Numerical analysis of heat transfer in unsteady nanofluids in a small pipe with pulse pressure

In the present paper, developing turbulence forced convection flows were numerically investigated by using water-Al2O3 nano-fluid through a circular compact pipe which has 4.5mm diameter. Each model has a steady state and uniform heat flux(UHF) at the wall. The whole numerical experiments were processed under the RPM 100 to 500 and the nano-fluid models were made by the Alumina volume fraction. A single-phase fluid models were defined through nano-fluid physical and thermal properties calculations, Two-phase models(mixture granular model) were processed in 100nm diameter. The results show that comparison of nusselt number and heat transfer rate are improved as the Al2O3 volume fraction increased. All of the numerical flow simulations are processed by the FLUENT. The results show an increase from volume fraction concentration and an increase in heat transfer coefficient with increasing RPM.


Introduction
Heat transfer fluids play an important role in many industries, including power plants, production processes, transportation and electronics, and the heat transfer characteristics of thermal fluids play an important role in the development of energy efficient heat transfer devices. Past improvements have been based on structural changes and the addition of heat transfer areas, vibrations on the surface of the heat, injection or inhalation of fluids and the application of electrons or magnetic fields. These enhancement techniques rarely meet the increase in heat transfer coefficient and, in this connection, there is a strong demand for the development of advanced heat transfer fluids with higher heat transfer properties. Therefore, a number of recent studies on nanofluids for experimental convective heat transfer through circular tubes have been conducted by senior scholars. However, nanofluid research is still in the hot debate and investigation. In addition, research on the pulse pressure has been actively carried out all over the world, and many research results have been published especially in the field of noise vibration. Non-steady pulsating flow phenomena will be generated by internal smoke and reciprocating compressors. The pulsating pressure in the internal combustion engine will be the 2

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The silencer part. The function of this silencer is to reduce the pulsation pressure inside the silencer as well as to reduce the back pressure. Maxwell [1,2] has demonstrated that increasing the volume fraction of solid particles can increase the thermal conductivity of the mixture. The particle diameter currently available for particle manufacturing technology development is smaller than 100 nm, called nano-size. This effort allows the particle mixing fluid to increase the thermal conductivity of the heat transfer fluid by increasing the critical thermal conductivity. In addition, solid nanoparticle colloids are very stable and do not exhibit significant sedimentation under static conditions after weeks or months. In addition, solid colloids float easily when you reduce particle size. Therefore, nanofluidic technology is expected to be suitable for heat transfer fluids. Mohamad and viskanta [3] studied the abnormal natural convection for a low prandtl number of fluids in the cavity, and patterson and Imberger [4] conducted a study on the abnormal natural circulation in a square cavity. Hellims and Churchill [5] numerically studied the natural convection in an unsteady state in a closed vessel. Therefore, this study focuses on the nanofluid only for pulsating pressure in a small tube with a pulse pressure. The purpose of this study is to verify the numerical analysis technique in terms of the fluidity of the nanofluids in a small tube with a pulsating pressure through numerical analysis. The purpose is to secure the data. Fig. 1a shows the actual model of geometry and Fig. 1b is the part of the Two-dimensional Mesh. One of the main purpose of this simulation is trying to understand the near wall behavior of nano-particles, velocity distribution perpendicular to the pipe surface and drag coefficient at the near of pipe wall, so the relatively concentrated mesh in the near wall area is needed. As a result, the mesh has a nonuniform quadratic mesh. The bottom horizontal line is an axis which makes Three-dimensional pipe model at the axisymmetric environment. The upper horizontal line is a wall with Uniform heat flux. The tube consisted with a diameter (D) of 4.5 mm and a length (L) of 1.17 m. Nanofluids is composed of Al2O3 particles and water have the physical properties such as Table.1 [6]. The total flow rate for each fluid model is input at a constant temperature of 293K and the axial velocity is defined as pressure change over time at 100,300,500RPM and the wall surface has a Heat flux of 5000 (w / m2) The single-phase model is investigated for the comparison of mixture model as prescribed. Following equations are representing the mathematical formulation of the single-phase model and of the continuous phase of the mixture model. The exact k-ε equations contain many unknown and unmeasurable term [6][7][8] Energy equation:

Geometry and boundary coundition
The And k-ε equation of represents velocity component in corresponding direction (u i ) , represents component of rate of deformation(E ij ) , represents eddy viscosity(μ t ) (Rate of change of k or ε +Transport of k or ε by convection = Transport of k or ε by diffusion + Rate of production of k or ε -Rate of destruction of k or ε) Conservation of mass : Where is the mass-averaged velocity: and is the mixture density with volume fraction of phase k: Momentum equation for single-phase: Momentum equation for multi-phase: The compression and viscous lose by heat are assumed to be excluded in the energy equation. The source/sink terms S m and S e represent the unitive effects of energy and momentum exchange with base fluid. These are zero value in the single-phase model. Momentum equation of multi-phase are affected by volume fraction ( ), velocity of phase( ), diffusion velocity ( ). The determinations of particle motion are particle mass(m ), cross-sectional area of the particle(A ), drag coefficient(C ), slip velocity( ). The drag force in this study is following Clift et al equation (7) for single rigid spherical particle in a fluid: Numerical approach The computational fluid dynamic code FLUENT 16.1 is employed to solve the present problem. The governing Eqs. (1)-(3) are solved by control volume approach. The algebraic "discretize equations," resulting from spatial inter-fraction process, are sequentially solved throughout the physical domain considered. ANSYS Fluent 16.1 solves the systems resulting from discretization schemes using a 4

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The numerical method. For the convective and diffusive terms, a second order upwind method was used. Pressure and velocity were coupled using Semi Implicit Method for Pressure Linked Equations(SIMPLE) in single-phase. To calculate the pulse pressure, Figure 2. the PISO algorithm was used to calculate the anomalous state as a complete negative solution. The continuity equation and the momentum equation are used to calculate the pressure inside the small tube. The turbulence model is based on the standard model k -ε model which has already proved its engineering validity. The convergence judgment of the residuals was regarded as convergence when the residual value reached 10 or less.

Figure 2. Folw chart of PISO algorithm
As already seen for the SIMPLE algorithm, the steps 4 and 5 can be repeated for a prescribed number of times to correct for non-orthogonality.

Results
In this work a number of numerical simulations have been perfomed to study forced convective heat transfer of Al2O3-water in a circular tube under turbulence flow and results were conducted to employing the single phase and mixture model for φ=1% to 4%, 100to500RPM as q=5000 W⁄m^2 with a constant state. In all cases the size of the spherical particles is 100 nm. Thermal entrance length depends on Prandtl number. [9] So when concentration increases Pr number also increases and consequently, thermal entrance length becomes greater. As shown in Fig. 3 (a), the difference between 0% and 1% seems to be insignificant in the range of 0.1x / Lmm, but the heat transfer rate of 4% Al2O3 is 2 times larger than 0,1% Respectively. Likewise, in figure (b) The transmission rate of 0 and 1% Al2O3 is less than 10, but 4% nanofluids can be seen to have more than twice the Nusselt number. In Fig. 4 (a), unlike 100RPM, the phenomena appearing more than twice as much as 0%, 1% and 4% are not shown in the figure. This phenomenon can be grasped by increasing the internal pressure at 500 RPM. Also, in Fig. (B), the Nusselt number seems to be closer to 1% Al2O3 than 4%. , however, the heat transfer coefficient and the number of nuclei for RPM changes of the same 1% Al2O3 can be confirmed. The heat transfer rate and the number of nunts are significantly lower than those of 300 and 500 RPM . However, at 300 RPM, it can be confirmed that the heat transfer coefficient and the nunner are higher than 500 RPM in the early stage.

Conclusion
Numerical analysis of the heat transfer of the nanofluid in the unsteady state in the small tube into which the pulsating pressure is introduced showed that the effect of the content of Al2O3, which is a nanofluid, was further increased in the low 100 RPM. In addition, it was confirmed that the nanofluids of 0% and 1% compared to 0% and 1% of Al 2 O 3 have a data difference of more than 2 times. In 500 RPM, the difference in content is not significant compared to 100 RPM, but nanofluids with high Al 2 O 3 The heat transfer coefficient and the number of nuns were better. And the increase in the heat 6

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The transfer coefficient of the nanofluid to the RPM change shows better results as the RPM increases. Therefore, nanofluid with high Al2O3 content and high RPM can improve the thermoelectric coefficient and increase the number of nuts. But the CFD should be progressed with constant and transient numerical investigation parallel. Basically, It would be pace with the experiment especially different model scale study. Also,uniform heat flux sample, wall shear stress, body force researches does not include this paper. This compact size model is not usual model on the nano-fluid CFD study so these factors need to be proved.