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Effect of Density Variation on Rarefied and Non-rarefied Gaseous Flows in Developing Region of Microtubes

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Abstract

The present study analyzes the rarefaction and non-rarefaction effects on heat transfer characteristics of hydrodynamically and thermally developing air flow through microtubes having a constant wall heat flux boundary condition. The problem is especially simulated with two microtubes having diameters 50 µm and 150 µm. The rarefaction effect is taken into consideration using Maxwell slip flow and temperature jump boundary conditions. The fluid property variation is considered as a non-rarefaction effect which plays a significant influence on convection through a microtube. It is observed that the rarefaction and non-rarefaction effects significantly affect the convective heat transfer. The non-rarefaction effect decreases the Nusselt number (Nu) as compared to constant property solution; however, the rarefaction effect increases the Nu compared to constant property solution.

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Abbreviations

A :

Cross-sectional area of the microtube

c :

Velocity of sound \(\left( {\sqrt {\gamma \cdot R \cdot T_{\text{m}} } } \right)\) (m s−1)

D :

Diameter of microtube (m)

k :

Thermal conductivity of the fluid (W m−1 K−1)

L :

Length of microtube (m)

\(q_{\text{w}}^{\prime \prime }\) :

Heat flux at wall (W m−2)

T w :

Wall temperature (K)

T m :

Bulk mean fluid temperature (K)

u m :

Mean axial velocity (m s−1)

v :

Radial velocity (m s−1)

T(r):

Temperature profile in radial direction

u(r):

Radial profile of axial velocity

v(r):

Radial profile of radial velocity

ρ(p, T):

Pressure- and temperature-dependent density (kg m−3)

ρ(T):

Temperature-dependent density (kg m−3)

µ :

Dynamic viscosity of the fluid (kg m−1 s−1)

γ :

Specific heat ratio

Kn:

Knudsen number (λ/D)

Ma:

Mach number (um/c)

Nu:

Nusselt number (h·D/km)

Po:

Poiseuille number (f·ReD)

Re:

Reynolds number (ρm·um·D/μm)

CP:

Constant properties

D:

Diameter

ex:

Value at outlet

in:

Value at inlet

m:

Mean value of properties calculated at bulk mean temperature (Tm)

VP:

Variable properties

w:

Condition at wall

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Acknowledgements

The authors thank the seed grant research project no. IITM/SG/SPM/28 of Indian Institute of Technology (IIT) Mandi, Himachal Pradesh. The authors are grateful to IIT Bombay for granting deputation (in public interest) to Prof. Shripad P. Mahulikar at IIT Mandi from June 1, 2013, to December 31, 2014, vide Office Order no. Admn-I/246/2013. The authors are grateful to Dr. Syed Abbas, Assistant Professor, School of Basic Sciences, IIT Mandi, India, for the administrative support.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Dr. B R Ambedkar National Institute of Technology, Jalandhar, Punjab, 144001, India

    Rajan Kumar

  2. Department of Aerospace Engineering, Indian Institute of Technology Bombay, P.O. IIT Powai, Mumbai, 400076, India

    Shripad P. Mahulikar

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  1. Rajan Kumar
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Correspondence to Rajan Kumar.

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Kumar, R., Mahulikar, S.P. Effect of Density Variation on Rarefied and Non-rarefied Gaseous Flows in Developing Region of Microtubes. Iran J Sci Technol Trans Mech Eng 45, 415–425 (2021). https://doi.org/10.1007/s40997-020-00347-8

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  • DOI: https://doi.org/10.1007/s40997-020-00347-8

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