Effect of axial conduction on heat transfer in a rectangular microchannel with local heat flux

Abstract

Based on the continuum assumption and Navier-Stokes equation, three-dimensional fluid flow and conjugate heat transfer in heat sinks with rectangle microchannels have been studied by numerical simulation. The validation of this approach has been demonstrated by comparisons with analytical solutions. Results were obtained for the detailed description of the local and average heat transfer characteristics including wall and fluid temperatures, heat flux, Nusselt number (Nu). Effects of the Peclet number (Pe), the relative conductivity (k w /k f ) and the relative thickness (W/D) of solid substrate were presented and discussed. At low Pe flow, axial conduction dominates the heat transfer, which results in a large upstream region which is pre-warmed by axial conduction, so axial conduction cannot be neglected at small Pe. The increase of Pe induces an enhancement of convection, the heat exchange mainly happens on heat region by convection under this condition. A more uniform streamwise temperature distribution at fluid-solid interface indicates the enhancement of the pre-warmed effect along with the increase of k w /k f . The study also reveals that the Nu x of low k w /k f material is higher than the Nu x of high k w /k f material. The increase of wall thickness has an effect on axial distribution of the Nu x , the trend is similar to that of an increase of the wall thermal conductivity k w /k f . It was concluded that the average Nusselt number is proportional to thermal conductivity of the wall. For low Pe, the fluid is heated by the wall by means of convection on heat region, when Pe ≤ 1, a slight increase of the Nu on heat region is shown as the increase of Pe. When Pe > 10, the convection is the dominant factor in heat transfer, an obvious increase of Nu is shown with increase of Pe. For high Pe flow, the heat transfer enhancement as increase of Pe is weak. KeywordsNomenclature a thermal diffusivity, m 2 .s A wall cross-sectional area of the microchannel, m 2

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“…Cole et al [ 100 ] found that the effect of axial heat conduction in the channel wall is significant under the following conditions: (i) when the microchannel has a small length-over-height ratio; (ii) when the Peclet ( Pe ) number is small; (iii) when the wall thickness relative to the channel height is large; and (iv) when the wall conductivity of the wall material is high relative to the thermal conductivity of the fluid. Yu et al [ 101 ] also found that axial heat conduction dominated the heat transfer process in low Pe number flows. With the increase of the Pe number, the influence of axial heat conduction gradually decreased until the convective heat transfer was completely dominated.…”

Strain tunable band structure of a new 2D carbon allotrope C568

“…However, axial heat conduction should be considered when Re > 150 and M > 0.01. In addition, the effect of axial heat conduction is neglected in the studies of Cole and Cetin 96 and Yu et al 97 for high Pe number values (Pe > 100). Cole and Cetin 96 also stated that the thermal conductivity of the wall should be lower than the thermal conductivity of the fluid to neglect axial conduction.…”

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“…However, axial heat conduction should be considered when Re > 150 and M > 0.01. In addition, the effect of axial heat conduction is neglected in the studies of Cole and Cetin 96 and Yu et al 97 for high Pe number values ( Pe > 100). Cole and Cetin 96 also stated that the thermal conductivity of the wall should be lower than the thermal conductivity of the fluid to neglect axial conduction.…”