Application of a Simplified Velocity Profile to the Prediction of Pipe-Flow Heat Transfer

1968 ◽  
Vol 90 (2) ◽  
pp. 191-198 ◽  
Author(s):  
R. D. Haberstroh ◽  
L. V. Baldwin
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Velocity Profile ◽  
Pipe Flow ◽  
Energy Equation ◽  
Momentum Equation ◽  
Turbulent Pipe Flow ◽  
Transfer Coefficients ◽  
Constant Property ◽  
Wide Range

The temperature profiles and heat-transfer coefficients are predicted for fully developed turbulent pipe flow with constant wall heat flux for a wide range of Prandtl and Reynolds numbers. The basis for integrating the energy equation comes from a continuously differentiable velocity profile which fits the physical boundary conditions and is a rigorous (though not necessarily unique) solution of the Reynolds equations. This velocity profile is the semiempirical relation proposed by S. I. Pai, reference [12]. The assumptions are those of steady, incompressible, constant-property, fully developed, turbulent flow of Newtonian fluids in smooth, circular pipes with constant heat flux at the wall. The ratio of the turbulent thermal diffusivity to the turbulent momentum diffusivity is taken to be unity. The thermal quantities are obtained by numerical integration of the energy equation, and they are presented as curves and tables. A compact formula for the Nusselt number is given for a wide range of Reynolds and Prandtl numbers. The results degenerate identically to the case of laminar flow. The heat-transfer calculation requires neither adjustable factors nor data-fitting beyond the empirical constants in the momentum equation; thus this analysis constitutes a heat-transfer prediction to be tested against heat-transfer data.

Progress in the Modeling and Simulation of Flow Boiling Heat Transfer of Binary Fluids Using Advanced Multi-Fluid Modeling Techniques

2012 ◽  
Author(s):  
Vedanth Srinivasan ◽  
Rok Kopun
Keyword(s):  
Heat Transfer ◽  
Mass Transfer ◽  
Heat Flux ◽  
Phase Change ◽  
Bubble Dynamics ◽  
Flow Boiling ◽  
Three Dimensional ◽  
Transfer Model ◽  
Transfer Coefficients ◽  
Wide Range

In this paper, we discuss the implementation and testing of a novel boiling mass transfer model to simulate the thermal and phase transformation behavior, generated due to boiling of binary mixtures, using the commercial CFD code AVL FIRE® v2011. The phase change model, based on detailed bubble dynamics effects, is solved in conjunction with incompressible phasic momentum, turbulence and energy equations in a segregated fashion, to study the flow boiling process inside a rectangular duct. Full three dimensional validation studies including the effect of flow velocity and exit pressure conditions, acting on a wide range of operating wall (superheat) temperatures, clearly shows the suppression of heat and mass transfer coefficients with enhancement in flow convection. Competing mechanisms such as phase change process and turbulent convection are identified to influence the heat transfer characteristics. In particular, the varying influence of the mass transfer effects on the heat flux characteristics with alteration in wall temperature is well demonstrated. Comparisons of the predicted total heat flux, computed as the sum of the convection and phase change components, indicate a very good agreement with experimental data, wherever available. Description of the flow field inclusive of phasic fraction, temperature and velocity field provides extensive details of the multiphase behavior of the boiling flow. Some preliminary results on the phase change work flow to model heat transfer in cooling jackets, for automotive applications, is also discussed.

Free Jet Impingement Heat Transfer of a High Prandtl Number Fluid Under Conditions of Highly Varying Properties

1999 ◽  
Vol 121 (3) ◽  
pp. 592-597 ◽  
Author(s):  
J. E. Leland ◽  
M. R. Pais
Keyword(s):  
Heat Transfer ◽  
Heated Surface ◽  
Jet Impingement ◽  
Turbulent Jets ◽  
Heat Fluxes ◽  
Lubricating Oil ◽  
Fluid Temperature ◽  
Transfer Coefficients ◽  
Constant Property ◽  
Wide Range

An experimental investigation was performed to determine the heat transfer rates for an impinging free-surface axisymmetric jet of lubricating oil for a wide range of Prandtl numbers (48 to 445) and for conditions of highly varying properties (viscosity ratios up to 14) in the flowing film. Heat transfer coefficients were obtained for jet Reynolds numbers from 109 to 8592, nozzle orifice diameters of 0.51, 0.84 and 1.70 mm and a heated surface diameter of 12.95 mm. The effect of nozzle to surface spacing (1 to 8.5 mm), was also investigated. Viscous dissipation was found to have an effect at low heat fluxes. Distinct heat transfer regimes were identified for initially laminar and turbulent jets. The data show that existing constant property correlations underestimate the heat transfer coefficient by more than 100 percent as the wall to fluid temperature difference increases. Over 700 data points were used to generate Nusselt number correlations which satisfactorily account for the highly varying properties with a mean absolute error of less than ten percent.

A Numerical Analysis of Heat Transfer to Fluids Near the Thermodynamic Critical Point Including the Thermal Entrance Region

1976 ◽  
Vol 98 (4) ◽  
pp. 609-615 ◽  
Author(s):  
N. M. Schnurr ◽  
V. S. Sastry ◽  
A. B. Shapiro
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Heat Fluxes ◽  
Entrance Region ◽  
Graphical Form ◽  
Constant Property ◽  
Thermodynamic Critical Point ◽  
Wide Range ◽  
Flux Parameter ◽  
Flow Through

A two-dimensional numerical method has been developed to predict heat transfer to near critical fluids in turbulent flow through circular tubes. The analysis is applicable to the thermal entry region as well as fully developed flows. Agreement with experimental data for water at 31.0 MN/m2 is quite good. A correlation in the form of the heat flux parameter of Goldmann was found to be satisfactory for water at that pressure. Results are presented in graphical form which apply to a wide range of heat fluxes, mass velocities, and tube diameters. Preliminary results in the entrance region show that film coefficients remain well above the corresponding fully developed values for a larger distance downstream than would be the case with a constant property fluid. This effect becomes more pronounced as the heat flux is increased.

Heat transfer in a radial liquid jet

1964 ◽  
Vol 20 (3) ◽  
pp. 501-511 ◽  
Author(s):  
Z. H. Chaudhury
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Heat Flux ◽  
Similarity Solution ◽  
Thermal Boundary Layer ◽  
Energy Equation ◽  
Momentum Equation ◽  
Liquid Jet ◽  
Initial Development ◽  
Initial Heating

The heat transfer in a radial liquid jet is investigated. In the region where a similarity solution of the momentum equation is available solutions of the energy equation describing the effects of viscous dissipation, initial heating and wall heating are obtained in closed form. Two examples illustrating the work are discussed. In the second of these an approximate method, based on the heat flux equation, is used to describe the initial development of the thermal boundary layer.

Heat Transfer and Pressure Drop Characteristics Induced by a Slat Blockage in a Circular Tube

1980 ◽  
Vol 102 (1) ◽  
pp. 64-70 ◽  
Author(s):  
E. M. Sparrow ◽  
K. K. Koram ◽  
M. Charmchi
Keyword(s):  
Heat Transfer ◽  
Fluid Flow ◽  
Pipe Flow ◽  
Turbulent Pipe Flow ◽  
Working Fluid ◽  
Transfer Coefficients ◽  
Cross Sectional ◽  
Pressure Drops ◽  
Heat Transfer Coefficients ◽  
Flow Experiments

Complementary heat transfer and fluid flow experiments were performed to determine transfer coefficients and pressure drops associated with the presence of a slat-like blockage in a tube. Water was the working fluid for the heat transfer studies (Pr = 4), while for the fluid flow experiments, which were performed under isothermal conditions, air was employed. The flow was turbulent in all cases, with the Reynolds number ranging from 10,000 to 60,000. Three blockage elements were used which respectively blocked 1/4, 1/2, and 3/4 of the tube cross-sectional area. Downstream of the blockage, heat transfer coefficients were measured around the circumference of the tube as well as along its length. The heat transfer coefficients in the region just downstream of the blockage were found to be several times as large as those for a corresponding conventional turbulent pipe flow. With increasing downstream distance, the coefficients diminish and thermal development is completed (to within five percent) at about 10, 15, and 18 diameters from the respective blockages. The blockage-induced circumferential variations of the heat transfer coefficient are dissipated by about five diameters. The pressure losses induced by the blockage are high, with values for the respective blockages that are 1.2, 5.2, and 33.2 times the velocity head in the pipe flow in which the blockage is situated. These losses are comparable to those for a gate valve.

A New Transient High Heat Flux Convection Calibration Facility for Heat Transfer Gauges in High Enthalpy Flows

2018 ◽  
Vol 140 (4) ◽  
Author(s):  
R. J. Lubbock ◽  
S. Luque ◽  
B. R. Rosic
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Calibration Method ◽  
High Heat ◽  
High Heat Flux ◽  
Transfer Coefficients ◽  
Transient Heating ◽  
High Enthalpy ◽  
Wide Range ◽  
Calibration Facility

This paper presents a novel transient method for calibrating heat transfer gauges for convective wall heat flux measurements in high enthalpy flows. The new method relies on the transient heating of sensor substrates under rapid exposure to a hot flow in order to obtain the necessary reference heat flux. Compared to previous calibration facilities, the new facility is simple, inexpensive, easy to adapt for different flow configurations and sensor geometries, and quick to run across a wide range of conditions. In this paper, the design of the new calibration facility is described and the transient calibration method explained. The method is demonstrated by calibrating a Gardon gauge at convective heat transfer coefficients between 300 and 600 W/m2 K. Typical facility data and calibration results are presented in terms of voltage-heat flux sensitivity and calibration correction ratio. These results are shown to agree with theoretical estimates within the estimated calibration uncertainty.

Local Friction and Heat Transfer Behavior of Water in a Turbulent Pipe Flow With a Large Heat Flux at the Wall

1995 ◽  
Vol 117 (2) ◽  
pp. 283-288 ◽  
Author(s):  
E. Choi ◽  
Y. I. Cho
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Local Heat Transfer ◽  
Local Heat ◽  
Turbulent Pipe Flow ◽  
Turbulent Heat Transfer ◽  
Transfer Coefficients ◽  
Viscosity Change ◽  
Heat Transfer Coefficients ◽  
Large Heat

The present study investigated the behavior of friction and heat transfer coefficients of water flowing turbulently in a relatively long (i.e., 950 diameter long) circular pipe. When a large heat flux was applied at the wall, the viscosity of water significantly decreased along the axial direction due to the increasing temperature of water. A concept of a “redeveloping region” was introduced, where the local heat transfer coefficient increased while the local friction coefficient decreased due to the above-mentioned viscosity change. The present study proposed the use of local bulk-mean temperature to determine local Nusselt numbers by using local Reynolds (ReLB) and Prandtl numbers (PrLB), a method that automatically took into account the effect of axial viscosity change on the evaluation of local heat transfer coefficients. A new turbulent heat transfer correlation for the prediction of the local Nusselt number is given as Nux=0.00425ReLB0.979PrLB0.4(μw/μb)−0.11.

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