# Numerical Study of Heat Transfer Enhancement for Laminar Nanofluids Flow
## 1 Introduction  
Heat transfer is an essential component in nearly all industrial processes [1; 2; 3; 4; 5]. Consequences of improper heat transfer include nonreproducible processing conditions and lower product quality. Straight tube heat exchangers are the most common type of heat exchanger used in industrial processes due to ease of manufacturing and lower cost [1]. There are several experimental works available in the literature that study forced convective heat transfer in nanofluids as it continues to be a subject of growing importance in many applications [2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19]. A straight tube heat exchanger with laminar flow condition has a lower heat transfer coefficient (HTC) as compared to turbulent flow conditions. Conventional heat transfer fluids such as water, ethylene glycol, and engine oil have relatively low thermal conductivity values, which thus limit the heat transfer rates. The heat transfer performance can be enhanced either by geometry perturbation or by the improvement of the fluid properties. The nanofluids are considered the next-generation heat transfer fluids because of the new possibilities (i.e., more heat transfer surface between particles and fluids, reduced pumping power to achieve equivalent heat transfer intensification, etc.) compared to pure liquids. The term nanofluids refers to a two-phase mixture composed of a continuous phase, usually a saturated liquid, and a dispersed phase constituted of extremely fine metallic particles of a size below 100 nm called nanoparticles. It has been shown that the thermal properties of a nanofluid appear to be higher than those of the base fluid. Hence, nanofluids appear to be an interesting alternative for advanced thermal applicationsfor microscale and nanoscale heat transfer. Alumina oxide nanoparticles (Al\({}_{2}\)O\({}_{3}\)) has been widely used for both experimental and numerical work [20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30]. [PERSON] and [PERSON] [20] developed a series of experiments using Al\({}_{2}\)O\({}_{3}\)-water nanofluids in a circular tube. They observed that the local HTC was enhanced by 47% using Al\({}_{2}\)O\({}_{3}\) nanoparticles for \(\phi_{b}\) = 1.6%, in the laminar flow regime. [PERSON] et al. [21] investigated Al\({}_{2}\)O\({}_{3}\)-water and Al\({}_{2}\)O\({}_{3}\)-ethylene glycol under constant heat flux boundary condition. The reported results show a 63% enhancement in HTC for \(\phi_{b}\) = 7.5%. [PERSON] et al. [22] studied the laminar convective heat transfer of CuO-water and Al\({}_{2}\)O\({}_{3}\)-water nanofluids flow in the straight tube and reported that the HTC increases with an increase in particle loading and a decrease in the particle size. The HTC was augmented by 40% for Al\({}_{2}\)O\({}_{3}\)-water at \(\phi_{b}\) = 2.5%. [PERSON] et al. [23] conducted experiments using an aqueous solution of Al\({}_{2}\)O\({}_{3}\)-water in the developing region of a pipe flow to calculate the HTC considering the influence of particle size. The experimental results showed a 25% HTC enhancement for a 45-nm particle size and 11% for a 150-nm particle size. It was concluded that heat transfer enhancement was not only due to the intensification in thermal conductivity but also because of the effects of particle migration and thermal dispersion. [PERSON] et al. [24] measured the pressure drop and convective heat transfer of water-based Al\({}_{2}\)O\({}_{3}\) nanofluids flowing through a uniformly heated circular tube in the fully developed laminar flow regime. The experimental results showed that the HTC increases up to 8%, at \(\phi_{b}\) = 0.3% as compared to water. [PERSON] et al. [25] performed simulations to investigate the heat transfer characteristics of water-based Al\({}_{2}\)O\({}_{3}\) nanofluid with \(\phi_{b}\) = 0.5%-2.5%, in a circular tube under constant heat flux and laminar flow conditions. It was reported that HTC enhanced marginally by 6% at \(\phi_{b}\) = 2.5%, as compared to the water. [PERSON] et al.