Modeling the interaction of coolant flows at the liquid-solid boundary with allowance for the laminar boundary layer

Abstract

INTRODUKTIONIn the current energy crisis, the issue of energy efficiency of heat exchange processes and equipment for their provision in food, chemical, pharmaceutical, processing and other technologies becomes decisive. To increase the heat transfer coefficients in heat exchangers, various methods are used, in particular, the modification of the structural elements of boilers and other equipment [1], the increase in the turbulence of the refrigerant flows [2], the use of liquids with the optimal concentration of surfactants (SAS). For example, the maximum rate of heat exchange was observed when a nonionic surfactant was added to water [3]. The authors of [3] believed that the maximum rate of heat exchange in the first place may be due to the fact that this additive has a minimum capacity for the formation of foam. In addition, it is known that surfaceactive substances significantly, approximately 2 times, reduce the coefficients of surface tension of water and other liquids. PROBLEM FORMULATIONAfter analyzing the literature sources, we came to the conclusion that the rate of heat exchange in liquid refrigerants through the laminar boundary layer (LBL) depends on the following main factors: -laminar flow is responsible for the turbulent flow, but is less energy-efficient [2,4]; -LBL, namely its average thickness is responsible for the total thermal resistance of the system [5,6]; -the thermal resistance depends on the coefficient of surface tension of the refrigerant [7]; -the intensity of heat exchange depends on the hydrophilicity or hydrophobicity of the wetting surface [8];Based on the foregoing, the purpose of this article was to offer a model for the interaction of refrigerants with a separating solid wall, which will cover all the above factors as much as possible. : 0392-8764 Vol. 35, No. 3, September 2017, pp. 678-682 DOI: 10.18280 INTERNATIONAL JOURNAL OF HEAT AND TECHNOLOGY ISSN ABSTRACTThe forces acting on the elementary volume of liquid in the pipeline in the laminar boundary layer are considered. A new dimensionless complex the surface number and the concept of the turbulence coefficient laminar boundary layer is proposed. The calculation of Froude, Euler numbers, the inverse Reynolds number and the surface number in laminar boundary layer for water under normal conditions is given. It is shown that the Froude number and the inverse Reynolds number are 4-5 orders of magnitude smaller than the surface number and Euler number in laminar boundary layer, which allows neglecting the forces of gravitation and friction in these conditions. Equations are proposed for calculating the average thickness of laminar boundary layer. The dependence of the surface number on the coefficient of surface tension of the refrigerant is obtained. It is shown that a decrease in the surface tension coefficient minimizes the average thickness of the laminar boundary layers in the wall system of the pipeline and liquid and increases the average velocities of the coolant flows in these layers, as a result of which such a s...

The Laws of Distribution of the Values of Turbulent Thermo-physical Characteristics in the Volume of the Flows of Heat Carriers Taking into Account the Surface Forces

“…In the work [9], we proposed the same concept as in the works [5][6][7], only for the surface of a metal and a moving fluid. This is the concept of the movement of a fluid near a solid metal wall (coolant flow -tube walls), taking into account surface tension forces, the values of which in an LBL are commensurate with pressure forces and significantly exceed gravity, friction and inertia.…”

“…In the work [9], using the example of two model liquids (water and milk), we proposed a new method of thermal and hydraulic calculations, using the example of a shell-and-tube heat exchanger, taking into account the thermal conductivities of laminar and turbulent zones of coolant flows, based on the transfer of velocity and heat pulses in the radial direction of the pipeline cross-section. Based on the work of Reichardt and Ludwig [1,3], and based on the fact that the turbulent Prandl number in the transitional zone of the LBL is unity, we used this to obtain new formulas (3), (4) and (5) calculation of the transitional viscosity and thermal conductivity in the transitional zones of LBLs, as well as to calculate the dimensionless number denoted by us Bl [11].…”

Specific features of heat exchangers calculation considering the laminar boundary layer, the transitional and turbulent thermal conductivity of heat carriers

“…We argue [5] (2017) that a strong field of surface tension forces acts on the solid-liquid interface, which keeps fluid flow with the formation of LBL. Based on the forces analysis in the elementary volume of liquid in LBL, we derived a formula (1) for calculating the average thickness LBL, where the coefficient of surface tension of the coolant and the hydrophilicity of the wetting surface appear [5]. It is noteworthy that many researchers in their works by various methods influence the behavior of LBL in heat exchange systems, in particular in heat exchangers, in order to reduce their total thermal resistance.…”

“…Proceeding from the fact that the thermal resistance of the zones depends on the corresponding thermal conductivities and average thicknesses of these zones, we can write the equation of the overall heat transfer coefficient in the form (5). Instead of the convection coefficients hh and hc in the scheme and in formula (5), we used the thermal conductivites and average thickness of all the listed heat exchange zones (Figure 1).…”

“…-check the efficiency of the previously proposed formula for calculating the average thickness of LBL in the pipes and shell of the shell-and-tube heat exchanger [5];…”