wall layer model