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Research Papers: Forced Convection

The Role of the Shear Work in Microtube Convective Heat Transfer: A Comparative Study

[+] Author and Article Information
K. Ramadan

Department of Mechanical Engineering,
Mu'tah University,
P. O. Box 7,
Karak 61710, Jordan
e-mail: rkhalid@mutah.edu.jo

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received December 28, 2013; final manuscript received May 6, 2015; published online August 11, 2015. Assoc. Editor: Sujoy Kumar Saha.

J. Heat Transfer 138(1), 011701 (Aug 11, 2015) (11 pages) Paper No: HT-13-1674; doi: 10.1115/1.4031107 History: Received December 28, 2013

Convective heat transfer of a thermally developing rarefied gas flow in a microtube with boundary shear work, viscous dissipation, and axial conduction is analyzed numerically for both constant wall temperature (CWT) and constant wall heat flux (CHF) boundary conditions. Analytical solutions for the fully developed flow conditions including the boundary shear work are also derived. The proper thermal boundary condition considering the sliding friction at the wall for the CHF case is implemented. The sliding friction is also included in the calculation of the wall heat flux for the CWT case. A comparative study is performed to quantify the effect of the shear work on heat transfer in the entrance—and the fully developed—regions for both gas cooling and heating. Results are presented in both graphical and tabular forms for a range of problem parameters. The results show that the effect of shear work on heat transfer is considerable and it increases with increasing both the Knudsen number and Brinkman number. Neglecting the shear work in a microtube slip flow leads to over- or underestimating the Nusselt number considerably. In particular, for the CWT case with fully developed conditions, the contribution of the shear work to heat transfer can be around 45% in the vicinity of the upper limit of the slip flow regime, regardless of how small the nonzero Brinkman number can be.

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Figures

Grahic Jump Location
Fig. 2

Variation of Nusselt number with Peclet number in the entrance region for both CWT and CHF conditions: verification of the numerical solution method

Grahic Jump Location
Fig. 3

Effect of shear work on the fully developed Nusselt number as a function of the Knudsen number for CWT boundary condition

Grahic Jump Location
Fig. 4

Variation of the Nusselt number with Knudsen number in the entrance region at low Peclet number (Pe = 1) and gas cooling (BrT = 0.2) for CWT condition

Grahic Jump Location
Fig. 5

Variation of the Nusselt number with Knudsen number in the entrance region at Peclet number (Pe = 1000) and gas cooling (BrT = 0.2) for CWT condition

Grahic Jump Location
Fig. 6

Variation of the Nusselt number with Brinkman number in the entrance region for gas heating with CWT condition and Kn = 0.05, Pe = 1000

Grahic Jump Location
Fig. 7

Variation of the gas mean temperature in the entrance region for gas heating with CWT condition

Grahic Jump Location
Fig. 8

Variation of the Nusselt number with Brinkman number in the entrance region for CWT condition with Kn = 0.05, Pe = 100

Grahic Jump Location
Fig. 9

Variation of the Nusselt number with Peclet number in the entrance region for Kn = 0.01 and gas cooling (BrT = 0.1) with CWT condition

Grahic Jump Location
Fig. 10

Variation of the fully developed Nusselt number with Knudsen number for gas cooling and heating with CHF boundary condition

Grahic Jump Location
Fig. 11

Variation of the fully developed Nusselt number with Brinkman number for gas cooling and heating with CHF boundary condition

Grahic Jump Location
Fig. 12

Variation of Nusselt number with Peclet number in the entrance region for gas heating with CHF boundary condition

Grahic Jump Location
Fig. 13

Variation of Nusselt number with Peclet number in the entrance region for gas cooling with CHF boundary condition

Grahic Jump Location
Fig. 14

Variation of Nusselt number with Knudsen number in the entrance region for gas heating with CHF boundary condition

Grahic Jump Location
Fig. 15

Variation of Nusselt number with Knudsen number in the entrance region for gas heating with CHF boundary condition

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