scholarly journals Time-Dependent Heat Transfer Calculations with Trefftz and Picard Methods for Flow Boiling in a Mini-Channel Heat Sink

Energies ◽  
2021 ◽  
Vol 14 (7) ◽  
pp. 1832
Author(s):  
Magdalena Piasecka ◽  
Sylwia Hożejowska ◽  
Beata Maciejewska ◽  
Anna Pawińska
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Heat Sink ◽  
Flow Boiling ◽  
Time Dependent ◽  
Heated Wall ◽  
Trefftz Method ◽  
Mini Channels ◽  
The Heat Transfer Coefficient

The intensification of heat transfer using two-phase boiling flow in mini-channels is widely used to dissipate the high heat fluxes in miniaturized electronic devices. However, the process itself is not fully recognized and still requires experimental studies and developing computation methods appropriate for them. The main aim of this work was the mathematical modeling of time-dependent heat transfer process in FC-72 flow boiling in a mini-channel heat sink with five parallel mini-channels of 1 mm depth. Channels have an asymmetrically heated wall while its outer temperature was measured by infrared thermography. The opposite wall of the mini-channels was transparent, helping to record flow patterns due to a high-speed digital camera. The objective of the numerical calculations was to determine the heat transfer coefficient on the wall-fluid contact surface from the Robin boundary condition. The problem was solved using methods based on the Trefftz-type functions. Three mathematical methods were applied in calculations: the FEM with Trefftz type basis functions, the Classical Trefftz Method, and the Hybrid Picard-Trefftz Method. The results were compared with the values of the heat transfer coefficient obtained from theoretical correlations from the literature.

scholarly journals The heat transfer coefficient determination with the use of the Beck-Trefftz method in flow boiling in a minichannel

2018 ◽  
Vol 180 ◽  
pp. 02099 ◽  
Author(s):  
Kinga Strąk ◽  
Beata Maciejewska ◽  
Magdalena Piasecka
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Boiling Heat Transfer ◽  
Transfer Problem ◽  
Heat Conduction Problem ◽  
Flow Boiling ◽  
Inverse Heat Conduction Problem ◽  
Heated Wall ◽  
Trefftz Method

In this paper, the solution of the two-dimensional inverse heat transfer problem with the use of the Beck method coupled with the Trefftz method is proposed. This method was applied for solving an inverse heat conduction problem. The aim of the calculation was to determine the boiling heat transfer coefficient on the basis of temperature measurements taken by infrared thermography. The experimental data of flow boiling heat transfer in a single vertical minichannel of 1.7 mm depth, heated asymmetrically, were used in calculations. The heating element for two refrigerants (FC-72 and HFE-7100, 3M) flowing in the minichannel was the plate enhanced on the side contacting with the fluid. The analysis of the results was performed on the basis of experimental series obtained for the same heat flux and two different mass flow velocities. The results were presented as infrared thermographs, heated wall temperature and heat transfer coefficient as a function of the distance from the minichannel inlet. The results was discussed for the subcooled and saturated boiling regions separately.

scholarly journals Characteristics of Refrigerant Boiling Heat Transfer in Rectangular Mini-Channels during Various Flow Orientations

Energies ◽  
2021 ◽  
Vol 14 (16) ◽  
pp. 4891
Author(s):  
Magdalena Piasecka ◽  
Kinga Strąk
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Channel Length ◽  
Heat Transfer Process ◽  
Heated Wall ◽  
Working Fluid ◽  
Two Phase ◽  
Mini Channels ◽  
The Heat Transfer Coefficient

This paper reports the results of heat transfer during refrigerant flow in rectangular mini-channels at stationary conditions. The impacts of selected parameters on boiling are discussed, i.e., thermal and flow parameters, dimensions and orientation of the channels. Four refrigerants (FC-72, HFE-649, HFE-7000 and HFE-7100) were used as the working fluid. Research was carried out on the experimental set-up with the test section with a single rectangular mini-channel of 180 mm long and with a group of five parallel mini-channels, each 32 mm long. The temperature of the mini-channel’s heated wall was measured by infrared thermography. Local values of the heat transfer coefficient at the contact surface between the fluid and the plate were calculated using the 1D mathematical method. The results are presented as the relationship between the heat transfer coefficient and the distance along the mini-channel length and boiling curves. Two-phase flow patterns are shown. Moreover, the results concerning various refrigerants and the use of modified heater surfaces are discussed. The main factors influencing the heat transfer process were: mini-channel inclination to the horizontal pane (the highest heat transfer coefficient at 270° and 0°), using modified heater surfaces (especially electroerosion texturing and vibration-assisted laser No. 2 texturing) and working fluids (FC-72 and HFE-7000).

Flow Boiling in a Heat Sink Embedded With Hexagonally Linked Minichannels

2016 ◽  
Vol 138 (8) ◽  
Author(s):  
Shubhankar Chakraborty ◽  
Omprakash Sahu ◽  
Prasanta Kr. Das
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Heat Sink ◽  
Flow Boiling ◽  
Heat Sinks ◽  
Vapor Quality ◽  
Maximum Heat ◽  
Maximum Heat Transfer ◽  
The Heat Transfer Coefficient

The thermal hydraulic performance of a miniature heat sink during flow boiling of distilled water is presented in this article. The unique design of the heat sink contains a number of microchannels of 1 mm × 1 mm cross section arranged in a regular hexagonal array. The design facilitates repeated division and joining of individual streams from different microchannels and thereby can enhance heat transfer. Individual slug bubble experiences a typical route of break up, coalescence, and growth. The randomness of these processes enhances the transport of heat. With the increase of vapor quality the heat transfer coefficient increases, reaches the maximum value, and then drops. The maximum heat transfer coefficient occurs at an exit vapor quality much higher than that observed in conventional parallel microchannel heat sinks. Repeated redistribution of the coolant in the interlinked channels and the restricted growth of the slug bubbles may be responsible for this trend.

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.

Flow Boiling Study in Mini-Channels

2006 ◽  
Author(s):  
Francesc Madrid ◽  
Nadia Caney ◽  
Philippe Marty
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Test Section ◽  
Heat Exchangers ◽  
Flow Boiling ◽  
Two Phase ◽  
Mini Channels ◽  
Vapour Quality ◽  
The Heat Transfer Coefficient

Mini-channel heat exchangers improve thermal performance in comparison to conventional macro-channel heat exchangers, being highly efficient, compact and requiring low fluid mass. However, classical correlations for two-phase flow in macro-channels fail in predicting the heat transfer coefficient in mini-channels. Therefore, new studies are needed in order to provide better knowledge on flow boiling phenomena in confined spaces. The proposed paper presents an experimental study on two-phase vertical flow boiling in mini-channels. The aim of this work is to determine the heat transfer coefficient and to study the pressure drop in a mini-channel heat exchanger (hydraulic diameter of 840μm) in order to obtain better understanding of the flow boiling mechanisms. A vertical upward flow test section is connected to a primary HFE-7100 circuit. A preheater imposes a given sub-cooled fluid temperature or a given two-phase vapour quality at the inlet. Downstream in the test loop, the fluid is condensed and pumped again into the test section. The pressure drop and the heat transfer coefficient in the test section have been measured for a variety of conditions. Different heat flux, inlet vapour quality and mass flow rate values have been tested. For the heat transfer coefficient, a correlating model is proposed as a function of the superficial velocity. This parameter appears to be much more appropriate than the vapour quality or the mass flow rate for dry-out occurrence prediction. A single critical velocity value has been found.

Time-dependent study of boiling heat transfer coefficient in a vertical minichannel

2019 ◽  
Vol 30 (6) ◽  
pp. 2953-2969 ◽  
Author(s):  
Beata Maciejewska ◽  
Magdalena Piasecka
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Heat Exchangers ◽  
Flow Boiling ◽  
Basis Functions ◽  
Time Dependent ◽  
Heated Wall ◽  
Content Type ◽  
Saturated Boiling

Purpose The purpose of this paper is to determine the time-dependent heat transfer coefficient during FC-72 flow boiling in a 1.7-mm-deep vertical and asymmetrically heated minichannel. Design/methodology/approach The temperature of the minichannel heated wall was recorded continuously with the use of thermocouples. The heat transfer coefficients for the subcooled and saturated boiling regions at the heated wall–fluid contact surface were calculated from the Robin boundary condition. Both the wall and fluid temperatures were obtained from the solution of the inverse nonstationary problems in two adjacent domains: the heated wall and flowing fluid. The FEM with Trefftz-type basis functions was applied to solve the inverse problem. Findings The obtained time-dependent heat transfer coefficient in subcooled boiling achieved rather low values, whereas in saturated boiling, the coefficient was the highest at the channel inlet. The boiling curves were plotted to illustrate the results. Practical implications The results of experiments are the best source of information for the design of minichannel cooling systems used for thermoregulation of components and heat exchangers. High-tech minichannel heat exchangers are applied in various industrial applications as microelectronics devices, gas turbines, internal combustion engines, nuclear reactors, X-ray sources and organic rankine cycle (ORC) modules. Originality/value In the study, the Trefftz functions for the nonstationary Fourier–Kirchhoff equation with the factor describing void fraction were determined and then used to construct the time-dependent basis functions in FEM.

scholarly journals The heat transfer and instabilities results during the onset of flow boiling in minichannels

2019 ◽  
Vol 128 ◽  
pp. 01016
Author(s):  
Beata Maciejewska ◽  
Magdalena Piasecka ◽  
Artur Piasecki
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Flow Boiling ◽  
Thin Foil ◽  
Time Dependent ◽  
Flow Boiling Heat Transfer ◽  
Boiling Incipience ◽  
The Heat Transfer Coefficient ◽  
Heated Element

The paper discusses the results of flow boiling heat transfer in minichannels obtained on the basis of time-dependent experiments. The main interest of the work was to investigate the occurrence of the accompanying instabilities during the boiling incipience. The essential part of the experimental standwas a test section with two minichannels, each of 1.7 mm depth. The heated element for FC–72flowing along the minichannels was a thin foil. In the tested minichannel, the temperature of the outer surface of the foil was measured due to thermoelements. The onset of flow boiling in minichannels was induced by increasing the heat flux supplied to the heater. The main aims of the investigation were to determine the heat transfer coefficient by means of the FEM with time—dependent Trefftz–type basis functions based on the Hermite interpolation and to recognize dynamic instabilities during boiling incipience. The results were illustrated as: the heat transfer coefficient, the mass flow rate and the inletpressure versustime and as boiling curves.

Flow Boiling Heat Transfer in a Silicon Microchannel Heat Sink Using Liquid Crystal Thermography

2008 ◽  
Author(s):  
Ayman Megahed ◽  
Ibrahim Hassan ◽  
Tariq Ahmad
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Pressure Drop ◽  
Transfer Coefficient ◽  
Heat Sink ◽  
Boiling Heat Transfer ◽  
Flow Boiling ◽  
Heat Fluxes ◽  
Working Fluid ◽  
Microchannel Heat Sink

The present study focuses on the experimental investigation of boiling heat transfer characteristics and pressure drop in a silicon microchannel heat sink. The microchannel heat sink consists of a rectangular silicon chip in which 45 rectangular microchannels were chemically etched with a depth of 295 μm, width of 254 μm, and a length of 16 mm. Un-encapsulated Thermochromic liquid Crystals (TLC) are used in the present work to enable nonintrusive and high spatial resolution temperature measurements. This measuring technique is used to provide accurate full and local surface-temperature and heat transfer coefficient measurements. Experiments are carried out for mass velocities ranging between 290 to 457 kg/m2.s and heat fluxes from 6.04 to 13.06 W/cm2 using FC-72 as the working fluid. Experimental results show that the pressure drop increases as the exit quality and the flow rate increase. High values of heat transfer coefficient can be obtained at low exit quality (xe < 0.2). However, the heat transfer coefficient decreases sharply and remains almost constant as the quality increases for an exit quality higher than 0.2.

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