Mode of Heat transfer
• Conduction
• Convection
• Radiation
Heat transfer between two
bodies in contact or from one
point of a body to another
point of the same body.
Atoms in hotter regions have
more kinetic energy which
they transfer to neighboring
a conductor of
length L and cross-section A.
If one end of the conductor is
at high temperature TH and
the other end at a lower
temperature Tc, then the
heat current H, is defined as
the rate of heat flow through
the conductor
 Heat
transfer by electromagnetic radiation
(through empty space).
A - surface area of the object, m2
e - emissivity (ranges from 0 to 1)
H - Heat Current (rate at which an object radiates or
emits radiant energy (J/s or W)
T – Absolute temperature (K)
ΔH = Aeσ(T4body-T4S)
A - surface area of the object, m2
e - emissivity (ranges from 0 to 1
ΔH - Net Rate of Heat loss or gain of energy by
radiation(J/s or W)
Tbody – Absolute temperature of the radiating body
TS – Absolute temperature of surroundings
1) The rod is made of copper is 45 cm long and has a cross
sectional area of 1.25 cm2. Let TH = 100oC and TC =
0oC. (Use thermal conductivity of copper =
a) What is the final steady-state temperature
gradient along the rod?
b) What is the heat current in the rod in the final steady
c) What is the final steady-state temperature at a
point in the rod 12 cm from its left end?
2) One end of the insulated metal rod is maintained at
100oC, and the other end is maintained at 0oC by an icewater mixture. The rod is 60 cm long and has crosssectional area of 1.25 cm2. The heat conducted by the
rod melts 8.50 g of ice in 10 min. Find the thermal
conductivity k of the metal.
3.A long rod, insulated to prevent heat loss along its
sides, is in perfect thermal contact with boiling water (at
atmospheric pressure) at one end and with an ice-water
mixture at the other end. The rod consists of 1 m long
copper (one end in boiling water) joined end to end to a
length L2 of steel (one end in ice-water). Both sections of
the rod have cross-sectional areas of 4 cm2. The
temperature of the copper-steel junction is 65oC after a
steady state has been set-up.
K cu = 385 W/m.K
K steel = 50.2 W/m.K
How much heat per second flows from the steam bath
to the ice-water mixture?
What is the length L2 of the steel section?
Find the mass of ice melted in one hour.
4) An insulating wall consist of 4 cm of material of
thermal conductivity K1 and a 2nd layer 8.0 cm thick
whose conductivity K2 = 4K1. The innermost and
outermost surfaces are kept at -10˚C and 76 ˚C
respectively. Calculate the temperature of the interface.
5)The surface area of the sun has a temperature of
about 5800 K. Taking the radius of the sun to be
equal to be equal to 6.86 X 108 m, calculate the energy
radiated by the sun each day. (Assume e = 1)
6) An aluminum kettle (K al = 238 W/m.C°) has a
circular cross-section and is 8 cm in radius and 0.3
cm thick. It is placed on a hot plate and filled with 1
kg of water. If the bottom of the kettle is maintained
at 101°C and the inside at 100°C, find (a) the rate of
heat flow into the water and (b) the time it takes for
all the water to boil away. (Neglect heat transferred
from the sides.)

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