OBRABOTKAMETALLOV Vol. 23 No. 3 2021 MATERIAL SCIENCE EQUIPMENT. INSTRUMENTS 7 5 2. A constant heat flux boundary condition was applied to the pipe wall. 3. A pressure outlet boundary condition was applied at the pipe exit. The k-ε turbulence model was used to resolve turbulence effects. Validation The present study was validated against the results of Elshafie et al. [43], who investigated pulsating turbulent flow (10,000 ≤ Re ≤ 40,000; 6.6–68 Hz) in heated pipes. Numerical accuracy was confirmed by Fig. 4, which demonstrates excellent agreement in the average Nusselt number (Nu) between the present simulations and those of Elshafie et al. Fig. 5 depicts the transient variations in the surface heat transfer coefficient (h). The fluctuations stabilize after t = 2.5 s; therefore, t = 6 s was deemed sufficient for steady-state calculations. In all cases, h increases with Re. Fig. 4. Comparison of the average Nusselt number with the theoretical and experimental results of Elshafie [43] Fig. 5. Surface HT coefficient (h) obtained for different Re Effects of Surface Roughness Surface roughness enhances heat transfer (HT) by disrupting the thermal boundary layer [44], although it also increases pressure drop [45, 46]. Due to the complexity of the phenomena, extensive experimental research is required [47]. MacDonald et al. [48] demonstrated the impact of roughness on drag using direct numerical simulation (DNS) across sinusoidal surfaces (k⁺ = 10, λ = 0.05–0.54). Meyer et al. [49] reported that roughness increases HT in laminar flow but has a negligible influence in turbulent regimes. Abdelfattah et al. [56] investigated 48-element impinging jets with hemispherical, droplet, and cylindrical roughness elements; cylinders enhanced HT, while droplets reduced drag. Wall roughness affects momentum and energy transport [57]. Investigations of roughened pipes indicate that the log-law behavior is altered by a roughness function fr, based on the roughness height Ks+. Equation (10) is used to account for roughness in the velocity profile, where k = 0.4187 (von Karman constant). ANSYS Fluent classifies hydrodynamically smooth, transitional, and completely rough regimes based on the Cebeci-Bradshaw method, using ΔB and Ks+. 1 * * ln / p p w u u u y E B k ρ = − ∆ τ ρ µ (10)
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