Inverse Determination of Steady Heat Convection Coefficient Distributions

1998 ◽  
Vol 120 (2) ◽  
pp. 328-334 ◽  
Author(s):  
T. J. Martin ◽  
G. S. Dulikravich
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Boundary Conditions ◽  
Measurement Data ◽  
Cost Effective ◽  
Heat Fluxes ◽  
Transfer Coefficients ◽  
Simple Modification ◽  
Heat Transfer Coefficients ◽  
Thermal Boundary Conditions

An inverse Boundary Element Method (BEM) procedure has been used to determine unknown heat transfer coefficients on surfaces of arbitrarily shaped solids. The procedure is noniterative and cost effective, involving only a simple modification to any existing steady-state heat conduction BEM algorithm. Its main advantage is that this method does not require any knowledge of, or solution to, the fluid flow field. Thermal boundary conditions can be prescribed on only part of the boundary of the solid object, while the heat transfer coefficients on boundaries exposed to a moving fluid can be partially or entirely unknown. Over-specified boundary conditions or internal temperature measurements on other, more accessible boundaries are required in order to compensate for the unknown conditions. An ill-conditioned matrix results from the inverse BEM formulation, which must be properly inverted to obtain the solution to the ill-posed problem. Accuracy of numerical results has been demonstrated for several steady two-dimensional heat conduction problems including sensitivity of the algorithm to errors in the measurement data of surface temperatures and heat fluxes.

The Concept of Adiabatic Heat Transfer Coefficient and its Application to Turbomachinery

2013 ◽  
Author(s):  
Reinaldo A. Gomes ◽  
Reinhard Niehuis
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Boundary Conditions ◽  
Transfer Coefficient ◽  
Constant Heat Flux ◽  
Transfer Coefficients ◽  
Constant Wall Temperature ◽  
Heat Transfer Coefficients ◽  
Thermal Boundary Conditions ◽  
Critical Components

Typical turbomachinery flows are too complex to be predicted by analytical solutions alone. Therefore numerous correlations and test data are used in conjunction with numerical tools in order to design thermally critical components. This approach can be problematic because these correlations and data are not fully independent of the boundary conditions applied. The heat transfer coefficients obtained are not only dependent on the aerodynamics of the flow but also on the thermal boundary layer created along the surface. The adiabatic heat transfer coefficient is the only one which is independent of the thermal boundary conditions, as long as the energy equation can be considered linear with respect to the temperature. However, a proper prediction of the surface temperature cannot be obtained with the adiabatic heat transfer coefficient alone. This paper first reviews the concept of adiabatic heat transfer coefficient and its application to turbomachinery flows. Later, a concept is introduced to allow interchanging between different definitions of heat transfer coefficient and boundary conditions, i.e. constant heat flux or constant wall temperature. Finally, a typical configuration for measuring the adiabatic heat transfer coefficient on a turbine blade and the conversion to other definitions of heat transfer coefficient is presented and evaluated. It is shown that with the technique presented here even small deficiencies of some experiments can be compensated for.

Reconstruction of the heat transfer coefficients and heat fluxes in heat conduction problems

2021 ◽  
Author(s):  
Talaat Abdelhamid ◽  
Ammar H. Elsheikh ◽  
Olatunji Mumini Omisore ◽  
N.A. Saeed ◽  
T. Muthuramalingam ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Heat Fluxes ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients

Heat Transfer Contributions of Pins and Endwall in Pin-Fin Arrays: Effects of Thermal Boundary Condition Modeling

1999 ◽  
Vol 121 (2) ◽  
pp. 257-263 ◽  
Author(s):  
M. K. Chyu ◽  
Y. C. Hsing ◽  
T. I.-P. Shih ◽  
V. Natarajan
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Boundary Conditions ◽  
Transfer Coefficient ◽  
Transfer Coefficients ◽  
Pin Fin ◽  
Heat Transfer Coefficients ◽  
Thermal Boundary Conditions ◽  
The Individual ◽  
Pin Fin Arrays

Short pin-fin arrays are often used for cooling turbine airfoils, particularly near the trailing edge. An accurate heat transfer estimation from a pin-fin array should account for the total heat transfer over the entire wetted surface, which includes the pin surfaces and uncovered endwalls. One design question frequently raised is the actual magnitudes of heat transfer coefficients on both pins and endwalls. Results from earlier studies have led to different and often contradicting conclusions. This variation, in part, is caused by imperfect or unrealistic thermal boundary conditions prescribed in the individual test models. Either pins or endwalls, but generally not both, were heated in those previous studies. Using a mass transfer analogy based on the naphthalene sublimation technique, the present experiment is capable of revealing the individual heat transfer contributions from pins and endwalls with the entire wetted surface thermally active. The particular pin-fin geometry investigated, S/D = X/D = 2.5 and H/D = 1.0, is considered to be one of the optimal array arrangement for turbine airfoil cooling. Both inline and staggered arrays with the identical geometric parameters are studied for 5000 ≤ Re ≤ 25,000. The present results reveal that the general trends of the row-resolved heat transfer coefficients on either pins or endwalls are somewhat insensitive to the nature of thermal boundary conditions prescribed on the test surface. However, the actual magnitudes of heat transfer coefficients can be substantially different, due to variations in the flow bulk temperature. The present study also concludes that the pins have consistently 10 to 20 percent higher heat transfer coefficient than the endwalls. However, such a difference in heat transfer coefficient imposes very insignificant influence on the overall array-averaged heat transfer, since the wetted area of the uncovered endwalls is nearly four times greater than that of the pins.

scholarly journals Heat Transfer Contributions of Pins and Endwall in Pin-Fin Arrays: Effects of Thermal Boundary Condition Modeling

1998 ◽  
Author(s):  
M. K. Chyu ◽  
Y. C. Hsing ◽  
T. I.-P. Shih ◽  
V. Natarajan
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Boundary Conditions ◽  
Transfer Coefficient ◽  
Transfer Coefficients ◽  
Pin Fin ◽  
Heat Transfer Coefficients ◽  
Thermal Boundary Conditions ◽  
The Individual ◽  
Pin Fin Arrays

Short pin-fin arrays are often used for cooling turbine airfoils, particularly near the trailing edge. An accurate heat transfer estimation from a pin-fin array should account for the total heat transfer over the entire wetted surface which includes the pin surfaces and uncovered end walls. One design question frequently raised is the actual magnitudes of heat transfer coefficients on both pins and endwalls. Results from earlier studies have led to different and often contradicting conclusions. This variation, in part, is caused by imperfect or unrealistic thermal boundary conditions prescribed in the individual test models. Either pins or endwalls, but generally not both, were heated in those previous studies. Using a mass transfer analogy based on the naphthalene sublimation technique, the present experiment is capable of revealing the individual heat transfer contributions from pins and endwalls with the entire wetted surface thermally active. The particular pin-fin geometry investigated, S/D = X/D = 2.5 and H/D = 1.0, is considered to be one of the optimal array arrangement for turbine airfoil cooling. Both inline and staggered arrays with the identical geometric parameters are studied for 5,000 ≤ Re ≤ 25,000. The present results reveal that the general trends of the row-resolved heat transfer coefficients on either pins or endwalls are somewhat insensitive to the nature of thermal boundary conditions prescribed on the test surface. However, the actual magnitudes of heat transfer coefficients can be substantially different, due to variations in the flow bulk temperature. The present study also concludes that the pins have consistently 10 to 20% higher heat transfer coefficient than the endwalls. However, such a difference in heat transfer coefficient imposes very insignificant influence on the overall array-averaged heat transfer, since the wetted area of the uncovered endwalls is nearly four times greater than that of the pins.

scholarly journals Pool Boiling Heat Transfer Coefficients in Mixtures of Water and Glycerin

Processes ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 830
Author(s):  
Viktor Vajc ◽  
Radek Šulc ◽  
Martin Dostál
Keyword(s):  
Heat Transfer ◽  
Dynamic Method ◽  
Water Mass ◽  
Heat Fluxes ◽  
Static Method ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients ◽  
Mean Relative Error ◽  
Mixture Effects ◽  
Mass Fractions

Heat transfer coefficients were investigated for saturated nucleate pool boiling of binary mixtures of water and glycerin at atmospheric pressure in a wide range of concentrations and heat fluxes. Mixtures with water mass fractions from 100% to 40% were boiled on a horizontal flat copper surface at heat fluxes from about 25 up to 270kWm−2. Experiments were carried out by static and dynamic method of measurement. Results of the static method show that the impact of mixture effects on heat transfer coefficient cannot be neglected and ideal heat transfer coefficient has to be corrected for all investigated concentrations and heat fluxes. Experimental data are correlated with the empirical correlation α=0.59q0.714+0.130ωw with mean relative error of 6%. Taking mixture effects into account, data are also successfully correlated with the combination of Stephan and Abdelsalam (1980) and Schlünder (1982) correlations with mean relative error of about 15%. Recommended coefficients of Schlünder correlation C0=1 and βL=2×10−4ms−1 were found to be acceptable for all investigated mixtures. The dynamic method was developed for fast measurement of heat transfer coefficients at continuous change of composition of boiling mixture. The dynamic method was tested for water–glycerin mixtures with water mass fractions from 70% down to 35%. Results of the dynamic method were found to be comparable with the static method. For water–glycerin mixtures with higher water mass fractions, precise temperature measurements are needed.

scholarly journals Systematic heat transfer measurements in highly viscous binary fluids

2021 ◽  
Author(s):  
Ann-Christin Fleer ◽  
Markus Richter ◽  
Roland Span
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Volatile Component ◽  
Test Tube ◽  
Heat Fluxes ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients ◽  
Low Viscosity ◽  
The Heat Transfer Coefficient

AbstractInvestigations of flow boiling in highly viscous fluids show that heat transfer mechanisms in such fluids are different from those in fluids of low viscosity like refrigerants or water. To gain a better understanding, a modified standard apparatus was developed; it was specifically designed for fluids of high viscosity up to 1000 Pa∙s and enables heat transfer measurements with a single horizontal test tube over a wide range of heat fluxes. Here, we present measurements of the heat transfer coefficient at pool boiling conditions in highly viscous binary mixtures of three different polydimethylsiloxanes (PDMS) and n-pentane, which is the volatile component in the mixture. Systematic measurements were carried out to investigate pool boiling in mixtures with a focus on the temperature, the viscosity of the non-volatile component and the fraction of the volatile component on the heat transfer coefficient. Furthermore, copper test tubes with polished and sanded surfaces were used to evaluate the influence of the surface structure on the heat transfer coefficient. The results show that viscosity and composition of the mixture have the strongest effect on the heat transfer coefficient in highly viscous mixtures, whereby the viscosity of the mixture depends on the base viscosity of the used PDMS, on the concentration of n-pentane in the mixture, and on the temperature. For nucleate boiling, the influence of the surface structure of the test tube is less pronounced than observed in boiling experiments with pure fluids of low viscosity, but the relative enhancement of the heat transfer coefficient is still significant. In particular for mixtures with high concentrations of the volatile component and at high pool temperature, heat transfer coefficients increase with heat flux until they reach a maximum. At further increased heat fluxes the heat transfer coefficients decrease again. Observed temperature differences between heating surface and pool are much larger than for boiling fluids with low viscosity. Temperature differences up to 137 K (for a mixture containing 5% n-pentane by mass at a heat flux of 13.6 kW/m2) were measured.

The Effects of Nucleate Boiling Versus Film Boiling on Heat Transfer in Power Boiler Tubes

1962 ◽  
Vol 84 (4) ◽  
pp. 365-371 ◽  
Author(s):  
H. S. Swenson ◽  
J. R. Carver ◽  
G. Szoeke
Keyword(s):  
Heat Transfer ◽  
Nucleate Boiling ◽  
Steel Tube ◽  
Heat Fluxes ◽  
Inside Surface ◽  
Film Boiling ◽  
Stainless Steel Tube ◽  
Transfer Coefficients ◽  
Steam Quality ◽  
Heat Transfer Coefficients

In large, subcritical pressure, once-through power boilers heat is transferred to steam and water mixtures ranging in steam quality from zero per cent at the bottom of the furnace to 100 per cent at the top. In order to provide design information for this type of boiler, heat-transfer coefficients for forced convection film boiling were determined for water at 3000 psia flowing upward in a vertical stainless-steel tube, AISI Type 304, having an inside diameter of 0.408 inches and a heated length of 6 feet. Heat fluxes ranged between 90,000 and 180,000 Btu/hr-sq ft and were obtained by electrical resistance heating of the tube. The operation of the experimental equipment was controlled so that nucleate boiling, transition boiling, and stable film boiling occurred simultaneously in different zones of the tube. The film boiling data were correlated with a modified form of the equation Nu = a a(Re)m(Pr)n using steam properties evaluated at inside surface temperature. Results of a second series of heat-transfer tests with tubes having a helical rib on the inside surface showed that nucleate boiling could be maintained to much higher steam qualities with that type of tube than with a smooth-bore tube.

High Heat Flux Boiling Heat Transfer for Laser Diode Arrays

2016 ◽  
Author(s):  
Todd M. Bandhauer ◽  
Taylor A. Bevis
Keyword(s):  
Heat Transfer ◽  
Thermal Management ◽  
Laser Diode ◽  
Boiling Heat Transfer ◽  
Single Phase ◽  
Laser Diodes ◽  
Heat Fluxes ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients ◽  
Laser Diode Arrays

The principle limit for achieving higher brightness of laser diode arrays is thermal management. State of the art laser diodes generate heat at fluxes in excess of 1 kW cm−2 on a plane parallel to the light emitting edge. As the laser diode bars are packed closer together, it becomes increasingly difficult to remove large amounts of heat in the diminishing space between neighboring diode bars. Thermal management of these diode arrays using conduction and natural convection is practically impossible, and, therefore, some form of forced convective cooling must be utilized. Cooling large arrays of laser diodes using single-phase convection heat transfer has been investigated for more than two decades by multiple investigators. Unfortunately, either large fluid temperature increases or very high flow velocities must be utilized to reject heat to a single phase fluid, and the practical threshold for single phase convective cooling of laser diodes appears to have been reached. In contrast, liquid-vapor phase change heat transport can occur with a negligible increase in temperature and, due to a high enthalpy of vaporization, at comparatively low mass flow rates. However, there have been no prior investigations at the conditions required for high brightness edge emitting laser diode arrays: >1 kW cm−2 and >10 kW cm−3. In the current investigation, flow boiling heat transfer at heat fluxes up to 1.1 kW cm−2 was studied in a microchannel heat sink with plurality of very small channels (45 × 200 microns) using R134a as the phase change fluid. The high aspect ratio channels (4.4:1) were manufactured using MEMS fabrication techniques, which yielded a large heat transfer surface area to volume ratio in the vicinity of the laser diode. To characterize the heat transfer performance, a test facility was constructed that enabled testing over a range of fluid saturation temperatures (15°C to 25°C). Due to the very small geometric features, significant heat spreading was observed, necessitating numerical methods to determine the average heat transfer coefficient from test data. This technique is crucial to accurately calculate the heat transfer coefficients for the current investigation, and it is shown that the analytical approach used by many previous investigations requires assumptions that are inadequate for the very small dimensions and heat fluxes observed in the present study. During the tests, the calculated outlet vapor quality exceeded 0.6 and the base heat flux reached a maximum of 1.1 kW cm−2. The resulting experimental heat transfer coefficients are found to be as large a 58.1 kW m−2 K−1 with an average uncertainty of ±11.1%, which includes uncertainty from all measured and calculated values, required assumptions, and geometric discretization error from meshing.

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