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Effect of conjugate heat transfer in single-phase laminar flow through partially heated microtubes

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Abstract

To analyze conjugate effect under partially heated condition, two-dimensional numerical study is performed for single-phase laminar flow through microtubes. Constant heat flux is applied on outer surface along the heating length of the microtube. For partial heating, the microtube is divided into three parts of 6 mm (L1), 48 mm (L2) and 6 mm (L3). Three cases are considered for partial heating: (a) insulated across L1 and L3 and heating across L2, (b) insulated across L1 and heating across L2 and L3 and (c) insulated across L3 and heating across L1 and L2. For direct comparison, heating across full length of the microtube is also considered. Parametric variations include microtube wall thickness to inner radius ratio (δsf), and solid to fluid conductivity, ratio (ksf) and flow Re. Presence of axial wall conduction is assessed in terms of dimensionless wall temperature and heat flux at the solid–fluid interface, dimensionless bulk fluid temperature, and local and average Nusselt number. The results indicate that there exists an optimal value of average Nusselt number for certain value of ksf at which dominance of axial wall conduction is smaller. Additionally, to highlight the effect of axial wall conduction, local heat flux distribution at the solid–fluid interface is also explored.

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Abbreviations

c p :

Specific heat of fluid, J/kgK

D i :

Inner diameter of microtube, m

D o :

Outer diameter of microtube, m

h z :

Local heat transfer coefficient, W/m2K

k s :

Solid thermal conductivity, W/mK

k f :

Fluid thermal conductivity, W/mK

k sf :

Ratio of ks to kf

L :

Total length of tube, m

Nuz :

Local Nusselt number

Nuavg :

Average Nusselt number

Pr:

Prandtl number

\({\text{q}}_{{{\text{applied}}}}^{^{\prime\prime}}\) :

Heat flux applied on the outer surface of the microtube, W/m2

\({\text{q}}_{{{\text{interface}}}}^{^{\prime\prime}}\) :

Actual heat flux experienced at the solid–fluid interface of the microtube, W/m2

\({\text{q}}_{{\text{i}}}^{^{\prime\prime}}\) :

Ideal heat flux experienced at the solid–fluid interface of the microtube, W/m2

r i :

Inner radius of microtube, m

r o :

Outer radius of microtube, m

Re:

Reynolds number

T :

Temperature, K

u :

Velocity in the axial direction, m/s

ū :

Average velocity at inlet, m/s

z :

Axial coordinate, m

z * :

Non-dimensional axial coordinate

δ f :

Inner radius of the tube, m

δ s :

Thickness of the tube wall, m

δ sf :

Ratio of δs to δf (–)

∂:

Differential parameter

µ :

Dynamic viscosity, Pa-s

ρ :

Density, kg/m3

ϕ :

Non-dimensional local heat flux (–)

Θ :

Non-dimensional temperature (–)

f:

Fluid

i:

Inner surface of tube

o:

Outer surface of tube

s:

Solid

w:

Outer wall surface of tube

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Authors and Affiliations

  1. School of Mechanical Engineering, Vellore Institute of Technology, Vellore, India

    Nishant Tiwari

  2. Department of Mechanical Engineering, National Institute of Technology Rourkela, Rourkela, 769008, India

    Manoj Kumar Moharana

Authors
  1. Nishant Tiwari
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  2. Manoj Kumar Moharana
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Correspondence to Nishant Tiwari.

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Tiwari, N., Moharana, M.K. Effect of conjugate heat transfer in single-phase laminar flow through partially heated microtubes. Sādhanā 46, 28 (2021). https://doi.org/10.1007/s12046-021-01561-z

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  • DOI: https://doi.org/10.1007/s12046-021-01561-z

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