Heat and Mass Transfer

, Volume 40, Issue 3–4, pp 253–259 | Cite as

Heat transfer for laminar flow in internally finned pipes with different fin heights and uniform wall temperature

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Abstract.

An analysis is presented for fully developed laminar convective heat transfer in a pipe provided with internal longitudinal fins, and with uniform outside wall temperature. The fins are arranged in two groups of different heights. The governing equations have been solved numerically to obtain the velocity and temperature distributions. The results obtained for different pipe-fins geometries show that the fin heights affect greatly flow and heat transfer characteristics. Reducing the height of one fin group decreases the friction coefficient significantly. At the same time Nusselt number decreases inappreciably so that such reduction is justified. Thus, the use of different fin heights in internally finned pipes enables the enhancement of heat transfer at reasonably low friction coefficient.

Nomenclature

Af

dimensionless flow area of the finned pipe, Eq. (8)

af

flow area of the finned pipe

Cp

specific heat at constant pressure

f

coefficient of friction, Eq. (12)

H1, H2

dimensionless fin height h1/roh2/ro

h1, h2

fin heights

\(\bar h\)

average heat transfer coefficient at solid-fluid interface

KR

fin conductance parameter, βks/kf

kf

thermal conductivity of fluid

ks

thermal conductivity of fin

l

pipe length

ṁ

mass flow rate

N

number of fins

Nu

Nusselt number, Eqs. (15) and (16)

P

pressure

Q

total heat transfer rate at solid fluid interface

Qf1, Qf2

heat transfer rate at fin surface

qw

average heat flux at pipe-wall, Q/(2 πrol)

R

dimensionless radial coordinate r/ro

Re

Reynolds Number, Eq. (13)

r

radial coordinate

ro

radius of pipe

r1, r2

radii of fin tips

T

temperature

Tb

bulk temperature

U

dimensionless velocity, Eq. (2)

Ub

dimensionless bulk velocity

uz

axial velocity

z

axial coordinate

α

angle between the flanks of two adjacent fins

β

half the angle subtended by a fin

γ

angle between the center-lines of two adjacent fins

θ

angular coordinate

μ

dynamic viscosity

ρ

density

ϕ

dimensionless temperature, Eq. (6)

ϕb

dimensionless bulk temperature

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Copyright information

© Springer-Verlag 2004

Authors and Affiliations

  1. 1.Mech. Eng. Dept., King Saud University, P.O. box 800, 11421 Riyadh, Saudi Arabia

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