Convective Heat Transfer Project

8/13/2019 Convective Heat Transfer Project

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Abstract

The Second law characteristics of heat transfer and fluid flow due to forced

convection of steady laminar flow of incompressible fluid inside channel with

circular cross section and channel made of two parallel plate is analysed. Different

problems are analysed with respective entropy generation profiles and heat transferirreversibility characteristics. In each case analytical expression for entropy

generation number(Ns) and e!an number(e) are derived in dimensionless forms

using velocity and temperature profiles.

Introduction

The foundation of "nowledge of entropy production goes bac" to #lausius and

$elvin%s studies on the irreversible aspects of the second law of thermodynamics.

Since then the theories based on these foundations have rapidly developed

however the entropy production resulting from temperature differences has remind

untreated by classical thermodynamics & which motivates many researchers toconduct analysis of fundamental and applied engineering problems based on

second law (of thermodynamics). 'ntropy generation is associated with

thermodynamics irreversibility& which is common in all types of heat transfer

process. Different sources are responsible for generation of entropy li"e heat

transfer across finite temperature gradient& characteristics of convective heart

transfer & viscous effect etc.. e!an focused on the different reason for the entropy

generation in applied thermal engineering. eneration of entropy destroys available

wor" of a system. Therefore it ma"es good engineering sense to focus on

irreversibility of heat transfer and fluid flow processes and try to understand the

function of entropy generation mechanism. Second law analysis focusing onentropy generation and its minimiation has been paying a luminant role in recent

times to understand the irreversibility in applied engineering and transport process.

*luid flow and heat transfer characteristics inside a channel with circular cross+

section and a channel made of two parallel plates at different boundary conditions

is one of the fundamental researches in engineering. ,nalyses of simple system are

often useful to understand some important features of complex patterns forming

processes in various fields of science and technology. This type of geometry appears

in many engineering application as single unit or as a combination. e!an presented

simplified analytical expression for entropy generation rate in a circular duct with

constant heat flux at the wall. This analysis is then extended by calculatingoptimum -eynolds number as a function of prandtl%s number and duty parameter.

*urther extension is done by Sahin who introduced the second law analysis of

viscous fluid in a circular duct at isothermal boundary condition. Sahin again

presented the effect of variable viscosity on entropy generation rate for constant

heat flux boundary condition for circular duct.


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The main ob!ect of this article is to analye the mechanism of entropy generation in

basic configuration encountered in convective heat transfer in this article we see"

to identify the origin of entropy production and its distribution through fluid flows

most commonly found in convective heat transfer situation. 'ight different types of

problems are selected in the present study and analysed. These are forced

convection inside a channel with

/. 0ne fixed plate and one moving plate&

1. Two fixed plate &

2. #ircular cross+section for Newtonian fluid&

3. #ircular annulus&

4. ,xially moving concentric cylinder&

5. -otating concentric cylinder&

6. #ircular cross+section for non+Newtonian fluid&

7. Non Newtonian fluid through a channel with two parallel plates.

1) ENTROPY GENERATION IN CONVECTION HEAT TRANSFER

*ig./ 'ntropy generation analysis for an infinitesimal element dx8dy in convectiveheat transfer

Sgen 9Sgen(thermal) : Sgen(friction).

#onsidering a point (x&y) in a fluid with convective heat transfer. The fluid element

dx+dy surrounding this point is part of thermal flow system. Thus The small element

dx+dy can be regarded as an open thermodynamic system& sub!ected to mass


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fluxes& energy transfer and entropy transfer interactions that penetrate the fixed

control surface.

*rom the second law of thermodynamics on the #lausius definition ds9

*rom the figure

;.(/)

The first four terms on the right side of the eriting the ibbs e


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In many fundamental convective heat transfer problems& velocity and

temperature distributions are simplified assuming that the flow is hydro+dynamically

developed (@A?@x 9 B) and thermally developing (@T?@x C B) or developed (@T ?@x 9

B). *or example& see references by e!an & urmeister &Shah and ondon and >hite.

In such situations& '


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'ntropy is generated in a process or system due to the presence of irreversibility. In

convection problem & both fluid friction and heat transfer have contribution to the

rate of entropy generation. 'xpression of entropy generation number(NS) is good for

generating spatial entropy profile& but fails to give any idea which of the fluid

friction or heat transfer dominates. ,ccording to e!an the irreversibility distribution

ratio(L) ta"es care of the above problem L is e


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The second sith proper scaling the dimensionless forms pf '


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3"3 CONVECTION IN ROUN TU!E

The third example is fluid flow through a circular pipe(Goiseuille flow) with

constantheat flux boundary condition. *ully developed laminar flow is considered

here.The expressions for boundary layer according to ird et al are

;;;;;;;;.(17)

;;;;;;;;..(1)

>ith proper scaling&the dimensionless form of '


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3"( CONVECTION IN CIRCULAR ANNULUS

The next problem is convective heat transfer inside a circular annulus. The innerand the outer radii of the annulus are riand ro. The velocity profile inside theannular space& according to is

;;(23)

#/ and #1 are two constants and can be defined as a function of U (9 ri?rB) by using

the following relations

;;..(24) ;;;;. (21)

>ith proper scaling& the dimensionless form of '


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;;;;;;;;;;.(3B)

#omparing ee get&

;;;;;(3/)

Now e!an number&

V

;;;;;;;;;;;;;;(31)

3" A*ia++, -o.in/ conc0ntric c,+ind0r1

Aelocity distribution inside the annular space can be expressed by the following

eith proper scaling& the dimensionless form of above e


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;;;;;.(34)

In above e


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YZ is the velocity ratio ([B?[i) and U is the radius ratio (ri?rB). - is e


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;;;;;..(43)

Now from this we get the expression for dimensionless temperature distribution

where is a constant of integration.

;;;;;..(45)

#omparing e


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u 9 H/+(;;;;;;;;(4)

>here&9 half length of the channel

9 max. velocity

The solutions are given as;;;..;;;;;;;(5B)

;;;;;;;;;.(5/)

In the above expressions& y and x are scaled with and 1um?E& respectively. W is aconstant of integration. Rsing '

Convective Heat Transfer Project

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