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Viscous dissipation effect on heat transfer characteristics of rectangular microchannels under slip flow regime and H1 boundary conditions

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Abstract

Viscous dissipation effect on heat transfer characteristics of a rectangular microchannel is studied. Flow is governed by the Navier–Stokes equations with the slip flow and temperature jump boundary conditions. Integral transform technique is applied to derive the temperature distribution and Nusselt number. The velocity distribution is taken from literature. The solution method is verified for the case where viscous dissipation is neglected. It is found that, the viscous dissipation is negligible for gas flows in microchannels, since the contribution of this effect on Nu number is about 1%. However, this effect should be taken into account for much more viscous flows, such as liquid flows. Neglecting this effect for a flat microchannel with an aspect ratio of 0.1 for Br=0.04 underestimates the Nu number about 5%.

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Abbreviations

a :

long side of microchannel

A n :

constant defined by Eq. 25

b :

short side of microchannel

b 1, b 2, b 3 :

constants defined by Eqs. 22, 23, 24

B n :

constant defined by Eq. 26

Br :

Brinkman number

c P :

specific heat

C n :

constant defined by Eq. 42

C ′1,n , C ′2,n , C ′3,n , C ′4,n , C ′5,n , C ′6,n , C ′7,n :

constants defined by Eqs. 46, 47, 48, 49, 50, 51, 52

C 1,n , C 2,n , C 3,n , C 4,n :

constants defined by Eqs. 53, 54, 55, 56

D h :

hydraulic diameter

D n :

constant defined by Eq. 75

E n :

constant defined by Eq. 44

F t :

thermal accommodation coefficient

F v :

tangential momentum accommodation coefficient

G :

constant defined by Eq. 43

k :

thermal conductivity

k 1, k 2,...,k 14 :

constants defined in Eqs. 60, 61, 62, 63, 64, 65 and Eqs. 67, 68, 69, 70, 71, 72, 73, 74

K :

Kernel

Kn :

Knudsen number

Nu :

Nusselt number

p :

fluid pressure

P :

normalized pressure gradient

Pr :

Prandtl number

q :

heat flux

R :

specific heat ratio

S 1, S 2, S 3, S 4 :

constants introduced for simplicity

T :

temperature

\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{T}\) :

nondimensional temperature

u :

fluid velocity

\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{u}\) :

nondimensional fluid velocity

x, y, z :

nondimensional coordinates

γ:

aspect ratio

λmfp :

molecular mean free path

μ:

eigenvalues

ρ:

density

θ:

dependent variable defined by Eq. 34

\(\bar{\theta}\) :

transformed dependent variable defined by Eq. 39

ξ, η, ζ:

coordinates

b:

bulk property

m:

mean value

n :

index

s :

fluid property near the wall

w:

wall value

0:

inlet property

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Authors and Affiliations

  1. Department of Mechanical Engineering, School of Engineering and Architecture, Yeditepe University, 26 Agustos Yerlesimi, Kayisdagi Caddesi, 81120, Kayisdagi, Istanbul, Turkey

    Tolga N. Aynur & Nilüfer Eğrican

  2. Mechanical Engineering Department, Istanbul Technical University, 80191, Gumussuyu, Istanbul, Turkey

    Lütfullah Kuddusi

Authors
  1. Tolga N. Aynur
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  2. Lütfullah Kuddusi
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  3. Nilüfer Eğrican
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Correspondence to Tolga N. Aynur.

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Aynur, T.N., Kuddusi, L. & Eğrican, N. Viscous dissipation effect on heat transfer characteristics of rectangular microchannels under slip flow regime and H1 boundary conditions. Heat Mass Transfer 42, 1093–1101 (2006). https://doi.org/10.1007/s00231-005-0075-5

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  • DOI: https://doi.org/10.1007/s00231-005-0075-5

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