A New Universal Numerical Equation and a New Method for Calculating Heat-Exchange Equipment Using Nanofluids

Abstract

This article analyzes the vast material of works devoted to the use of nanofluids in heat exchange equipment. It is proved that the use of the classical theories and equations for calculating the viscosities and thermal conductivities of nanofluids is not correct, since it does not coincide with the experimental results of most independent authors. A model of the chaotic motion of a nanoparticle is presented taking into account surface tension forces in a liquid coolant. The experimental results of the work of Malaysian and Iran authors on the effect of TiO2 nanoparticles with a concentration of 0.5%; 1.0% and 1.5% in the main liquid solution of ethylene glycol (EG) in water in a volume ratio of 40:60% in terms of heat transfer coefficient are compared with our theoretical studies. The results of the experiments presented in: an increase in heat transfer coefficients by 9.72%, 22.75%, 28.92% for 1.5% volume concentration of TiO2 nanoparticles at a coolant temperature of 30℃, 50℃, 70℃, respectively. Our theoretical result: increase in the obtained heat transfer coefficients by 9.79%, 22.22%, 29.09% according to our formulas (9, 10, 15) for calculating turbulent viscosities and thermal conductivities, which takes into account the effect of surface tension forces on the total flow of nanofluids in the channels of heat exchange equipment. A new method for calculating heat exchange equipment using nanofluids is presented, taking into account the action of surface tension forces, as well as predetermining the calculation of turbulent viscosities and thermal conductivity of nanofluids. A theoretical calculations a plate heat exchangers for a technological task performed by classical and new method is presented. Similar results were obtained, which differ by about 0.5 of a percent. The plate heat exchanger was calculated using a new method using TiO2 nanoparticles in water and in a mixture of EG in water in a ratio of 40:60%, as well as when pumpkin vegetable oil was added to milk with the optimal concentration.

Substantiation of a New Calculation and Selection Algorithm of Optimal Heat Exchangers with Nanofluid Heat Carriers Taking into Account Surface Forces

“…The calculation of the complex in paragraph 1 showed that the use of classical numerical equations for calculating heat exchangers using nanofluids at high temperatures (70℃) is not accurate and inherently erroneous. Complex (44 a, b) in Table 4 decreases, which should indicate a decrease in the heat transfer coefficient when using H2O + EG (60:40) + 1.5% TiO2, but the results [36] and our computer analysis [16], indicate an increase.…”

“…However, unfortunately, it was not indicated what kind of force it is, what its nature is [23]? Based on our previous studies [16,[24][25][26], we argue that this resistance force of the base fluid to the movement of the nanoparticle is the interfacial surface tension force at the interface between the solid nanoparticle and the fluid, which depends on hydrophilicity (cosine of the contact angle, cos 0° = 1 and cos 90° = 0), which, in turn, can significantly change its vector and scalar value. Since the action of surface forces is molecular in nature, we argue that this approach has a completely acceptable basis.…”

“…Such calculations using classical empirical equations have lost their versatility and cannot be used for an express assessment of the efficiency of specific nanofluids in specific heat exchange equipment. (4) Pak and Cho, (1998) [4] Experimental study Turbulent flow Al2O3/water nanofluids TiO2/water nanofluids: Gnielinski (1976) [7] Numerical study Fully developed turbulent flow: In our work [16], we proposed to move away from the practice of empirical calculations of heat exchangers with nanofluidic coolants using classical numerical equations based on classical similarity numbers, and to propose a new universal one, in which not the fractional and concentration compositions of nanofluids, but their main thermophysical quantities for turbulent coolant flow (turbulent viscosity and thermal conductivity). We also proposed to consider the flow of a coolant with nanofluids taking into account surface forces [16].…”

“…The well-known classical numerical equations for calculating heat exchange equipment cannot provide reliable calculation and selection of optimal heat exchangers when using nanofluids in chemical, food and other heat technologies, especially at temperatures above 50℃ [16]. This is due to the fact that these numbers contain the thermophysical characteristics (dynamic viscosity and thermal conductivity) of heat transfer fluids in a static (stationary) state.…”

“…This is due to the fact that these numbers contain the thermophysical characteristics (dynamic viscosity and thermal conductivity) of heat transfer fluids in a static (stationary) state. In addition, surface forces are not taken into account [16,[24][25][26]. At the same time, all heat exchange equipment is selected and calculated taking into account the turbulent movement of heat carriers.…”