Heat Transfer Coefficient in Ducts With Constant Wall Temperature

1983 ◽  
Vol 105 (4) ◽  
pp. 878-883 ◽  
Author(s):  
A. Haji-Sheikh ◽  
M. Mashena ◽  
M. J. Haji-Sheikh
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Heat Transfer Coefficient ◽  
Numerical Calculation ◽  
Transfer Coefficient ◽  
Cross Sections ◽  
Wall Temperature ◽  
Constant Wall Temperature ◽  
Circular Pipes ◽  
The Heat Transfer Coefficient

An analytical method for the numerical calculation of the heat transfer coefficient in arbitrarily shaped ducts with constant wall temperature at the boundary is presented. The flow is considered to be laminar and fully developed, both thermally and hydrodynamically. The method presented herein makes use of Galerkin-type functions for computation of the Nusselt number. This method is applied to circular pipes and ducts with rectangular, isosceles triangular, and right triangular cross sections. A three-term or even a two-term solution yields accurate solutions for circular ducts. The situation is similar for right triangular ducts with two equal sides. However, for narrower ducts, a larger number of terms must be used.

High Resolution Heat Transfer Measurements on the Stator Endwall of an Axial Turbine

2014 ◽  
Vol 137 (4) ◽  
Author(s):  
Benoit Laveau ◽  
Reza S. Abhari ◽  
Michael E. Crawford ◽  
Ewald Lutum
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
High Resolution ◽  
Surface Temperature ◽  
Transfer Coefficient ◽  
Mass Flow ◽  
Wall Temperature ◽  
Adiabatic Wall ◽  
Axial Turbine ◽  
The Heat Transfer Coefficient

In order to continue increasing the efficiency of gas turbines, an important effort is made on the thermal management of the turbine stage. In particular, understanding and accurately estimating the thermal loads in a vane passage is of primary interest to engine designers looking to optimize the cooling requirements and ensure the integrity of the components. This paper focuses on the measurement of endwall heat transfer in a vane passage with a three-dimensional (3D) airfoil shape and cylindrical endwalls. It also presents a comparison with predictions performed using an in-house developed Reynolds-Averaged Navier–Stokes (RANS) solver featuring a specific treatment of the numerical smoothing using a flow adaptive scheme. The measurements have been performed in a steady state axial turbine facility on a novel platform developed for heat transfer measurements and integrated to the nozzle guide vane (NGV) row of the turbine. A quasi-isothermal boundary condition is used to obtain both the heat transfer coefficient and the adiabatic wall temperature within a single measurement day. The surface temperature is measured using infrared thermography through small view ports. The infrared camera is mounted on a robot arm with six degrees of freedom to provide high resolution surface temperature and a full coverage of the vane passage. The paper presents results from experiments with two different flow conditions obtained by varying the mass flow through the turbine: measurements at the design point (ReCax=7.2×105) and at a reduced mass flow rate (ReCax=5.2×105). The heat transfer quantities, namely the heat transfer coefficient and the adiabatic wall temperature, are derived from measurements at 14 different isothermal temperatures. The experimental data are supplemented with numerical predictions that are deduced from a set of adiabatic and diabatic simulations. In addition, the predicted flow field in the passage is used to highlight the link between the heat transfer patterns measured and the vortical structures present in the passage.

scholarly journals Transient behavior of a plate-fin-and-tube heat exchanger taking into account different heat transfer coefficients on the individual tube rows

2019 ◽  
Vol 128 ◽  
pp. 04001
Author(s):  
Dawid Taler ◽  
Jan Taler ◽  
Katarzyna Wrona
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Heat Transfer Coefficient ◽  
Heat Exchanger ◽  
Transfer Coefficient ◽  
Analytical Formula ◽  
Cfd Modeling ◽  
Tube Heat Exchanger ◽  
Individual Tube ◽  
The Heat Transfer Coefficient

Experimental studies of multi-row plate-fin heat exchangers show that the highest average heat transfer coefficient on the air side occurs in the first row of tubes when the air velocity in front ofthe exchanger is less thanapproximately 3.5 m/s. In the subsequent rows of tubes up to about the fourth row the heat transfer coefficient decreases. In the fifth and further rows, it can be assumed that the heat transfer coefficient is equal in each tube row. It is necessary to find the relationships fortheair–side Nusselt number on each tube row to design a plate–fin and tube heat exchanger(PFTHE) with the appropriate number of tube rows. The air–side Nusselt number correlations canbe determined experimentally or by CFD modeling (Computational and Fluid Dynamics). The paper presents a newmathematical model of the transient operation of PFTHE, considering that the Nusselt numbers on the air side of individual tube rows are different. The heat transfer coefficient on an analyzed tube row was determined from the equality condition of mass– average air temperature differences on agiven tube row determined using the analytical formula and CFD modeling. The results of numerical modelingwere compared with the results of the experiments.

Heat Transfer With Insulated Combustion Chamber Walls and Its Influence on the Performance of Diesel Engines

1988 ◽  
Vol 110 (3) ◽  
pp. 482-488 ◽  
Author(s):  
G. Woschni ◽  
W. Spindler
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Combustion Chamber ◽  
Fuel Consumption ◽  
Temperature Difference ◽  
Wall Temperature ◽  
Cooling Water ◽  
Great Expectations ◽  
The Heat Transfer Coefficient

Recently great expectations were put into the insulation of combustion chamber walls. A considerable reduction in fuel consumption, a marked reduction of the heat flow to the cooling water, and a significant increase of exhaust gas energy were predicted. In the meantime there exists an increasing number of publications reporting on significant increase of fuel consumption with total or partial insulation of the combustion chamber walls. In [1] a physical explanation of this effect is given: Simultaneously with the decrease of the temperature difference between gas and wall as a result of insulation, the heat transfer coefficient between gas and wall increases rapidly due to increasing wall temperature, thus overcompensating for the decrease in temperature difference between gas and wall. Hence a modified equation for calculation of the heat transfer coefficient was presented [1]. In the paper to be presented here, recent experimental results are reported that confirm the effects demonstrated in [1], including the influence of the heat transfer coefficient, which depends on the wall temperature, on the performance of naturally aspirated and turbocharged engines.

Design Charts for Transient Temperature and Thermal Stress Distributions in Thermally Thick Plates

1960 ◽  
Vol 11 (3) ◽  
pp. 269-284
Author(s):  
J. S. Przemieniecki
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Thermal Stress ◽  
Transfer Coefficient ◽  
Wall Temperature ◽  
Transient Temperature ◽  
Stress Distributions ◽  
Adiabatic Wall ◽  
Design Charts ◽  
The Heat Transfer Coefficient

SummaryA set of design charts is presented for the calculation of transient temperature and thermal stress distributions in thermally thick plates subjected to aerodynamic heating.The method is particularly useful for determining temperatures and thermal stresses in plates with an arbitrary variation of the heat transfer coefficient and the adiabatic wall temperature of the boundary layer. The present method is based on repetitive applications of the exact analytical solution to a unit triangular variation of the adiabatic wall temperature and a constant heat transfer coefficient. The actual variation of the adiabatic wall temperature is represented as a series of straight lines while the heat transfer coefficient is approximated by a step function. The temperature distribution through the plate is separated into linear and “self-equilibrating” temperature distributions to facilitate thermal stress calculations; these distributions can be obtained directly from the design charts presented in this paper.The general principle of this semi-numerical method is also applied to thermally thin plates subjected to arbitrary heating conditions.

High Resolution Heat Transfer Measurements on the Stator Endwall of an Axial Turbine

2014 ◽  
Author(s):  
Benoit Laveau ◽  
Reza S. Abhari ◽  
Michael E. Crawford ◽  
Ewald Lutum
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
High Resolution ◽  
Surface Temperature ◽  
Transfer Coefficient ◽  
Mass Flow ◽  
Wall Temperature ◽  
Adiabatic Wall ◽  
Axial Turbine ◽  
The Heat Transfer Coefficient

In order to continue increasing the efficiency of gas turbines, an important effort is made on the thermal management of the turbine stage. In particular understanding and accurately estimating the thermal loads in a vane passage is of primary interest to engine designers looking to optimize the cooling requirements and ensure the integrity of the components. This paper focuses on the measurement of endwall heat transfer in a vane passage with a 3D airfoil shape and cylindrical endwalls. It also presents a comparison with predictions performed using an in-house developed RANS solver featuring a specific treatment of the numerical smoothing using a flow adaptive scheme. The measurements have been performed in a steady state axial turbine facility on a novel platform developed for heat transfer measurements and integrated to the nozzle guide vane row of the turbine. A quasi-isothermal boundary condition is used to obtain both the heat transfer coefficient and the adiabatic wall temperature within a single measurement day. The surface temperature is measured using infrared thermography through small view ports. The infrared camera is mounted on a robot-arm with six degrees of freedom to provide high resolution surface temperature and a full coverage of the vane passage. The paper presents results from experiments with two different flow conditions obtained by varying the mass flow through the turbine: measurements at the design point (ReCax = 7,2.105) and at a reduced mass flow rate (ReCax = 5,2.105). The heat transfer quantities, namely the heat transfer coefficient and the adiabatic wall temperature, are derived from measurements at 14 different isothermal temperatures. The experimental data are supplemented with numerical predictions that are deduced from a set of adiabatic and diabatic simulations. In addition, the predicted flow field in the passage is used to highlight the link between the heat transfer patterns measured and the vortical structures present in the passage.

On Selection of Reference Temperature of Heat Transfer Coefficient for Complicated Flows

2007 ◽  
Author(s):  
X. C. Li ◽  
J. Zhou ◽  
K. Aung
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Heat Transfer Coefficient ◽  
Surface Temperature ◽  
Transfer Coefficient ◽  
Wall Temperature ◽  
Convective Heat Transfer Coefficient ◽  
Internal Heat ◽  
Reference Temperature ◽  
The Heat Transfer Coefficient

One of the most fundamental concepts in heat transfer is the convective heat transfer coefficient, which is closely related with the flow Reynolds number, flow geometry and the thermal conditions on the heat transfer surface. To define the heat transfer coefficient, a reference temperature is needed besides the surface temperature and heat flux. The reference temperature can be chosen differently, such as the fluid bulk mean temperature (for internal flows) and the temperature at the far field (for external flows). For complicated flows, the adiabatic wall temperature, defined as the wall temperature when the surface heat flux is zero, is commonly adopted as the reference temperature. Other options can also be applied to complicated flows. This paper analyzed some of the potential selections of the reference temperature for different flow settings, including film cooling, jet impingement with cross flows and a mixing flow in a straight duct with or without internal heat source. Both laminar and turbulent flows are considered with different boundary conditions. Dramatic changes of heat transfer coefficient are observed with different reference temperatures. In some special conditions the heat transfer coefficient becomes negative, which means the heat flux has a different direction with the driving temperature difference defined. An innovative method is proposed to calculate the heat transfer coefficient of complicated flows with constant surface temperature.

A Novel Transient Liquid Crystal Technique to Determine Heat Transfer Coefficient Distributions and Adiabatic Wall Temperature in a Three-Temperature Problem

2003 ◽  
Vol 125 (3) ◽  
pp. 538-546 ◽  
Author(s):  
Andrew C. Chambers ◽  
David R. H. Gillespie ◽  
Peter T. Ireland ◽  
Geoffrey M. Dailey
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Liquid Crystal ◽  
Transfer Coefficient ◽  
Wall Temperature ◽  
Analytical Techniques ◽  
Single Test ◽  
Start Time ◽  
Adiabatic Wall ◽  
The Heat Transfer Coefficient

Transient liquid crystal techniques are widely used for experimental heat transfer measurements. In many instances it is necessary to model the heat transfer resulting from the temperature difference between a mixture of two gas streams and a solid surface. To nondimensionally characterize the heat transfer from scale models it is necessary to know both the heat transfer coefficient and adiabatic wall temperature of the model. Traditional techniques rely on deducing both parameters from a single test. This is a poorly conditioned problem. A novel strategy is proposed in which both parameters are deduced from a well-conditioned three-test strategy. The heat transfer coefficient is first calculated in a single test; the contribution from each driving gas stream is then deduced using additional tests. Analytical techniques are developed to deal with variations in the temperature profile and transient start time of each flow. The technique is applied to the analysis of the heat transfer within a low aspect ratio impingement channel with initial cross flow.

scholarly journals Physical and numerical simulation of the thermal and mechanical characteristics of stationary flows in the gasair paths of piston engines

2019 ◽  
Vol 21 (5) ◽  
pp. 22-28
Author(s):  
L. V. Plotnikov ◽  
Yu. M. Brodov ◽  
B. P. Zhilkin ◽  
A. M. Nevolin ◽  
M. O. Misnik
Keyword(s):  
Heat Transfer ◽  
Numerical Simulation ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Cross Sections ◽  
Experimental Studies ◽  
Hydraulic Systems ◽  
Reciprocating Engines ◽  
The Heat Transfer Coefficient ◽  
Exhaust Systems

Thermomechanical perfection of intake and exhaust systems largely determine the efficiency of the working process of reciprocating engines (ICE). The article presents the results of numerical simulation and experimental study of the heat transfer of gas flows in profiled gas- air systems of ICEs. A description of the numerical simulation technique, experimental setup, configurations of the studied hydraulic systems, measuring base and features of the experiments are given. On the basis of numerical modeling, it has been established that the use of profiled sections with cross sections in the shape of a square or a triangle in exhaust systems of an ICEs leads to a decrease in the heat transfer coefficient by 5-11%. It is shown that the use of similar profiled sections in the intake system of reciprocating engines also leads to a decrease in the heat transfer coefficient to 10 % at low air flow rates (up to 40 m/s) and an increase in the heat transfer coefficient to 7% at high speeds. Experimental studies qualitatively confirm the simulation results.

Convective heat transfer and fluid flow characteristics in fin and oval-tube heat exchanger

2021 ◽  
Vol 15 (2) ◽  
pp. 7936-7947
Author(s):  
Yamina Abdoune ◽  
Sahel Djamel ◽  
Benzeguir Redouane ◽  
Alem Karima
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Heat Transfer Coefficient ◽  
Heat Exchanger ◽  
Transfer Coefficient ◽  
Friction Factor ◽  
Tube Heat Exchanger ◽  
Baseline Case ◽  
Oval Tube ◽  
The Heat Transfer Coefficient

The forced convective heat transfer behavior of a turbulent air flow, steady and Newtonian over a fin and oval-tube heat exchanger has been examined numerically. Where, the effect of the tube tilt angle (α) on the heat transfer coefficient and the friction factor was tested. The inclination angle of the oval-tubes going from 0° (Baseline case) to 90° with a step of 10°. The fluid flows and heat transfer characteristics are presented for Reynolds numbers ranging from 3.000 to 12.000. All investigations are carried out with the help of the CFD ANSYS Fluent. Heat transfer coefficient results in the term of the Nusselt number are validated with the available experimental data and a maximum deviation of 9 % is observed. Reasonable agreement is found. The obtained results show that the tube's inclination angle of 20° is the best design which significantly removes the hot spots behind the tubes, thus giving an increase in the heat transfer coefficient of 13 % compared to the baseline case. In addition, useful correlations are developed to predict Nusselt number and friction factor in the fin and oval-tube heat exchanger.

A Transient Infrared Thermography Method for Simultaneous Film Cooling Effectiveness and Heat Transfer Coefficient Measurements From a Single Test

2004 ◽  
Vol 126 (4) ◽  
pp. 597-603 ◽  
Author(s):  
Srinath V. Ekkad ◽  
Shichuan Ou ◽  
Richard B. Rivir
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Liquid Crystal ◽  
Transfer Coefficient ◽  
Infrared Thermography ◽  
Wall Temperature ◽  
Film Cooling ◽  
Initial Model ◽  
Adiabatic Wall ◽  
The Heat Transfer Coefficient

In film cooling situations, there is a need to determine both local adiabatic wall temperature and heat transfer coefficient to fully assess the local heat flux into the surface. Typical film cooling situations are termed three temperature problems where the complex interaction between the jets and mainstream dictates the surface temperature. The coolant temperature is much cooler than the mainstream resulting in a mixed temperature in the film region downstream of injection. An infrared thermography technique using a transient surface temperature acquisition is described which determines both the heat transfer coefficient and film effectiveness (nondimensional adiabatic wall temperature) from a single test. Hot mainstream and cooler air injected through discrete holes are imposed suddenly on an ambient temperature surface and the wall temperature response is captured using infrared thermography. The wall temperature and the known mainstream and coolant temperatures are used to determine the two unknowns (the heat transfer coefficient and film effectiveness) at every point on the test surface. The advantage of this technique over existing techniques is the ability to obtain the information using a single transient test. Transient liquid crystal techniques have been one of the standard techniques for determining h and η for turbine film cooling for several years. Liquid crystal techniques do not account for nonuniform initial model temperatures while the transient IR technique measures the entire initial model distribution. The transient liquid crystal technique is very sensitive to the angle of illumination and view while the IR technique is not. The IR technique is more robust in being able to take measurements over a wider temperature range which improves the accuracy of h and η. The IR requires less intensive calibration than liquid crystal techniques. Results are presented for film cooling downstream of a single hole on a turbine blade leading edge model.

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