TITLE.PM5

812 ENGINEERING THERMODYNAMICS

dharm

\M-therm\Th15-2.pm5

Case II : The heat flow through an insulated wire when critical thickness is used is given
by

Q 2 =^212 0 00343 0 001

012

1

35 0 00343

1

1

ππLt t 1

rr

khr

air Lt t

c

oc

() air

ln ( / )

.

()

ln (. /. )

.

.

−

+

= − +

×

=^2

18 6

πLt t() 1 air

.

− ...(ii)

∴ Percentage increases in heat flow by using critical thickness of insulation

=

QQ

Q

21

1

−

× 100 =

1

18.6

1

20.77

1

20.77

−

× 100 = 11.6%. (Ans.)

15.3. Heat Transfer by Convection

l The rate equation for the convective heat transfer (regardless of particular nature)

between a surface and an adjacent fluid is prescribed by Newton’s law of cooling (Refer

Fig. 15.29)

Q = hA(ts – tf) ...(15.44)

where, Q = Rate of conductive heat transfer,

A = Area exposed to heat transfer,

ts = Surface temperature,

tf = Fluid temperature, and

h = Co-efficient of conductive heat transfer.

The units of h are, h =

Q

At t()s f

W

− mC^2

=

°

or W/m^2 °C or W/m^2 K

The coefficient of convective heat transfer ‘h’ (also known as film heat transfer coefficient)
may be defined as ‘‘the amount of heat transmitted for a unit temperature difference between the
fluid and unit area of surface in unit time.’’
The value of ‘h’ depends on the following factors :
(i) Thermodynamic and transport properties (e.g., viscosity, density, specific heat etc.) ;
(ii) Nature of fluid flow ;
(iii) Geometry of the surface ;
(iv) Prevailing thermal conditions.
Since ‘h’ depends upon several factors, it is difficult to frame a single equation to satisfy all
the variations, however a dimensional analysis gives an equation for the purpose which is given as
under :

h

k

D Z CD

a

= F

HG

I

KJ

ρ

π

c

k

D

L

p

F μ b c

HG

I

KJ

F

HG

I

KJ ...(15.45)

or Nu = Z (Re)a (Pr)b D
L

F c

HG

I

KJ

where, Nu = Nusselt number h

k

F D

HG

I

KJ

,

Re = Reynolds number

ρ

μ

F uD

HG

I

KJ

,