In this study, numerical investigations are conducted for forced convective heat transfer in an annular helicoidal tube under uniform wall temperature condition for laminar flow including developing region. The numerical computations reveal the developments and distributions of heat transfer and flow fields in the annular helicoidal tube when the outer tube wall is heated and the inner tube wall is insulated. The effects of Reynolds number, curvature ratio, and coil pitch on the circumferential average friction factor and Nusselt number at different axial locations, and the non-dimensional entropy generation number of laminar convection in an annular helicoidal tube are investigated. In addition, the differences of flow and heat transfer characteristics between the annular helicoidal tube and circular helicoidal tube are also described.

A numerical method for simulating three-dimensional laminar forced convective heat transfer in a helical coiled passage with annular cross section under uniform wall temperature condition is presented. The helical coiled passage is fabricated by bending a 0.03m inner diameter and 0.05m outer diameter straight tube into a helical-coil of two turns. The results presented in this paper cover a Reynolds number range of 200~1000, a pitch range of 0.1~0.2 and a curvature ratio range of 0.1~0.3. The numerical computations reveal the development and distribution of heat transfer and flow fields in the helical coiled passage when the inner annular wall is heated and the outer annular wall is insulated. In addition, the effects of Reynolds number, curvature ratio, and coil pitch on the average friction factor, average Nusselt number at different axial cross-section have been discussed. The results show that the secondary flow is weak and can be neglected at the entrance region, but the effect of the secondary flow is enhanced, the maximum velocity perpendicular to axial cross section shifts toward the outer side of helical coiled passage. Furthermore, the average Nusselt number and friction factor at every different axial location present different characteristics when the Reynolds number, curvature ratio and pitch change. Compared with the curvature ratio, the pitch has relatively little influence on the heat transfer and flow performance.

Three-dimensional turbulent forced convective heat transfer and flow characteristics, and the non-dimensional entropy generation number in a helical coiled tube subjected to uniform wall temperature are simulated using the k–ε standard turbulence model. A finite volume method is employed to solve the governing equations. The effects of Reynolds number, curvature ratio, and coil pitch on the average friction factor and Nusselt number are discussed. The results presented in this paper cover a Reynolds number range of 2 × 104 to 6 × 104, a pitch range of 0.1–0.2 and a curvature ratio range of 0.1–0.3. The results show that the coil pitch, curvature ratio and Reynolds number have different effects on the average friction factor and Nusselt number at different cross-sections. In addition, the flow and heat transfer characteristics in a helical coiled tube with a larger curvature ratio for turbulent flow are different from that of smaller curvature ratio for laminar and turbulent flow in certain ways. Some new features that are not obtained in previous researches are revealed. Moreover, the effects of Reynolds number, curvature ratio, and coil pitch on the non-dimensional entropy generation number of turbulent forced convection in a helical coiled tube are also discussed.

A numerical method for simulating the developments and distributions of heat transfer and flow fields was proposed.The effects of Reynolds number,curvature ratio,and coil pitch on the average friction factor,average Nusselt number at different axial cross-sections and the total entropy generation rate in a helical coiled tube with uniform heat flux was presented when Reynolds number is 200～1 000,dimensionless pitch 0.1～0.2 and dimensionless curvature ratio 0.1～0.3.The results show that the effect of the secondary flow is enhanced with the increase of turning angle,the maximum velocity perpendicular to axial cross section shifts toward the outer side of helical coiled tube and two Dean roll cells appear with the increase of axial turning angle.Furthermore,the average friction factor,average Nusselt number at different axial cross-sections and the total entropy generation rate present different characteristics when the Reynolds number,curvature ratio and pitch change.Compared with the curvature ratio,the pitch has relatively little influence on convective heat transfer performance and the total entropy generation.In the meantime,the entropy generation caused by viscous flow is much less than that caused by heat transfer and can be neglected.

Two-stage glass transitions combined with two supercooled liquid regions were observed before the completion of crystallization for Zr60−xYxAl15Ni25 amorphous alloys containing 15–35 at.% Y. The phase transition of these amorphous alloys on heating takes place in the sequence amorphous solid, first-stage reactions of glass transition, supercooled liquid and crystallization, and then the second-stage reactions of glass transition, supercooled liquid and crystallization. The first-stage reactions are due to a Y-rich YAlNi amorphous phase, and the remaining Zr-rich ZrAlNi amorphous phase causes the second-stage reactions. The first-stage exothermic reactions results from the homogeneous precipitation of crystalline particles with a size of about 3 nm. The remaining amorphous phase, which coexists with the nanoscale Y-rich crystalline particles, exhibits a large temperature range of supercooled liquid of up to 104 K, and has optimum structural and bonding states in which no extra consistent atoms with a weak bonding nature are included.

A Zr33Y27Al15Ni25 amorphous alloy was found to exhibit a two-stage glass transition and crystallization processes because of the insoluble nature between Zr and Y. The first-stage exothermic reaction is due to the precipitation of the nanoscale Y-rich phase from the amorphous matrix and the precipitates cause the suppression of the decrease in viscosity and elasticity in the supercooled liquid region.

An amorphous phase exhibiting two distinguishable supercooled liquid regions was found in quaternary (Zr–Y)60Al15Ni25 alloys in which the main constituent elements of Zr and Y are immiscible in a solid state. The first- and second-stage supercooled liquid regions are observed in the temperature ranges of 640 to 664 K and 763 to 810 K, respectively, accompanied by the two-distinguishable exothermic peaks due to crystallization after the appearance of the supercooled liquid regions. The temperatures of the first- and the second-reactions appear to correspond to those for ternary Y60Al15Ni25 and Zr60Al15Ni25 amorphous alloys, respectively. The simultaneous dissolution of the immiscible Zr and Y elements is essential for the appearance of the two-stage supercooled liquid regions. From the appearance of the second-stage supercooled liquid region, it is concluded that the precipitation of the primary crystalline phase does not exert detrious influence on the appearance of the supercooled liquid region.

An amorphous phase exhibiting two distinguishable supercooled liquid regions was found in quaternary (Zr-Y)60Al15Ni25 alloys in which the main constituent elements of Zr and Y are immiscible in a solid state. The first- and second-stage supercooled liquid regions are observed in the temperature ranges of 640 to 664 K and 763 to 810 K, respectively, accompanied by the two-distinguishable exothermic peaks due to crystallization after the appearance of the supercooled liquid regions. The temperatures of the first- and the second-reactions appear to correspond to those for ternary Y60Al15Ni25 and Zr60Al15Ni25 amorphous alloys, respectively. The simultaneous dissolution of the immiscible Zr and Y elements is essential for the appearance of the two-stage supercooled liquid regions. From the appearance of the second-stage supercooled liquid region, it is concluded that the precipitation of the primary crystalline phase does not exert detrious influence on the appearance of the supercooled liquid region.