Department of Mechanical Engineering
MECHENG 211 Thermofluids
Content & Study Guide, Week 5, Semester 2
16 MECHANISMS OF HEAT TRANSFER
16-1 Introduction
• Science of heat transfer
• Heat and heat transfer; Fundamental requirement for heat transfer
• Modes of heat transfer: conduction, convection and radiation
16-2 Conduction
• Physical mechanisms for conduction in gases, liquids and solids.
• Vibrations, collisions, diffusion, free electrons
• Dependence of rate of heat conduction on geometry, thickness and material of the medium,
and the temperature difference across the medium.
• Fourier’s law of heat conduction = Conduction rate equation
• Thermal conductivity, Temperature gradient
• Thermal conductivity: of some materials; measurement; ranges for and mechanisms of
conduction in gases; liquids and solids; variation with temperature
• Thermal diffusivity
16-3 Convection
• What is convection?
• Physical mechanisms for convection; importance of fluid motion or bulk fluid motion
• Forced convection, Natural (or Free) convection; Change of phase – boiling and
condensation are also considered as convection heat transfer processes
• Newton’s law of cooling
• Convection heat transfer coefficient, its dependence on variables, typical values
16-4 Radiation
• Radiation, Thermal radiation
• Stefan-Boltzmann law and maximum rate of radiation
• Blackbody, blackbody radiation
• Radiation emitted by real bodies, Emissivity
• Absorptivity, perfect absorber, perfect emitter
• Assumption that Absorptivity equals emissivity
• Net rate of radiation heat transfer between a body and its surroundings
• The idea of a combined heat transfer coefficient at a surface to represent both convection
and radiation heat transfer at the surface
16-5 Simultaneous Heat Transfer Mechanisms
• Conduction only in opaque solids
• Conduction and radiation in semi-transparent solids
• Convection and radiation from surfaces, while conduction between surface and body inner
• Conduction and possibly radiation in a still fluid (no bulk fluid motion)
• Convection and possibly radiation in a moving or flowing fluid
• Radiation only through a vacuum
• Surface energy balance (refer lecture for detail)
P J Richards 2018/S Norris 2021
Department of Mechanical Engineering
MECHENG 211 Thermofluids
Tutorial Sheet HT1: MECHANISMS OF HEAT TRANSFER
1. Consider heat loss through the two walls of a house on a winter night. The walls are identical except
that one of them has a tightly fit glass window. Through which wall will the house lose more heat?
Explain. Discuss how the use of curtains and thermal drapes inside the window would affect your
answer?
2. The inner and outer surfaces of a 0.5 cm thick 2 m by 2 m window glass in winter are 10°C and 3°C
respectively. If the thermal conductivity of the glass is 0.78 W/m.K, determine the amount of heat loss
through the glass over a 5 hour period. What would your answer be for a 1 cm thick glass?
[78 624 kJ, 39 312 kJ]
3. What is the thickness required of a masonry wall having a thermal conductivity of 0.75 W/m.K if the
heat rate is to be three-quarters of the heat rate through a composite structural wall having a thermal
conductivity of 0.25 W/m.K and a thickness of 100 mm? Both walls are subjected to the same surface
temperature difference.
[400 mm]
4. One way of measuring thermal conductivity of a material is to
sandwich an electrical thermofoil heater between two identical
rectangular samples of the material and to heavily insulate the
four outer edges, as shown. Thermocouples attached to the inner
and outer surfaces of the samples record the temperatures.
During an experiment, two 0.5 cm thick samples 10 cm by 10
cm in size are used. When steady operation is reached, the heater
is observed to draw 35 W of electrical power, and the
temperature of each sample is observed to drop from 82°C at the
inner surface to 74°C at the outer surface. Determine the thermal
conductivity of the material.
[1.094 W/m.K]
5. Hot air at 80°C is blown over a 2 m by 4 m flat surface at 30°C. If the average convection heat transfer
coefficient is 55 W/m2.K, determine the rate of heat transfer from the air to the plate.
[22 kW]
6. An electric resistance heater is embedded in a long cylinder of diameter 30 mm. When water with a
temperature of 25°C and velocity of 1 m/s flows cross-wise over the cylinder, the power per unit length
required to maintain the surface at a uniform temperature of 90°C is 28 kW/m. When air, also at 25°C,
but with a velocity of 10 m/s is flowing, the power per unit length required to maintain the same surface
temperature is 400 W/m. Calculate and compare the convection coefficients for the flows of water and
air.
[4570.6 W/m2.K, 65.3 W/m2.K]
7. Consider a person whose exposed surface area is 1.7 m2, emissivity is 0.7, and surface temperature is
32°C. Determine the rate of heat loss from that person by radiation only to surroundings at 20°C. If the
convection heat transfer coefficient between the person and the surrounding air (at 20°C) is 7 W/m2.K,
what is the net heat loss?
[86.6 W, 229.4 W]
8. A 1000 W iron is left on the iron board with its base exposed to the air at 20°C. The convection heat
transfer coefficient between the base surface and the air is 35 W/m2.K. If the base has an emissivity of
0.6 and a surface area of 0.02 m2, determine the temperature of the base of the iron.
[Ans (Using EXCEL solver): 674°C]
9. The roof of a car in a parking lot absorbs a solar radiant flux of 800 W/m2, while the underside is
perfectly insulated. The convection coefficient between the roof and the ambient air is 12 W/m2.K. (a)
Neglecting radiation exchange, calculate the temperature of the roof under steady state conditions if the
ambient air is at 20°C. (b) If the surroundings are at the ambient air temperature, calculate the
temperature of the roof if its surface emissivity is 0.8. (c) The convection coefficient depends on
airflow conditions over the roof, increasing with increasing air velocity. Compute and plot the plate
temperature as a function of h for 2 ≤ h ≤ 200 W/m2.K.
[86.7°C, 65.1°C]
P J Richards 2018/S Norris 2021