Convective heat transfer can be enhanced by active as well as passive methods. While the former usually provide better enhancement, it requires additional external forces and/or equipment which can increase the complexity, capital, and operating costs of the system. In contrast, passive heat transfer enhancement can be achieved by changing flow geometry or modifying thermo-physical properties of working fluid. Hence, it is generally a more desirable approach when compared to an active method. In our previous study [1–3] (Sasmito AP, Kurnia JC, Mujumdar AS: Numerical evaluation of transport phenomena in a T-junction micro-reactor with coils of square cross section tubes, submitted), we have shown that coiled tubes provide better heat transfer performance relative to straight tubes under certain conditions. In this study, the potential application of coiled tubes using nanofluids to improve heat transfer performance is investigated.

Coiled tubes have been known as one of the passive heat transfer enhancement techniques in heat and mass transfer applications due to the presence of secondary flows which improve heat and mass transfer rates. They have been widely used in process industries, e.g., heat exchangers and chemical reactors, due to their compact design, high heat transfer rate, and ease of manufacture. Aside from their industrial applications, studies of the transport phenomena in coiled duct have also attracted many attention from engineering researchers. The presence of secondary flows induced by coil curvature and the complex temperature profiles caused by curvature-induced torsion are among significant phenomena which can be observed in coiled tubes. Numerous experimental [4–8] and numerical [1–3, 9–13] investigations on heat transfer and flow characteristics inside coiled tubes have already been reported. Furthermore, reviews on the flow and heat transfer characteristics and potential application of coiled tubes in process industries and heat transfer application can be found in [14, 15].

It is well known that conventional heat transfer fluids including water, oil, and ethylene glycol mixtures have poor heat transfer rate due to their low thermal conductivity. Therefore, over the past decade, extensive research have been conducted to improve thermal conductivity of these fluids by suspending nanoparticles of diverse materials in heat transfer fluids, called nanofluids [16]. Modern technology provides opportunities to process and produce particles below 50 nm. It is also expected that nanofluids should provide not only higher heat transfer rate, but also good stability of the suspension by eliminating possible agglomeration and sedimentation to permit long-term application [17]. To date, several experimental (see for example [18–23]) and numerical (see for example [24–28]) investigations to characterize heat transfer performance of nanofluids have been already reported. Choi et al. [18] showed that addition of small amounts of less than 1% nanoparticles can double the thermal conductivity of working fluids. Vajjha et al. [24] showed that heat transfer rate increases up to 94% by adding 10% Al_{2}O_{3} nanofluid and increase up to around 89% by adding 6% CuO nanofluid. In addition, the comprehensive reference on nanofluids can be found in the book of Das et al. [29], while several reviews of nanofluids are available in the literature [30–42].

It has been shown that coiled tubes geometry and nanofluids can passively enhanced heat transfer performance. Now, to maximize the advantages of the heat transfer enhancement, we propose to combine both techniques simultaneously; i.e., employing the combination of coiled tubes filled with nanofluids. Therefore, the aim of the study presented here is threefold: (i) to investigate the heat transfer performance of various configurations of coils of square tubes, e.g., conical spiral, in-plane spiral, and helical spiral, relative to the straight pipe; (ii) to evaluate simultaneous passive heat transfer enhancement-channel geometry and fluid thermo-physical properties-in coiled tubes filled with nanofluids; (iii) to study the heat performance of two different nanofluids, water-Al_{2}O_{3} and water-CuO, in coiled tubes at various nanoparticle concentrations. The most significant aspect of this study is to determine the potential advantages and limitations of heat transfer enhancement of coiled of square tubes filled with nanofluids and provide design guidelines for their applications through mathematical modeling.

The layout of the article is as follows. First, the mathematical model is introduced; it comprises conservation equations for mass, momentum, and energy. The nanofluid thermo-physical properties are treated as functions of particle volumetric concentration and temperature. The mathematical model is then solved numerically utilizing finite-volume-based CFD software Fluent 6.3.26, the User-Defined Function written in C language is used extensively to capture the nanofluid properties. The model is further validated against experimental data by Anoop et al. [19] in terms of heat transfer performance for both base-fluid and nanofluid. Fluid flow and heat transfer performance of various coiled tube designs filled with nanofluids is evaluated in terms of a figure of Merit Defined later. Parametric studies for particle concentration and nanofluid type are then carried out. Finally, conclusions are drawn and possible extensions of the study are highlighted.