**1. Introduction**

Currently, energy saving in thermal systems has grabbed considerable attention to reduce the heat losses and improve the heat transfer performance [1]. Due to restrictions on the further improvement in the thermophysical properties of conventional working fluids, the research trend is drastically shifting towards nanofluids applications in heat transfer systems [2]. Numerous studies were reported on heat transfer applications of nanofluids in the thermal systems such as tubes.

Firoozi et al. have conducted a numerical study to investigate the heat transfer and flow characteristics of Al2O3/water nanofluid flowing through tubes incorporated with various dimple configurations [3]. Ledari et al. have investigated the heat transfer and friction factor characteristics of oil based CuO and Fe3O<sup>4</sup> nanofluids flowing through the U-tube under the influence of various mass concentrations, flow rates and inclination angles [4]. Chaurasia and Sarviya have conducted experimental and numerical studies to analyze the thermal hydraulic and entropy generation performances of nanofluid flowing through helical screw insert tube with single and double strips [5]. Ying et al. have concluded that Al2O3/water nanofluid with 0.063% mass concentration shows improvement in heat transfer coefficient and Nusselt number by 7.29% and 6.90%, respectively

**Citation:** Garud, K.S.; Lee, M.-Y. Numerical Investigations on Heat Transfer Characteristics of Single Particle and Hybrid Nanofluids in Uniformly Heated Tube. *Symmetry* **2021**, *13*, 876. https://doi.org/ 10.3390/sym13050876

Academic Editor: Mikhail Sheremet

Received: 21 April 2021 Accepted: 12 May 2021 Published: 14 May 2021

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under the cosine heat flux condition and that by 7.25% and 6.85%, respectively under the Gaussian-cosine heat flux condition [6]. Saedodin et al. have compared the heat transfer performances of SiO2, Al2O3, CuO and TiO<sup>2</sup> nanofluids flowing through the straight tube with twisted turbulators [7]. Kristiawan et al. have investigated the thermal and friction factor characteristics of helical microfin tube comprises of TiO2/water nanofluid with various volume concentrations [8]. Tiwari et al. have compared thermal characteristics of triple tube heat exchanger with porous plate, twisted tape and rib type inserts using WO3/water nanofluid [9]. Shahsavar et al. have proposed PVT system with rifled serpentine tube comprises of three ribs and six ribs as the replacement of plain serpentine tube [10]. Mukherjee et al. have presented 94% enhancement in forced convective flow boiling heat transfer of Al2O3/water nanofluid flowing through a horizontal tube compared to water [11]. Heyhat et al. have analyzed the heat transfer and pressure drop characteristics of SiO2/water nanofluid flowing through a conically coiled tube considering the effects of volume concentrations, cone angle and cone pitch [12]. Ho et al. have experimentally and numerically explored the cooling performance characteristics of Al2O3/water nanofluid flowing through a copper tube under constant heat flux condition [13]. Sun et al. have compared the convective heat transfer and flow characteristics of smooth and inner grooved copper tubes considering flow of Fe2O3/water nanofluid [14]. Behzadnia et al. have proposed an optimum geometry of rectangular corrugated tube to maximize the heat transfer efficiency using Al2O3/water nanofluid [15]. Kaood et al. have investigated the thermal, hydraulic and energy performances of Al2O3/water and SiO2/water nanofluids flowing through a corrugated tube with curved ribs, rectangular, triangular and trapezoidal geometries [16]. Safaei et al. have numerically investigated the influences of volume fraction, particle size and velocity on pressure and friction factor of Cu/water nanofluid flow inside a pipe bend [17]. Qureshi et al. have investigated the heat transfer and entropy characteristics of Williamson nanofluid based on magnetohydrodynamics [18].

Yildirim et al. have proved that SiO<sup>2</sup> and Cu based mono and hybrid nanofluids show 15% better thermal performance compared with water for U-tube incorporated in an evacuated tube solar collector [19]. Saleh and Sundar have presented improvement in the thermal performance factor, Nusselt number, frictional entropy generation, friction factor and exergy efficiency by 14.19%, 19.67%, 210.6%, 15.11% and 17.54%, respectively and 22.93% decrease in the thermal entropy generation for Fe3O4/nanodiamond nanofluid compared to base fluid for circular tube [20]. Ramadhan et al. have shown the behavior of Nusselt number and friction factor of TiO2/SiO<sup>2</sup> nanofluid flowing through a plain tube for various Reynolds number and volume concentrations of nanofluid [21]. Han et al. have investigated the heat transfer performances of n-decane-ZnO nanofluid which is pressurized below supercritical pressure and flowing through a horizontal tube. The heat transfer and Nusselt number of n-decane-ZnO nanofluid have increased 20% under a supercritical pressure [22]. Akbar et al. have concluded that the hybrid nanofluid of alumina and titanium with low volume concentrations presents 30% enhanced heat transfer compared to water for a horizontal heated tube [23]. Azmi et al. have studied the effect of various composition ratios of TiO2/SiO<sup>2</sup> hybrid nanofluid on thermal-hydraulic performance of flow in a tube with wire coils [24]. Moldoveanu et al. have experimentally investigated the thermal conductivity of Al2O3/SiO<sup>2</sup> hybrid nanofluid under the influence of temperature and volume fraction [25]. Yang et al. have concluded that Al2O3/TiO<sup>2</sup> hybrid nanofluid exhibits superior Nusselt number, friction factor and performance evaluation criteria compared to Al2O3/ZrO<sup>2</sup> hybrid nanofluid for a parallel channel flow under the same pumping power [26]. Adriana has presented the enhancement of 12% in thermal conductivity of hybrid nanofluid and develop the Nusselt number correlation in terms of Reynolds number, Prandtl number and volume fraction [27].

There are numerous studies in the open literature which show the suitability of single particle nanofluids in heat transfer applications. The research work in heat transfer enhancement using hybrid nanofluids is comparatively less. Specifically, in the field of circular tubes used for solar receiver/collectors and multitube heat exchanger, the

investigations on the trade-off comparison between heat transfer characteristics considering different compositions of hybrid nanoparticles is not explored detailly and compared with single particle nanofluid and conventional working fluid results. There are very few studies which present the comprehensive comparison of conventional working fluid, single particle, and hybrid nanofluids based on heat transfer characteristics considering the effect of Reynolds number, volume fraction and composition of hybrid nanoparticles. The objective of the present study is to compare heat transfer coefficient, Nusselt number, pressure drop, friction factor and performance evaluation criteria as heat transfer characteristics for water, Al2O<sup>3</sup> and Al2O3/Cu nanofluids in a plain straight tube under symmetrical and uniform heat flux condition. The comparison is carried out for various Reynolds number, volume fractions and compositions of Al2O3/Cu nanoparticles. The novelty of the present work is to summarize the effects on heat transfer characteristics of hybrid nanofluid by mixing two nanoparticles, one with higher stability and lower thermal conductivity (Al2O3) and other one with lower stability and higher thermal conductivity (Cu) for different compositions of both nanoparticles. In addition, these results could give a guideline on how much propositions of both nanoparticles could be mixed in hybrid nanofluid to achieve the effective balance between heat transfer and pressure drop.
