Application of integral equations to heat conduction problems in which the heat transfer coefficient varies

1975 ◽  
Vol 28 (3) ◽  
pp. 392-395 ◽  
Author(s):  
I. M. Fedotkin ◽  
A. M. Aizen ◽  
I. A. Goloshchuk
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Heat Conduction ◽  
Transfer Coefficient ◽  
Integral Equations ◽  
The Heat Transfer Coefficient

Influence of the Finite Element Model on the Inverse Determination of the Heat Transfer Coefficient Distribution over the Hot Plate Cooled by the Laminar Water Jets / Wpływ Modelu Metody Elementów Skonczonych Na Współczynnika Wymiany Ciepła Wyznaczany Z Rozwiazania Odwrotnego Procesu Laminarnego Chłodzenia Płyty Metalowej

2013 ◽  
Vol 58 (1) ◽  
pp. 105-112 ◽  
Author(s):  
B. Hadała ◽  
Z. Malinowski ◽  
T. Telejko ◽  
A. Szajding
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Heat Transfer Coefficient ◽  
Heat Conduction ◽  
Transfer Coefficient ◽  
Shape Functions ◽  
Strip Surface ◽  
Coefficient Distribution ◽  
Laminar Jets ◽  
The Heat Transfer Coefficient

The industrial hot rolling mills are equipped with systems for controlled cooling of hot steel products. In the case of strip rolling mills the main cooling system is situated at run-out table to ensure the required strip temperature before coiling. One of the most important system is laminar jets cooling. In this system water is falling down on the upper strip surface. The proper cooling rate affects the final mechanical properties of steel which strongly dependent on microstructure evolution processes. Numerical simulations can be used to determine the water flux which should be applied in order to control strip temperature. The heat transfer boundary condition in case of laminar jets cooling is defined by the heat transfer coefficient, cooling water temperature and strip surface temperature. Due to the complex nature of the cooling process the existing heat transfer models are not accurate enough. The heat transfer coefficient cannot be measured directly and the boundary inverse heat conduction problem should be formulated in order to determine the heat transfer coefficient as a function of cooling parameters and strip surface temperature. In inverse algorithm various heat conduction models and boundary condition models can be implemented. In the present study two three dimensional finite element models based on linear and non-linear shape functions have been tested in the inverse algorithm. Further, two heat transfer boundary condition models have been employed in order to determine the heat transfer coefficient distribution at the hot plate cooled by laminar jets. In the first model heat transfer coefficient distribution over the cooled surface has been approximated by the witch of Agnesi type function with the expansion in time of the approximation parameters. In the second model heat transfer coefficient distribution over the cooled plate surface has been approximated by the surface elements serendipity family with parabolic shape functions. The heat transfer coefficient values at surface element nodes have been expanded in time by the cubic-spline functions. The numerical tests have shown that in the case of heat conduction model based on linear shape functions inverse solution differs significantly from the searched boundary condition. The dedicated finite element heat conduction model based on non-linear shape functions has been developed to ensure inverse determination of heat transfer coefficient distribution over the cooled surface in the time of cooling. The heat transfer coefficient model based on surface elements serendipity family is not limited to a particular form of the heat flux distribution. The solution has been achieved for measured temperatures of the steel plate cooled by 9 laminar jets.

scholarly journals Evaluation of localized heat transfer coefficient for induction heating apparatus by thermal fluid analysis based on the HSMAC method

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 504-511
Author(s):  
Satoshi Namiki ◽  
Tomoya Iino ◽  
Yoshifumi Okamoto
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Heat Conduction ◽  
Transfer Coefficient ◽  
Induction Heating ◽  
Thermal Design ◽  
Electrical Machines ◽  
Fluid Analysis ◽  
Thermal Fluid Analysis ◽  
The Heat Transfer Coefficient

AbstractWith the development of electrical machines for achieving higher performance and smaller size, heat generation in electrical machines has also increased. Consequently, the temperature rise in electrical machines causes unexpected heating of components and makes it difficult to operate properly. Therefore, in the development of electrical machines, the accurate evaluation of temperature increase is important. In the thermal design of electrical machines, heat-conduction analysis using the heat-transfer boundary set on the surface of a heated target has been frequently performed. However, because the heat-transfer coefficient is dependent on various factors, it is often determined based on experimental or numerical simulation results. Therefore, setting the heat-transfer coefficient to a constant value for the surface of the heated target degrades the analysis accuracy because the actual phenomenon cannot be modeled. To enhance the accuracy of the heat-transfer coefficient, the coupled electromagnetic field with heat-conduction analysis finite element method (FEM), thermal-fluid analysis using FEM, and the highly simplified marker and cell method is applied to the estimation of the distribution of the heat-transfer coefficient. Moreover, to accurately calculate the localized heat-transfer coefficient, the temperature distribution and flow velocity distribution around the heated target are analyzed in the induction-heating apparatus.

Evaporation of lignin-lean black liquor

TAPPI Journal ◽  
2015 ◽  
Vol 14 (7) ◽  
pp. 441-450
Author(s):  
HENRIK WALLMO, ◽  
ULF ANDERSSON ◽  
MATHIAS GOURDON ◽  
MARTIN WIMBY
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Black Liquor ◽  
Salt Content ◽  
Solubility Limit ◽  
Lignin Removal ◽  
Kraft Black Liquor ◽  
Black Liquors ◽  
The Heat Transfer Coefficient

Many of the pulp mill biorefinery concepts recently presented include removal of lignin from black liquor. In this work, the aim was to study how the change in liquor chemistry affected the evaporation of kraft black liquor when lignin was removed using the LignoBoost process. Lignin was removed from a softwood kraft black liquor and four different black liquors were studied: one reference black liquor (with no lignin extracted); two ligninlean black liquors with a lignin removal rate of 5.5% and 21%, respectively; and one liquor with maximum lignin removal of 60%. Evaporation tests were carried out at the research evaporator in Chalmers University of Technology. Studied parameters were liquor viscosity, boiling point rise, heat transfer coefficient, scaling propensity, changes in liquor chemical composition, and tube incrustation. It was found that the solubility limit for incrustation changed towards lower dry solids for the lignin-lean black liquors due to an increased salt content. The scaling obtained on the tubes was easily cleaned with thin liquor at 105°C. It was also shown that the liquor viscosity decreased exponentially with increased lignin outtake and hence, the heat transfer coefficient increased with increased lignin outtake. Long term tests, operated about 6 percentage dry solids units above the solubility limit for incrustation for all liquors, showed that the heat transfer coefficient increased from 650 W/m2K for the reference liquor to 1500 W/m2K for the liquor with highest lignin separation degree, 60%.

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.

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