Page 55 - Modelling in Transport Phenomena A Conceptual Approach

36 CHAPTER 2. MOLECULAR AND CONVECTNE TRANSPORT

2.2 The steady rate of heat loss through a plane slab, which has a surface area
of 3 m2 and is 7cm thick, is 72 W. Determine the thermal conductivity of the slab
if the temperature distribution in the slab is given as

T=5s+lO

where T is temperature in "C and 2 is the distance measured from one side of the
slab in cm.

(Answer: 0.048 W/ m. K)

2.3 The inner and outer surface temperatures of a 20cm thick brick wall are
30 "C and - 5 "C, respectively. The surface area of the wall is 25 m2. Determine the
steady rate of heat loss through the wall if the thermal conductivity is 0.72 W/ m. K.

(Answer: 3150 W)

2.4 Energy is generated uniformly in a 6cm thick wall. The steady-state tem-
perature distribution is

T = 145 + 3000 z - 1500 z2

where T is temperature in "C and z is the distance measured from one side of
the wall in meters. Determine the rate of heat generation per unit volume if the
thermal conductivity of the wall is 15 W/ m. K.

(Answer: 45 kW/ m3)

2.5 The temperature distribution in a one-dimensional wall of thermal conduc-
tivity 20 W/ m. K and thickness 60 cm is

T = 80 + 10 sin(.lrE)

where T is temperature in "C, t is time in hours, 6 = s/L is the dimensionless
distance with z being a coordinate measured from one side of the wall and L is the
wall thickness in meters. Calculate the total amount of heat transferred in half an
hour if the surface area of the wall is 15m2.
(Answer: 15,360 J)

2.6 The steady-state temperature distribution within a plane wall of lm thick
with a thermal conductivity of 8 W/ m. K is measured as a function of position as
follows: