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

Abstract

The article examines the problem of correct, accurate calculation and optimization of the choice of heat exchange equipment when using nanofluid heat carriers for heat treatment of liquid food products using milk as an example. To solve this problem, the motion of a metal nanoparticle in a turbulent flow of the main coolant was simulated using the methods of similarity theory, taking into account the action of surface forces in the laminar boundary layer. New formulas are obtained for a qualitative assessment of the average thickness of the laminar boundary layer that appears around a turbulently moving metal nanoparticle. A number of qualitative correlations with other literature sources that explain the behavior of nanoparticles in a turbulent liquid medium are shown. A new approach to heat transfer processes is considered taking into account the theory of J. Boussinesq, which gives an idea of turbulent viscosity and thermal conductivity, as well as a comparison of the resistance forces to the surface forces. The physical meaning of the previously obtained by us new similarity numbers Bl and Blturb. and their application in our new numerical equation for calculating heat exchangers is considered, and a new express method for evaluating the efficiency of using nanofluid heat carriers is proposed. The proposed method of express calculation shows that the mixture H2O + EG (60:40) improves the heat exchange properties of water by + 12.86%, and the mixture (H2O + EG (60:40) + 1.5% TiO2) and (milk + 0.5% pumpkin seed oil) - by + 16.75%, which corresponds to the experiments and our calculations, and the well-known express method based on classical numerical equations shows a deterioration by - 4.5% and, accordingly, by – 1.2%.

Improvement of the Method of Calculating Heat Transfer Coefficients Using Glycols Taking into Account Surface Forces of Heat Carriers

“…Our studies in papers, 3,4 cited above, show that the dominant factor -the surface energy of the liquid coolant is not included in the power equation, and therefore Eq. ( 1) is solved empirically, where the power indicators X, Y, and the constant B are determined experimentally.…”

“…Equations of type (1) lose their universality. Numerical equations for calculating heat transfer using TiO 2 nanoparticles with a classical structure (1) were compactly collected by us in works, 4,[10][11][12] and a corresponding analysis was also carried out. As one can see, these equations are far from analytical, from universal and have a specifically empirical character.…”

“…Equations of type (1) lose their universality. In works, 4,10 as well as in many other sources, dependences for determining the viscosity and thermal conductivity of nanofluids are given, for example, for the base fluid -water and for the base fluid -ethylene and propylene glycols. These equations are also not universal, as they also require numerous additional experiments for each specific heat carrier.…”

“…A similar situation is observed when using nanofluids as heat carriers. A corresponding force analysis was carried out by us in the literature, 4 which showed that surface forces also dominate the LBL that occurs around a nanoparticle during its turbulent motion in a mostly liquid medium. Meanwhile, the Reynolds number, which is present in almost all numerical empirical equations of heat transfer and is actually in the maximum degree (0.6-0.8), i.e., it is assumed that the influence of frictional forces in such systems is maximal.…”

“…A paradox appears. Using a simple comparison of the similarity numbers in LBL, 3,4 we get that the surface forces dominate, but they are not taken into account anywhere because the classical Nusselt, Reynolds and Prandtl similarity numbers do not account for them. To date, in such systems, during the movement of liquid in pipelines or channels to determine heat transfer coefficients, classical similarity numbers and the structure of numerical equations look like this (1):…”