A dynamic heat transfer coefficient between fractured rock and flowing fluid

Geothermics ◽  
2017 ◽  
Vol 65 ◽  
pp. 10-16 ◽  
Author(s):  
Thomas Heinze ◽  
Sahar Hamidi ◽  
Boris Galvan
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Fractured Rock ◽  
Flowing Fluid ◽  
Dynamic Heat Transfer

scholarly journals Heat Transfer Coefficient Determination during FC-72 Flow in a Minichannel Heat Sink Using the Trefftz Functions and ADINA Software

Energies ◽  
2020 ◽  
Vol 13 (24) ◽  
pp. 6647
Author(s):  
Magdalena Piasecka ◽  
Beata Maciejewska ◽  
Paweł Łabędzki
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Heat Sink ◽  
Transfer Problem ◽  
Heat Transfer Problem ◽  
Heated Wall ◽  
Inlet Temperature ◽  
Transfer Coefficients ◽  
Flowing Fluid

This work focuses on subcooled boiling heat transfer during flow in a minichannel heat sink with three or five minichannels of 1 mm depth. The heated element for FC-72 flowing along the minichannels was a thin foil of which temperature on the outer surface was measured due to the infrared thermography. The test section was oriented vertically or horizontally. A steady state heat transfer process and a laminar, incompressible flow of the fluid in a central minichannel were assumed. The heat transfer problem was described by the energy equations with an appropriate system of boundary conditions. Several mathematical methods were applied to solve the heat transfer problem with the Robin condition to determine the local heat transfer coefficients at the fluid/heated foil interface. Besides the 1D approach as a simple analytical method, a more sophisticated 2D approach was proposed with solutions by the Trefftz functions and ADINA software. Finite element method (FEM) calculations were conducted to find the temperature field in the flowing fluid and in the heated wall. The results were illustrated by graphs of local heated foil temperature and transfer coefficients as a function of the distance from the minichannel inlet. Temperature distributions in the heater and the fluid obtained from the FEM computations carried out by ADINA software were also shown. Similar values of the heat transfer coefficient were obtained in both the FEM calculations and the 1D approach. Example boiling curves indicating nucleation hysteresis are shown and discussed.

scholarly journals Numerical Solution of Axisymmetric Inverse Heat Conduction Problem by the Trefftz Method

Energies ◽  
2020 ◽  
Vol 13 (3) ◽  
pp. 705
Author(s):  
Sylwia Hożejowska ◽  
Magdalena Piasecka
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Boiling Heat Transfer ◽  
Flow Boiling ◽  
Heated Surface ◽  
Essential Element ◽  
Trefftz Method ◽  
Flowing Fluid ◽  
The Heat Transfer Coefficient

In this paper, the issue of flow boiling heat transfer in an annular minigap was discussed. The main aim of the paper was determining the boiling heat transfer coefficient at the HFE-649 fluid–heater contact during flow along an annular minigap. The essential element of the experimental stand was a test section vertically oriented with the minigap 2 mm wide. Thermocouples were used to measure the temperature of the heater and fluid at the inlet and the outlet to the minigap. The mathematical model assumed that the fluid flow was laminar and the steady–state heat transfer process was axisymmetric. The temperatures of the heated surface and of the flowing fluid were assumed to fulfill energy equations with adequate boundary conditions. The problem was solved by the Trefftz method. The local heat transfer coefficients at the fluid–test surface interface were calculated due to the third kind boundary condition at the saturated boiling. Graphs were used to illustrate: the measurement of the heater surface temperature, 2D temperature distributions in the pipe and fluid, and the heat transfer coefficient as a function of the distance from the minigap inlet. The measurement uncertainties and accuracy of the heat transfer coefficient determination were estimated.

scholarly journals Heat transfer coefficient determination using the FEM with time-dependent Trefftz-type basis functions in subcooled flow boiling in a minichannel

2018 ◽  
Vol 240 ◽  
pp. 01024
Author(s):  
Beata Maciejewska ◽  
Magdalena Piasecka
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Flow Boiling ◽  
Local Heat Transfer ◽  
Thin Foil ◽  
Local Heat ◽  
Basis Functions ◽  
Time Dependent ◽  
Flowing Fluid

Results concerning flow boiling heat transfer in a vertical minichannel of 1.7 mm depth were shown. The channel was asymmetrically heated by a thin foil. Its surface temperature was recorded continuously in points by thermocouples. Measurements were carried out in 0.01 s intervals. The objective of the numerical calculations was to determine the heat transfer coefficient on the heated foil–fluid contact surface in the minichannel from the Robin boundary condition. Both the foil and fluid temperatures were the result of solving the nonstationary two-dimensional problem in the foil and flowing fluid. The problem was solved by using the FEM combined with Trefftz-type basis functions. The values of the time-dependent local heat transfer coefficient were presented and discussed.

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%.

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