Turbulent forced convection heat transfer in triangular cross sectioned helically coiled tube

A three-dimensional turbulent forced convective heat transfer and ﬂow characteristic, in a helical triangular cross sectioned coiled tube is simulated using the k–ɛ standard turbulence model and compared to results corresponding to circular cross sectioned helical tube. A finite element method is employed to solve the governing equations. The effects of Reynolds number, on Nusselt number, velocity and temperature profiles are discussed. The numerical computations show the developments and distributions of heat transfer and flow fields in the tube. These profiles are altered by the effect of curvature inducing the centrifugal forces


Introduction
* Optimization of forced convection heat transfer from helical coiled tubes has a great importance in many fundamental and engineering applications especially in heat exchangers and storage tanks technologies.
An important number of theoretical, numerical and experimental studies investigated the effect of several parameters on the heat transfer from circular cross sectioned helical coiled tubes.
The rates of heat transfer in a straight tube and a helically heat exchanger were compared by Prabhanjan et al. (2002). Authors mentioned that the heat transfer coefficient changes by changing the geometrical configuration. Ko and Ting (2005), used the minimal entropy generation method to evaluate the effect of Reynolds number on the produced irreversibility's in the case of a fully developed laminar flow in a helically tube, the main results is that the entropy generation is insensitive to the coil pitch. Zheng et al (2000) studied numerically the coupled laminar forced convection and thermal radiation inside a helical pipe. The effects radiative transfer on the flow and heat transfer were measured. The comparison shows that thermal radiation has no significant effect on flow and temperature field but it enhances the total heat transfer. Ko (2006) optimized the mass flow rate for fully developed laminar forced convection of different fluids through circular cross section helically coiled tubes with constant heat flux at walls. The same configuration was treated by Shokouhmand and Salimpour (2007) to evaluate the entropy generation and optimal Reynolds number under constant wall temperature for water and air. An extension of this work was done by the same authors (Shokouhmand and Salimpour, 2007) for more general flow configurations.  studied numerically the turbulent flow inside a helical coiled tube. They mentioned that helical pitch and curvature affect the streamlines and the heat transfer.  investigated the laminar forced convection in helical coiled tubes, heat transfer and pressure losses increase as the curvature ratio of the helical coiled tubes increases. Jayakumar et al. (2008) studied numerically and experimentally the turbulent flow inside helical coils. The authors proposed a correlation of Nusselt number including different parameters.
As extension of their works Jayakumar et al. (2010) studied the effect of the changes of the thermo-physical properties of the fluid. They have shown that the pitch of the helical coil has little effect on Nusselt number An experimental investigation was carried out by Seban and McLaughlin (1963). Authors proposed a correlation to determine inner Nusselt number in tube coils for laminar and turbulent flow regimes, based on thermo physical properties of fluid at average temperature. Patankar et al. (1974) discussed the effect of Dean Number on friction factor and Nusselt number for developing and fully developed flows of helically coiled pipes. Authors mentioned that the centrifugal forces increase the heat transfer. Rakhsha et al. (2015) investigated experimentally and numerically the turbulent forced convection flow of CuO-water nanofluid. Results indicate that the maximum velocity and Nu number is located near of the outer wall due to the existence of centrifugal force. Naphon and Suwagrai (2007) numerically studied the effect of curvature ratios on Nusselt number and flow structure in spirally coiled tubes. Cioncolini and Santini (2006a); (2006b) investigated the transition from laminar to turbulent flow in helically coiled tubes for different curvature ratio.
This work intends to reveal numerically some features that are not obtained in previous researches, by focusing on the heat transfer and flow characteristics inside a helical coiled triangular cross sectioned tube, for different Reynolds numbers, curvatures ratio, and pitch. The flow structure and the distribution of temperature under different flow configurations are provided respectively in the form of streamlines and iso-surfaces.
To validate results, a comparison with results of circular cross sectioned helical tube established by other authors is done. Then a Comparison between the present numerical data with the previous works with circular cross-sectioned helical tubes to evaluate the thermal performance of such configuration. Fig. 1 shows a helical triangular sectioned coiled tube and the unstructured grid. The geometric parameters include the inner triangular cross section side, the curvature radius of the coil R, the coil pitch Pi,

Geometry, mathematical model and numerical method
The curvature ratio d is defined as = ⁄ , and the dimensionless pitch is defined as = 2 ⁄ . The Reynolds number Re, and Nusselt number Nu are defined as follows: = = ℎ ⁄ ⁄ (1) The flow inside the helical coiled tube is considered to be steady and constant thermal properties are assumed. To simulate the turbulent flow and heat transfer, the k-ɛ standard turbulence model is used.
The steady three-dimensional differential equations governing the phenomenon can be written as follows: Continuity equation: = 0 Momentum equation: The bulk temperature, heat transfer rate, local Nusselt number and average Nusselt number are respectively given by: To represent results, the dimensionless temperature and velocity are defied as:

Results and discussions
The effect of different parameters on the turbulent flow forced convective heat transfer and flow developments characteristics of water inside a helical triangular sectioned coiled tube is demonstrated. Results of the numerical simulations are presented, in term of Nusselt number, streamlines, velocity field and temperature field.

Conclusion
Three-dimensional turbulent flow and heat transfer in a helical triangular cross sectioned coiled tube have been investigated in this paper. The numerical computations show the developments and distributions of heat transfer and flow fields in the tube. These profiles are altered by the effect of curvature inducing the centrifugal forces.
The effects of various flow and geometric parameters on flow, temperature field and heat transfer were studied and. The most important results can be summarized as -The increase of Re number affect the structure of dimensionless velocity and temperature by moving the maximum velocity point toward the outer wall corner and makes the outer wall gradients more severe..
-The increase of curvature ratio generates higher centrifugal forces which cause the displacement of dimensionless temperature and dimensionless velocity closer to the outer wall.
-The increase of the curvature ratio provokes an intensification of gradient of temperature and velocity near of the walls.
-There is no sensitive modification of the structure by changing the Pitch number -The heat transfer using an ordinary circular cross section is found to be more important.