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Parametric analysis of axial wall conduction in a microtube subjected to two classical thermal boundary conditions

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Abstract

Heat transfer in laminar flow microtube is numerically explored with an objective of discriminating conjugate heat transfer process experienced in a microtube under two different thermal conditions. Two classical thermal conditions – constant heat flux and constant wall temperature – are imposed separately on the outer surface of a microtube. Wide parametric variations are considered in this study, for the two thermal conditions, albeit the problem under consideration being very classical from both geometry and thermal condition point of view. The parametric variations considered in this work include wall thickness, wall conductivity and coolant flow rate. An expression for Nusselt number in terms of radial (or transverse) and axial conduction number is presented and validated against existing theoretical correlation as well as reported experimental data for both circular and non-circular channels. Dominance of axial conduction over radial (or transverse) conduction is explored and it is found that the effect of wall material on conjugate heat transfer plays an important role. Additionally, it is also observed that with the increase in coolant flow rate, the ratio of radial to axial conduction number increases for both thermal boundary conditions.

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Abbreviations

A cf :

cross-sectional area of fluid domain, m2

A cs :

cross-sectional area of solid wall, m2

A surf :

surface area of solid–fluid interface, m2

c p :

specific heat of fluid, J/kgK

D :

inner 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

M :

conduction number in axial direction

Nu z :

local Nusselt number

Nu avg :

average Nusselt number

P :

parameter for axial conduction

Pr :

Prandtl number

q′′:

constant wall heat flux, W/m2

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

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

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

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

Q cond,|| :

conduction heat transfer in axial direction, W

Q cond,⊥ :

conduction heat transfer in radial/transverse direction, W

Q conv :

convective heat transfer, W

q w :

wall heat flux, W/m2

R :

conduction number in radial/transverse direction (–)

Re :

Reynolds number

R cond,|| :

conduction thermal resistance in axial direction, K/W

R cond,⊥ :

conduction thermal resistance in radial/transverse direction, K/W

R conv :

convective thermal resistance, K/W

R total :

total thermal resistance, K/W

r i :

inner radius of microtube, m

r o :

outer radius of microtube, m

T :

constant wall temperature, K

\({\bar{T}}_a\) :

average temperature of the surface when the thermal condition is imposed, K

\({\bar{T}}_f\) :

average temperature of the bulk, K

T b :

bulk temperature, K

\({\bar{T}}_i\) :

average temperature of the solid–fluid interface, K

T w :

wall temperature, K

T w, in :

wall temperature at the inlet cross-section, K

T w, out :

wall temperature at the outlet cross-section, K

U :

fluid velocity in the axial direction, m/s

Ū :

average fluid 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 (ro–ri), m

δ sf :

ratio of δs to δf

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 :

tube outer surface/wall

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Authors and Affiliations

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

    Nishant Tiwari & Manoj Kumar Moharana

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

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Tiwari, N., Moharana, M.K. Parametric analysis of axial wall conduction in a microtube subjected to two classical thermal boundary conditions. Sādhanā 44, 170 (2019). https://doi.org/10.1007/s12046-019-1151-8

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