Liquid Flow Forced Convection in Rectangular Microchannels With Nonuniform Heating: Toward Analytical Modeling of Hotspots

2020 ◽  
Vol 142 (8) ◽  
Author(s):  
Milad Azari ◽  
Arman Sadeghi ◽  
Morteza Dejam
Keyword(s):  
Heat Flux ◽  
Peclet Number ◽  
Nonuniform Distribution ◽  
Heat Fluxes ◽  
Wall Heat Flux ◽  
Nonuniform Heating ◽  
Rectangular Microchannel ◽  
Péclet Number ◽  
Accurate Design ◽  
Realistic Situation

Abstract The heat generated by microprocessors has an extremely nonuniform spatial distribution with hotspots that have heat fluxes several times larger than the background flux. Hence, for an accurate design of microchannel heat sinks used for cooling of micro-electronic devices, models are required that can take such a nonuniform distribution of wall heat flux into account. In this study, analytical solutions are obtained for hydrodynamically fully developed but thermally developing mixed electro-osmotic and pressure-driven (PD) flow in a rectangular microchannel with a peripherally uniform but axially nonuniform distribution of the wall heat flux. It is assumed that the heat flux is applied over a finite length, to mimic a physically more realistic situation, and the Péclet number is small so that lateral temperature variations are negligible as compared to the axial variations of temperature. By comparing the results with those of full numerical simulations for exponential (EHF), sinusoidal (SHF), and stepwise (STHF) distributions of wall heat flux, it is demonstrated that the solutions obtained are accurate up to a Péclet number of 10. Fortunately, this value is larger than the maximum Péclet number of electro-osmotic microflows. Furthermore, it is shown that smoother distributions of wall heat flux give rise to higher heat transfer rates. The model developed in this study can pave the way for modeling of hotspots in more complicated microfluidic devices.

Heat Transfer of Power Law Fluid at Low Peclet Number Flow

1983 ◽  
Vol 105 (3) ◽  
pp. 542-549 ◽  
Author(s):  
Vi-Duong Dang
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Power Law ◽  
Peclet Number ◽  
Wall Heat Flux ◽  
Power Law Fluid ◽  
Axial Conduction ◽  
Péclet Number ◽  
Constant Wall Heat Flux ◽  
Number Flow

An exact solution is presented for the temperature distribution and local Nusselt number of power law fluid in conduit at low Peclet number flow by considering axial conduction in both the upstream and the downstream regions while keeping the wall at constant temperature. Solutions are also reported for the parallel plate geometry for the aforementioned heat transfer condition and for constant wall heat flux boundary condition. The order of importance of axial conduction is established for different geometries and different boundary conditions. The effect of axial conduction is more significant when power law model index, s, increases for constant wall heat flux case, but the effect changes with Peclet number for constant wall temperature case.

Evaporative Thermal Performance of Vapor Chambers Under Nonuniform Heating Conditions

2008 ◽  
Vol 130 (12) ◽  
Author(s):  
Je-Young Chang ◽  
Ravi S. Prasher ◽  
Suzana Prstic ◽  
P. Cheng ◽  
H. B. Ma
Keyword(s):  
Heat Flux ◽  
Thermal Resistance ◽  
Thermal Performance ◽  
Hot Spots ◽  
Hot Spot ◽  
Heat Fluxes ◽  
Experimental Results ◽  
Nonuniform Heating ◽  
Test Results ◽  
Uniform Heating

This paper reports the test results of vapor chambers using copper post heaters and silicon die heaters. Experiments were conducted to understand the effects of nonuniform heating conditions (hot spots) on the evaporative thermal performance of vapor chambers. In contrast to the copper post heater, which provides ideal heating, a silicon chip package was developed to replicate more realistic heat source boundary conditions of microprocessors. The vapor chambers were tested for hot spot heat fluxes as high as 746 W/cm2. The experimental results show that evaporator thermal resistance is not sensitive to nonuniform heat conditions, i.e., it is the same as in the uniform heating case. In addition, a model was developed to predict the effective thickness of a sintered-wick layer saturated with water at the evaporator. The model assumes that the pore sizes in the sintered particle wick layer are distributed nonuniformly. With an increase of heat flux, liquid in the larger size pores are dried out first, followed by drying of smaller size pores. Statistical analysis of the pore size distribution is used to calculate the fraction of the pores that remain saturated with liquid at a given heat flux condition. The model successfully predicts the experimental results of evaporative thermal resistance of vapor chambers for both uniform and nonuniform heat fluxes.

Analysis of Laminar Slip-Flow Thermal Transport in Microchannels With Transverse Rib and Cavity Structured Superhydrophobic Walls at Constant Heat Flux

2011 ◽  
Author(s):  
D. Maynes ◽  
B. W. Webb ◽  
V. Soloviev
Keyword(s):  
Heat Flux ◽  
Nusselt Number ◽  
Laminar Flow ◽  
Thermal Transport ◽  
Peclet Number ◽  
Average Nusselt Number ◽  
Slip Flow ◽  
Constant Heat Flux ◽  
Constant Heat ◽  
Péclet Number

This paper presents an analytical investigation of the thermally developing and periodically fully-developed flow in a parallel-plate channel comprised of superhydrophobic walls. The superhydrophobic walls considered in this paper exhibit alternating micro-ribs and cavities positioned perpendicular to the flow direction and the transport scenario analyzed is that of constant wall heat flux through the rib surfaces with negligible thermal transport through the vapor cavity interface. Axial conduction is neglected in the analysis and the problem is one of Graetz flow with apparent slip-flow and periodicity of constant heating. Closed form solutions for the local Nusselt number and wall temperature are presented and are in the form of infinite series expansions. Previously it has been shown that significant reductions in the overall frictional pressure drop can be expected relative to the classical smooth channel laminar flow. The present results reveal that the overall thermal transport is markedly influenced by the relative cavity region (cavity fraction), the relative rib/cavity module width, and the flow Peclet number. The following conclusions can be made regarding thermal transport for a constant heat flux channel exhibiting the superhydrophobic surfaces considered: 1) Increases in the cavity fraction lead to decreases in the average Nusselt number; 2) Increasing the relative rib/cavity module length yields a decrease in the average Nusselt number; and 3) as the Peclet number increases the average Nusselt number increases. For all parameters explored, the limiting upper bound on the fully-developed average Nusselt number corresponds to the limiting case scenario of classical laminar flow through a smooth-walled channel with constant heat flux.

Experimental Study of a Single Microchannel Flow Under Nonuniform Heat Flux

2019 ◽  
Vol 12 (1) ◽  
Author(s):  
Ahmed Eltaweel ◽  
Ibrahim Hassan
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Heat Dissipation ◽  
Hot Spot ◽  
Management Strategies ◽  
Heat Fluxes ◽  
Heat Sinks ◽  
Nonuniform Heating ◽  
Maximum Heat ◽  
Microchannel Heat Sinks

Abstract Nonuniform heat fluxes are commonly observed in thermo-electronic devices that require distinct thermal management strategies for effective heat dissipation and robust performance. The limited research available on nonuniform heat fluxes focus mostly on microchannel heat sinks while the fundamental component, i.e., a single microchannel, has received restricted attention. In this work, an experimental setup for the analysis of variable axial heat flux is used to study the heat transfer in a single microchannel with fully developed flow under the effect of different heat flux profiles. Initially, a hot spot at different locations, with a uniform background heat flux, is studied at different Reynolds numbers, while varying the maximum heat fluxes in order to compute the heat transfer in relation to its dependent variables. Measurements of temperature, pressure, and flow rates at a different locations and magnitudes of hot spot heat fluxes are presented, followed by a detailed analysis of heat transfer characteristics of a single microchannel under nonuniform heating. Results showed that upstream hotspots have lower tube temperatures compared to downstream ones with equal amounts of heat fluxes. This finding can be of importance in enhancing microchannel heat sinks effectiveness in reducing maximum wall temperatures for the same amount of heat released, by redistributing spatially fluxes in a descending profile.

scholarly journals High-frequency wall heat flux measurement during wall impingement of a diffusion flame

2019 ◽  
pp. 146808741987804
Author(s):  
Julien Moussou ◽  
Guillaume Pilla ◽  
Julien Sotton ◽  
Marc Bellenoue ◽  
Fabien Rabeau
Keyword(s):  
Heat Flux ◽  
Time Resolution ◽  
Diffusion Flame ◽  
Internal Combustion Engines ◽  
Injection Pressure ◽  
Flux Measurement ◽  
Heat Fluxes ◽  
Wall Heat Flux ◽  
Gas Temperature ◽  
Thermal Exchange

The efficiency of internal combustion engines is limited by heat losses to the wall of the combustion chamber. A precise characterization of wall heat flux is therefore needed to optimize engine parameters. However, the existing measurements of wall heat fluxes have significant limitations; time resolution is often higher than the timescales of the physical phenomena of flame–wall interaction. Furthermore, few studies have investigated diesel flame conditions (as opposed to propagation flames). In this study, the heat flux generated by a diffusion flame impinging on a wall was measured with thin-junction thermocouple, with a time resolution of the whole acquisition chain better than 0.1 ms. The effects of variations in ambient gas temperature, injection pressure and injector–wall distance were investigated. Diesel spray impingement on the wall is shown to cause strong gas–wall thermal exchange, with convection coefficients of 6–12 kW/m2/K. Those results suggest the necessity of close-wall aerodynamic measurements to link macroscopic characteristics of the spray (injection pressure, impingement geometry) to turbulence values.

Measurements of Burnout Conditions for Flow of Boiling Water in a Vertical Annulus

1964 ◽  
Vol 86 (3) ◽  
pp. 393-404 ◽  
Author(s):  
K. M. Becker ◽  
G. Hernborg
Keyword(s):  
Heat Flux ◽  
Surface Heat Flux ◽  
Flow Model ◽  
Film Flow ◽  
Surface Heat ◽  
Heat Fluxes ◽  
Nonuniform Heating ◽  
Steam Quality ◽  
Internal Heating ◽  
Inner Surface

The present paper deals with measurements of burnout conditions for flow of boiling water in an annulus with an inner diameter of 9.92 mm, an outer diameter of 17.42 mm, and a heated length of 608 mm. Data were obtained in respect of external heating only, internal heating only, and dual uniform and nonuniform heating. The following ranges of variables were studied and 978 burnout measurements were obtained. Pressure: 8.5 < p < 37.5 kg/cm2; Inlet subcooling: 60 < Δtsub < 205 deg C; Steam quality: 0.10 < x < 0.91; Inner surface heat flux: 0 < (q/A)i < 303 W/cm2; Outer surface heat flux: 0 < (q/A)0 < 374 W/cm2; Mass velocity: 71 < m˙/F < 961 kg/m2sec. The results are presented in diagrams where the burnout steam qualities, xBO, were plotted against the pressure with the surface heat fluxes as parameters. The data have been correlated by curves. The scatter of the data around the curves is less than ±5 percent. In the case of equal heat fluxes on both walls of the annulus, burnout always occurred on the inner wall, and the data compared rather well with round duct data. When the annulus was heated internally only, the data showed very low burnout values in comparison with the results for dual heating and round ducts. This disagreement was explained by considering the climbing film flow model and by the fact that only a fraction of the channel perimeter was heated. For external heating the data are somewhat lower than corresponding round duct data, but rather high in comparison with internal heating. The climbing film flow model was also used to interpret this observation. For dual nonuniform heating it was found that the outer surface may be overloaded from 30 to 70 percent compared with the inner surface without reducing the margin of safety in respect to burnout for the annulus. It was further observed that when the heat flux for the wall on which burnout occurs is increased, the burnout steam quality for the channel decreases. If, however, the heat flux for the opposite wall is increased, the burnout steam quality also increases. It was also observed that the highest burnout values are obtained when burnout occurs simultaneously on both cylinders. Finally, the results have been compared with annuli and rod cluster data in published works, and a method for predicting burnout conditions in rod clusters has been proposed.

Rewetting of an Infinite Slab With Uniform Heating Under Quasi-Steady Conditions

2002 ◽  
Vol 124 (5) ◽  
pp. 875-880 ◽  
Author(s):  
A. K. Satapathy ◽  
R. K. Sahoo
Keyword(s):  
Heat Flux ◽  
Peclet Number ◽  
Constant Heat Flux ◽  
Model Parameters ◽  
Péclet Number ◽  
Infinite Slab ◽  
Hot Surface ◽  
Minimum Heat ◽  
Dimensionless Heat Flux ◽  
Dimensionless Heat

The two-dimensional quasi-steady conduction equation governing conduction controlled rewetting of an infinite slab, with one side flooded and the other side subjected to a constant heat flux, has been solved by Wiener-Hopf technique. The solution yields the quench front temperature as a function of various model parameters such as Peclet number, Biot number and dimensionless heat flux. Also, the critical (dryout) heat flux is obtained by setting the Peclet number equal to zero, which gives the minimum heat flux required to prevent the hot surface being rewetted.

Characteristics of the Dimensionless Temperature in Tubes With Axial Wall Heat Conduction

2017 ◽  
Author(s):  
Mei Lin ◽  
Shi-cong Li ◽  
Xue-fang Xu ◽  
Qiu-wang Wang
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Peclet Number ◽  
Circular Tube ◽  
Working Fluid ◽  
Dimensionless Temperature ◽  
Uniform Heat Flux ◽  
Wall Surface ◽  
Péclet Number ◽  
Inner Diameter

Characteristics of the dimensionless temperature, θ, are performed to investigate in laminar circular tube flow by numerical simulation with the presence of axial heat conduction. A uniform heat flux is imposed on outside wall surface. The smallest inner diameter of circular tube is only 200 μm. The heat transfer and flow can be described by traditional Navier-Stokes and energy equations. The results shows that θ is identical under the condition of different specified heat flux on the outside wall surface at the same Peclet number. Furthermore, the dimensionless temperature at the tube entrance θ(0) is independent on wall thickness, tube material, working fluid and boundary condition. Hence, the dimensionless temperature at the tube entrance θ(0) is only a function of Peclet number and the corresponding correlation of θ(0) in circular tube is obtained from numerical results and validated by other available cases. Moreover, the correlation of θ(0) is also applied with different cross-sectional shapes of heated solid surface when inner diameter of fluid region is not less than 2.0 mm.

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