**1. Introduction**

Nanofluids are one of the techniques for heat transfer enhancement [1,2]. The goal is obvious: to reduce the heat transfer surface area, thus reducing the consumption of materials and energy necessary for the manufacture of heat exchangers. However, in order for nanofluids to find practical applications, several problems must be solved. The first and foremost is to provide engineers with accurate and reliable methods to calculate heat transfer coefficients and friction factors. The second problem is the thermophysical properties of nanofluids, the determination of which is not easy [3,4]. The third problem that has so far held back the practical application of nanofluids is their stability [5,6]. Due to the costs of experimental research and the long design and construction time of measuring stands, as well as tedious measurements, numerical methods are an indispensable approach that allow for quick and precise assessment of new technologies. However, it should be remembered that each numerical work should be verified experimentally or, if possible, by an analytical solution. There are two main approaches in the modeling of nanofluid flows, e.g., [7–11]. Due to the size of nanoparticles (similar to the dimensions of liquid molecules), it is assumed that the resulting mixture forms a homogeneous liquid, the properties of which result from the properties of the base liquid and solid particles. Hence, the classical methods of continuum mechanics are used to solve the set of governing equations. In the second approach, a nanofluid is treated as two phase solid-liquid mixture.

This paper presents state of the art in the field of numerical modeling of the forced convection of nanofluids in straight, smooth, round tubes.
