Integral methods of calculation of heat transfer and drag under conditions of turbulent pipe flow of liquid of variable properties: Steady-state and quasi-steady-state flows in a round pipe with constant temperature on the wall

An integral method is suggested for the calculation of heat transfer and drag under conditions of flow of dropping liquid and gas in a pipe with constant wall temperature. It is found that the kind of thermal conditions on the wall (T _wall = const or q _wall = const) has insignificant effect on the Nusselt number and coefficient of friction drag for a steady-state flow of dropping liquid of variable viscosity. For a quasi-steady-state pulsating flow of dropping liquid, the thermal boundary conditions have an appreciable effect on the Nusselt number alone; in so doing, the degree of this effect increases with the oscillation amplitude and hardly depends on the temperature factor. For steady-state and quasi-steady-state flows of gas at high temperature factors, the values of heat transfer and drag at T _wall = const differ significantly from those at q _wall = const.     

Integral methods of calculation of heat transfer and drag under conditions of turbulent pipe flow of liquid of variable properties: Steady-state and quasi-steady-state flows in a round pipe with constant density of heat flux to the wall

Integral relations are derived for the calculation of the Nusselt number and coefficients of hydraulic drag and friction drag under conditions of pipe flow of dropping liquid and gas of temperature-dependent physical properties. In the limiting case of steady-state flow of liquid of constant properties, the expression for the Nusselt number transforms to the well-known Lyon integral. The results of calculation of heat transfer and drag by an integral method are compared with more exact results obtained using the numerical solution of the set of differential equations of convective heat transfer. An inference is made about the conditions under which integral methods may be employed. An algorithm is developed for the calculation by an integral method of heat transfer and drag under conditions of quasi-steady-state pulsating flow. It is demonstrated that the flow rate oscillations superposed on the flow in the pipe enhance the effect of the variability of the properties on heat transfer, and for gas on friction drag. For a dropping liquid under conditions of pulsating flow, the friction drag depends less significantly on the variability of the properties (viscosity) than in the case of steady-state flow. The degree of manifestation of the effects identified above is the higher, the higher the oscillation amplitude and the lower the value of the Reynolds number of averaged flow.     

The calculation of heat transfer and resistance under conditions of stabilized turbulent pipe flow of electrically conducting liquid in longitudinal magnetic field

The model of turbulence, developed previously for a flow in the field of mass forces (buoyancy, Coriolis) and for an unsteady flow, is applied to the case of liquid flow in magnetic field. The model describes the suppression of turbulence by the magnetic field and the laminarization of turbulent (at the pipe inlet) flow. The calculation results agree well with the experimental data on heat transfer and resistance obtained in the region of stabilized flow and heat transfer.     

Hydrodynamics and heat transfer in turbulent pipe flow of liquid under conditions of monotonic time variation of the flow rate

The available experimental and theoretical studies of hydrodynamics and heat transfer in turbulent pipe flow of liquid under conditions of monotonic increase or decrease of the flow rate are reviewed and analyzed. The reason is found why the effect of hydrodynamic nonstationarity on heat transfer and skin friction coefficient turns out to be different from that in the case of laminar flow. The differences in this effect on heat transfer and drag are treated. The experimentally observed effects are reproduced most accurately when simulated on the basis of equations for turbulent stresses and heat fluxes.__________Translated from Teplofizika Vysokikh Temperatur, Vol. 43, No. 2, 2005, pp. 212–222.Original Russian Text Copyright © 2005 by E. P. Valueva.     

Numerical evaluation of the heat transfer and the friction drag in a pipe with a turbulent flow of a gas with variable physical properties

The temperature field and the velocity field as well as the local coefficients of heat transfer and friction are determined in the entrance segment of a pipe where a turbulent flow of a gas with variable physical properties stabilizes thermally.Translated from Inzhenerno-Fizteheskii Zhurnal, Vol. 24, No. 4, pp. 730–734, April, 1973.     

Investigation of turbulent heat transfer and nanofluid flow in a double pipe heat exchanger

In present study, heat transfer and turbulent flow of water/alumina nanofluid in a parallel as well as counter flow double pipe heat exchanger have been investigated. The governing equations have been solved using an in-house FORTRAN code, based on finite volume method. Single-phase and standard k-ε models have been used for nanofluid and turbulent modeling, respectively. The internal fluid has been considered as hot fluid (nanofluid) and the external fluid, cold fluid (base fluid). The effects of nanoparticles volume fraction, flow direction and Reynolds number on base fluid, nanofluid and wall temperatures, thermal efficiency, Nusselt number and convection heat transfer coefficient have been studied. The results indicated that increasing the nanoparticles volume fraction or Reynolds number causes enhancement of Nusselt number and convection heat transfer coefficient. Maximum rate of average Nusselt number and thermal efficiency enhancement are 32.7% and 30%, respectively. Also, by nanoparticles volume fraction increment, the outlet temperature of fluid and wall temperature increase. Study the minimum temperature in the solid wall of heat exchangers, it can be observed that the minimum temperature in counter flow has significantly reduced, compared to parallel flow. However, by increasing Reynolds number, the slope of thermal efficiency enhancement of heat exchanger gradually tends to a constant amount. This behavior is more obvious in parallel flow heat exchangers. Therefore, using of counter flow heat exchangers is recommended in higher Reynolds numbers.     

Effect of variability of physical properties on heat transfer in the turbulent pipe flow of gases

The effect of variability of physical properties on heat transfer in the turbulent flow of different gases is studied on the basis of the limiting heat-transfer law.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 50, No. 4, pp. 533–535, April, 1986.     

Calculating drag and heat transfer in viscous,quasistable pipe flow of supercritical helium

An integral method allowing for thermal acceleration of the flow is used to obtain data on drag and heat transfer in the laminar flow of helium at supercritical pressure in a uniformly heated circular pipe.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 44, No. 3, pp. 373–379, March, 1983.     

Prediction of friction and heat transfer for viscoelastic fluids in turbulent pipe flow

Experimental measurements of the friction factor and the dimensionless heat-transfer j-factor were carried out for the turbulent pipe flow of viscoelastic aqueous solutions of polyacrylamide. The studies covered a wide range of variables including polymer concentration, polymer and solvent chemistry, pipe diameter, and flow rate. Degradation effects were also studied. It is concluded that the friction factor and the dimensionless heat transfer are functions only of the Reynolds number, the Weissenberg number, and the dimensionless distance, provided that the rheology of the flowing fluid is used.Nomenclature cp Specific heat of fluid, J · kg^–1 · K^–1 - d Diameter of tube, m - f Fanning friction factor, _w/(V²/2) - h Convective heat-transfer coefficient, q _w(T _w{T _b), W · m^–2 · K^–1 - k Thermal conductivity of fluid, W · m^–1 · K^–1 - j _H Heat-transfer j-factor, StPr _a ^2/3 - L _e Entrance length, m - Nu Nusselt number, hd/k - Pr _a Prandtl number based on apparent viscosity at the wall, c _p/k - q _w Heat flux at the wall, W · m^–2 - Re _a Reynolds number based on apparent viscosity at the wall, Vd/ - St Stanton number, Nu/(Re _a Pr _a) - T Temperature, K - T _b Bulk temperature of fluid, K - T _w Inside-wall temperature, K - V Average velocity, m · s^–1 - Ws Weissenberg number, V/d - x Axial coordinate, m Greek symbols g Shear rate, s^–1 - Apparent viscosity evaluated at the wall, P⁵ - ₀ Zero shear-rate viscosity, P⁵ - Apparent viscosity at infinite shear rate, P⁵ - Characteristic time of fluid, s - Density of fluid, kg · m^–3 - _w Wall shear stress, N · m^–2 Invited paper presented at the Ninth Symposium on Thermophysical Properties, June 24–27, 1985, Boulder, Colorado, U.S.A.     

Analogy between turbulent momentum and heat transfer under complex conditions

The analogy between turbulent momentum and heat transfer under complex conditions, i.e., under the action of several perturbing factors on the flow, is extended for a broad range of variation of the Prandtl number.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 49, No. 3, pp. 406–413, September, 1985.     

Heat transfer under conditions of turbulent pipe flow of electrically conducting liquid in longitudinal magnetic field in the region of hydrodynamic stabilization

Numerical simulation is performed of heat transfer under conditions of turbulent pipe flow in the vicinity of entry to longitudinal magnetic field. Use is made of the model of turbulence which was previously employed for performing calculations in the region of stabilized flow and heat transfer. The model describes the suppression of turbulence by the magnetic field and the laminarization of turbulent (at the pipe inlet) flow. The calculation results agree well with the experimental data on heat transfer and temperature profiles in the initial thermal region. The effect made on heat transfer by Joule heat release from electric currents caused by turbulent fluctuations is investigated.     

Multicomponent heat and mass transfer during the turbulent flow of liquid films

A method is proposed for calculating the parameters of simultaneous heat and mass transfer in turbulent multicomponent liquid films which is based on solving the system of differential equations for convective heat conduction and multicomponent convective diffusion.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 57, No. 1, pp. 16–22, July, 1989.     

Hydrodynamics and heat transfer in pulsating turbulent flow of gas in a heated pipe

The paper deals with the investigation of the effect produced by the dependence of the physical properties on temperature and flow rate fluctuations on heat transfer and drag under conditions of turbulent pipe flow of gas. The method of finite differences is used to solve numerically a set of equations of motion, continuity, and energy written in a narrow channel approximation. A model of turbulence is used which takes into account the effect of the variability of the properties and of the nonstationarity of flow on turbulent transfer. In the particular case of steady-state flow of gas being heated, the calculation results fit well the available experimental data. It is found that the heat transfer depends on the heating rate more significantly than the friction drag. In the case of pulsating flow, the part of hydraulic drag is estimated which is spent for the variation of longitudinal velocity along the pipe and is due to the thermal acceleration of gas. It is demonstrated that the main features of pulsating flow, which were previously investigated for a liquid of constant properties and for a dropping liquid of variable viscosity, are retained for the gas being heated as well. Comparison is made for the gas and dropping liquid of the effect made by various process parameters such as the Reynolds, Stokes, and Prandtl numbers, the heating rate, and the form of thermal condition on the wall on the period average Nusselt number and coefficient of friction drag.     

Numerical investigation of heat transfer under laminarization conditions of turbulent flows

Based on the mathematical boundary layer model, a numerical investigation of heat transfer is carried out for a wide range of turbulent Reynolds numbers in nozzles of experimental devices under laminarization conditions of turbulent flows.Translated from Inzhenerno-fizicheskii Zhurnal, Vol. 61, No. 2, pp. 223–229, August, 1991.     

垂直地埋管换热器传热模型及实用分析

介绍了垂直埋管地源热泵地下换热器的传热模型,给出一种适用于工程应用的近似计算方法,并就工程实践应用验证了其实用性。     

A steady viscous-thermogravitational flow of capillary liquid and heat transfer in a vertical cavity under asymmetric heat conditions

The problem of joint forced and free laminar convection and heat transfer for liquid with a variable viscosity under a linear temperature distribution between surfaces of a vertical two-dimensional channel is solved analytically. The dependences obtained manifest a strong difference (upon a relatively small variation in viscosity) of the distributions of velocity, friction drag coefficient, and heat transfer from the case of the full Boussinesq approximation while solving problems of mixed convection.     

Experimental investigation of heat transfer under conditions of laminarization of turbulent flows

The results of an experimental investigation of the temperature in model nozzles of an experimental setup under conditions of laminarization of turbulent flows are presented.Translated from Inzhenerno-fizicheskii Zhurnal, Vol. 60, No. 2, pp. 181–185, February, 1991.     

Effect of variability of physical properties of a gas on turbulent flow and heat transfer in a pipe with permeable walls

We have calculated turbulent quasideveloped flow and heat transfer in a circular pipe, taking account of the temperature dependence of the physical properties of the gas when there is injection through porous walls.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 50, No. 2, pp. 195–200, February, 1986.     

Pseudoboiling and heat transfer in a turbulent flow

Experimental data characterizing the onset of pseudoboiling in relation to flow rate, pressure, and tube diameter are presented for diisopropylcyclohexane (DICH).