TITLE.PM5

dharm

\M-therm\Th15-3.pm5

832 ENGINEERING THERMODYNAMICS

or hi =

k

d× 0.023 (Re)

0.8 (Pr)0.33 ...(i)

Re =

ρ

μ

Vd= ××

× −

1000 0 318 0 02

0 596 10^3

..

. = 10671
Substituting the values in eqn. (i), we get
hi =
0 635
002

.

. × 0.023 (10671)

0.8 (3.93)0.33 = 1915 W/m (^2) °C
The overall heat transfer coefficient is given by the relation,
111
Uh hio
=+
11
1915
1
U 10 10^3
=+
×
= 0.000622
∴ U =
1
0 000622. = 1607.7 W/m
(^2) °C
Further, θ 1 = tthc 11 – = 100 – 17 = 83°C
θ 2 = tthc 22 – = 100 – tc 2
∴ Arithmetic mean temperature difference,
AMTD = θθ^12
2
83 100
2

• = +−()tc (^2) = 91.5 – 0.5 t
  c 2
  The heat transfer rate is given by,
  Q = m&c cpc (^) (–)ttcc 21 = U As (AMTD) = U × (π d L × N) (AMTD)
  (where As = Surface area of all the tubes in both passes)
  or 10 × (4.18 × 10^3 ) (tc 2 – 17) = 1607.7 × (π × 0.02 × 2 × 200) × (91.5 – 0.5 tc 2 )
  41800 (tc 2 – 17) = 40406 (91.5 – 5 tc 2 )
  or tc 2 – 17 =
  40406
  41800 (91.5 – 0.5 tc^2 ) = 0.966 (91.5 – 0.5 tc^2 )
  = 88.39 – 0.483 tc 2
  or tc 2 = 71°C. (Ans.)

15.5. Heat Transfer by Radiation

15.5.1. Introduction

‘Radiation’ heat transfer is defined as “the transfer of energy across a system boundary by
means of an electromagnetic mechanism which is caused solely by a temperature difference.” Whereas
the heat transfer by conduction and convection takes place only in the presence of medium, radiation
heat transfer does not require a medium. Radiation exchange, in fact, occurs most effectively in
vacuum. Further, the rate of heat transfer by conduction and convection varies as the temperature
difference to the first power, whereas the radiant heat exchange between two bodies depends on the
difference between their temperature to the ‘fourth power’. Both the amount of radiation and the
quality of radiation depend upon temperature. The dissipation from the filament of a vacuum tube or
the heat leakage through the evacuated walls of a thermos flask are some familiar examples of heat
transfer by radiation.
The contribution of radiation to heat transfer is very significant at high absolute temperature
levels such as those prevailing in furnaces, combustion chambers, nuclear explosions and in space
applications. The solar energy incident upon the earth is also governed by the laws of radiation.