Heat and Mass Transfer

, Volume 42, Issue 12, pp 1093–1101

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

  • Tolga N. Aynur
  • Lütfullah Kuddusi
  • Nilüfer Eğrican
Original

DOI: 10.1007/s00231-005-0075-5

Cite this article as:
Aynur, T.N., Kuddusi, L. & Eğrican, N. Heat Mass Transfer (2006) 42: 1093. doi:10.1007/s00231-005-0075-5

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%.

List of symbols

a

long side of microchannel

An

constant defined by Eq. 25

b

short side of microchannel

b1, b2, b3

constants defined by Eqs. 22, 23, 24

Bn

constant defined by Eq. 26

Br

Brinkman number

cP

specific heat

Cn

constant defined by Eq. 42

C1,n, C2,n, C3,n, C4,n, C5,n, C6,n, C7,n

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

C1,n, C2,n, C3,n, C4,n

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

Dh

hydraulic diameter

Dn

constant defined by Eq. 75

En

constant defined by Eq. 44

Ft

thermal accommodation coefficient

Fv

tangential momentum accommodation coefficient

G

constant defined by Eq. 43

k

thermal conductivity

k1, k2,...,k14

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

S1, S2, S3, S4

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

Greek symbols

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

Subscripts

b

bulk property

m

mean value

n

index

s

fluid property near the wall

w

wall value

0

inlet property

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  • Tolga N. Aynur
    • 1
  • Lütfullah Kuddusi
    • 2
  • Nilüfer Eğrican
    • 1
  1. 1.Department of Mechanical Engineering, School of Engineering and ArchitectureYeditepe UniversityKayisdagi, IstanbulTurkey
  2. 2.Mechanical Engineering DepartmentIstanbul Technical UniversityGumussuyu, IstanbulTurkey