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Forced Convection

Optimum Nusselt Number for Simultaneously Developing Internal Flow Under Conjugate Conditions in a Square Microchannel

[+] Author and Article Information
Manoj Kumar Moharana, Piyush Kumar Singh

Department of Mechanical Engineering,  Indian Institute of Technology Kanpur, Kanpur, UP 208016, Indiasamkhan@iitk.ac.in

Sameer Khandekar1

Department of Mechanical Engineering,  Indian Institute of Technology Kanpur, Kanpur, UP 208016, Indiasamkhan@iitk.ac.in

It is to be noted here that Zhang et al.  [14] used the axial conduction number as revised by Li et al.  [13], i.e., Eq. 4.

1

Corresponding author.

J. Heat Transfer 134(7), 071703 (May 22, 2012) (10 pages) doi:10.1115/1.4006110 History: Received May 26, 2011; Revised December 20, 2011; Published May 22, 2012; Online May 22, 2012

A numerical study has been carried out to understand and highlight the effects of axial wall conduction in a conjugate heat transfer situation involving simultaneously developing laminar flow and heat transfer in a square microchannel with constant flux boundary condition imposed on bottom of the substrate wall. All the remaining walls of the substrate exposed to the surroundings are kept adiabatic. Simulations have been carried out for a wide range of substrate wall to fluid conductivity ratio (ksf  ∼ 0.17–703), substrate thickness to channel depth (δsf  ∼ 1–24), and flow rate (Re ∼ 100–1000). These parametric variations cover the typical range of applications encountered in microfluids/microscale heat transfer domains. The results show that the conductivity ratio, ksf is the key factor in affecting the extent of axial conduction on the heat transport characteristics at the fluid–solid interface. Higher ksf leads to severe axial back conduction, thus decreasing the average Nusselt number (Nu¯). Very low ksf leads to a situation which is qualitatively similar to the case of zero-thickness substrate with constant heat flux applied to only one side, all the three remaining sides being kept adiabatic; this again leads to lower the average Nusselt number (Nu¯). Between these two asymptotic limits of ksf , it is shown that, all other parameters remaining the same (δsf and Re), there exists an optimum value of ksf which maximizes the average Nusselt number (Nu¯). Such a phenomenon also exists for the case of circular microtubes.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 4

Axial variation of dimensionless peripheral averaged local wall temperature and bulk fluid temperature

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Figure 5

Axial variation of local Nusselt number, Nuz , for the range of simulation parameters

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Figure 6

Variation of average Nusselt number of the square microchannel as a function of conductivity ratio, ksf ; the thickness ratio (δsf ) and flow condition (Re) are varied

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Figure 7

Peripheral variation of dimensionless heat flux at a section in X-Y plane, midway along the length of the substrate (z = 60 mm or z* = 0.256) with varying conductivity ratio, ksf when, (a) Re = 100, δsf  = 1, (b) Re = 100, δsf  = 16, and (c) isotherms corresponding to Re = 100, δsf  = 1, and (i) ksf  = 0.8 and (ii) ksf  = 635

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Figure 8

Axial temperature distribution across the vertical plane of symmetry (Y-Z plane) showing isotherms in fluid and solid domain for different values of conductivity ratio, ksf (a) Re = 100, δsf  = 1, (b) Re = 100, δsf  = 16. Detailing, as done in (a)–(i) is applicable to all figures

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Figure 9

Average Nusselt number of a circular microtube as a function of conductivity ratio ksf ; the thickness ratio (δsf  = tube wall thickness/inner diameter) and flow condition (Re) are varied

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Figure 1

Details of the simulated domain: (a) Microchannel with conductive wall, (b) channel cross section, (c) the computational domain (chosen from symmetry conditions), and (d) transverse section (Y-Z) plane along the plane of symmetry

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Figure 2

Local Nusselt number as a function of dimensionless axial distance for different grids used to establish grid independence at δsf  = 1 and Re = 100

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Figure 3

Axial variation of dimensionless local surface heat flux at the fluid–solid interface

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