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Heat and Mass Transfer

, Volume 41, Issue 6, pp 535–544 | Cite as

Thermodynamic optimization of conjugate convection from a finned channel using genetic algorithms

  • Dibakar Rakshit
  • C. BalajiEmail author
Original

Abstract

For the first time, this study reports the results of numerical investigation of conjugate convection from a finned channel. The computational domain of investigation consists of a horizontal channel with vertical rectangular fins being mounted on outside of the channel. The equations governing two-dimensional, steady, incompressible, constant property laminar flow have been solved for the fluid flowing outside the channel. In doing this, Boussinesq assumption is assumed to be valid for the fluid flowing outside the channel along the fins. For the fluid flowing inside the channel, flow is assumed to be turbulent with forced convection as the mode of heat transfer. From a large volume of numerically generated data correlations have been proposed for (1) Nusselt number and (2) Entropy generated by the system. These correlations are finally used to obtain thermodynamic optimum where in we seek a solution with minimum total entropy generation rate for varying heat duties, by using the state-of-the art Genetic algorithms.

Keywords

Heat Transfer Nusselt Number Natural Convection Heat Transfer Rate Entropy Generation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of symbols

Cp

isobaric specific heat capacity (J kg−1 K−1)

\(\bar C_{\text{f}} \)

mean friction coefficient

D

channel spacing (m)

Dh

hydraulic diameter (m)

g

acceleration due to gravity (m s−2, 9.81 m s−2)

Gν

turbulence production (kg m−1 s−2)

H

height of fins

h

heat transfer coefficient of the fluid (Wm−2 K−1)

k

thermal conductivity of fin material (Wm−1 K−1)

L

length of the channel (m)

L/D

aspect ratio

mf

mass flow rate of the inside fluid (kg s−1)

n

number of fins

NuL

Nusselt number on the basis of length of channel

P

pressure (N m−2)

Pr

Prandtl number of fluid outside

Q

total heat transfer (W)

RaL

Rayleigh number, \((g\beta /\nu _o^2 )(T_{{\text{in}}} - T_\infty )L^3 \Pr \)

Re

Reynolds number of the internal flow (ρ uinDhin)

S

fin spacing (m)

Sfluid flow

entropy generation rate due to fluid flow (W K−1)

Sheat

entropy generation rate due to heat transfer (W K−1)

Sgen

total entropy generated by the system (W K−1)

S*gen

non dimensional entropy of the system (Sgen/Sheat)

T

temperature (K)

u

horizontal velocity (ms−1)

v

vertical velocity (ms−1)

W

pumping power due to fluid friction (W)

x

co-ordinate along the length of the channel (m)

x*

non dimensional distance (4xν/D2uin)

y

co-ordinate along the spacing of the channel (m)

Yv

turbulent destruction (kg m−1 s2)

Z

composite objective function

Greek symbols

αi

turbulent thermal diffusivity of the inside fluid (m2 s−1)

β

coefficient of thermal expansion (K−1)

γ

heat transfer per unit mass of the system

ΔT

temperature difference (K)

λ

penalty parameter

μ

dynamic viscosity (kg m−1 s−1)

μt

turbulent viscosity (kg m−1 s−1)

νi

kinematic viscosity (m2 s−1)

νi

turbulent kinematic viscosity of the inside fluid (m2 s−1)

ρ

density (kg m−3)

τ

wall shear stress (N m−2)

\({\bar \nu }\)

transported variable for the inside fluid (m2 s−1)

Subscripts

atm

atmosphere

al

aluminum

b

base temperature

c

critical value of properties

cs

cross sectional

d

design

e

outside

f

fluid

fin

finned

i

interface

in

inlet

s

surface

unfin

unfinned

ambient

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Copyright information

© Springer-Verlag 2004

Authors and Affiliations

  1. 1.Heat Transfer and Thermal Power Laboratory, Department of Mechanical EngineeringIndian Institute of Technology MadrasChennaiIndia

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