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

Abstract

The sources of the literature are analyzed in the article on the influence of the average thickness of the laminar boundary layer (LBL) on the heat transfer coefficient of the various heat-conducting systems. Different authors at different times established the explicit correlation dependence of the increase in heat transfer coefficients with a decrease in the average thickness of the LBL. The average thickness of the LBL according to the literature data was reduced in the various ways (using electric or magnetic field for the flow of the liquid, using the nanoparticles in the flow and various of the metallic spiral inserts, etc.). Applying the similarity theory and using dimensionless Euler, Froude and Reynolds numbers in the LBL, and also applying a new surface number, we previously derived the formula for the calculation of the average thickness of the LBL, which in this paper is used to the calculation the overall heat transfer coefficient of the shell-and-tube heat exchanger. We brought out new number of the turbulent thermal conductivity in the LBL transitional zone by the dimensional analysis method. The relations have also been obtained for the calculating of the transitional viscosity and of the transitional thermal conductivity in the transitional zone of the LBL. The article provides the examples the calculation of the shell-and-tube heat exchanger using the classical method and the proposed formulas. The calculation of the resistance of the LBL and the turbulent zones of the refrigerant flows is carried out the taking into account the coefficients of the turbulent thermal conductivity, as well as the coefficients of the surface tension of the liquids. We proposed the calculation of the shell-and-tube heat exchanger using of the refrigerant with an optimum concentration of the propylene glycol in the water (47%). The increase of the overall heat transfer coefficient of the heat exchanger is about 10%.

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

“…Based on our works [29][30][31][32][33][34], we concluded that our proposed model of contacting metal surfaces with regard to their the binding energy and surface energy [29][30][31], as well as consideration of the movement of heat-transfer fluids near the metal walls of the heat exchange equipment with taking into account surface forces [32][33][34], has the right to exist. Based on this, we set ourselves the following tasks in this work:…”

“…At the same time, the value 0 1 P CK  reflects the speed of thermal movement at the molecular level, having the dimension m/s, and the value V is the linear speed of movement of the coolant with the nanoparticles at T mode. We also remind that the transitional viscosity of a fluid, the value of which we derived in previous works [33,34], is the viscosity at the interface of LBL and turbulent flow, having dimension (Pa.s) and calculated by formula 3, and dimensionless turbulent number is the ratio of turbulent to transition viscosity (4) In addition, the dimensionless number Bl is (5) [33,34].…”

“…The average diameter of small nanoparticles is actually commensurate with the size of the molecules of the base fluid, and therefore this statement is quite acceptable and justified. However, in this work we attempted to circumvent these warnings, using the concept of turbulent viscosity and thermal conductivity of liquid coolants, which we followed in the calculation and selection of heat exchangers in the works [33,34].…”

“…Based on our works [32][33][34], having written the value of turbulent viscosity in the central part of the coolant flow, we obtain 2:…”

“…number we have derived, we compare turbulent viscosity and transitional viscosity (3). The transitional viscosity of the coolant is substantially higher than the molecular viscosity [33,34]. If we want to compare the turbulent and molecular viscosity, then it must be borne in mind that, in the LBL itself, the viscosity of the fluid decreases from the transitive viscosity to the molecular viscosity.…”