Heat Transfer by Conduction Exercises

People's Democratic Republic of Algeria
Ministry of Higher Education and Scientific Research
Blida 1 University. Faculty of Technology
Department of Renewable Energy 3rd Year MCIL – Thermal Conversion
Series 1
HEAT TRANSFER BY CONDUCTION
Exercise 1
Consider a plate of thickness L and thermal conductivity k subjected to a uniform heat flux φ0 at
the front surface x=0. At x=L, heat is dissipated by convection into a fluid at temperature T∞.
- Determine the expressions of the temperatures T1 and T2 at the surfaces x=0 and x=L,
respectively.
- Calculate the surface temperatures T1 and T2, given that L=2 cm, k=46 W/mK, T=50°C, φo =
1 kW/m2 et h=500 W/m2K.
Exercise 2
The wall of a furnace is made up of two layers. The first is refractory brick with thickness L1=0.2m
and thermal conductivity k1 = 1.38 W/m.K, The second is insulating brick with thickness L2 =0.1
m and thermal conductivity k2 = 0.17 W/m.K. The temperature inside the furnace is 1650°C, and
the convective heat transfer coefficient at the inner surface is 70 W/m2K. The ambient air
temperature is 25°C, and the convective heat transfer coefficient at the outer surface h2 = 10
W/m2K.
- Calculate the heat loss per unit area of the wall, the temperatures at the inner and outer surfaces,
and the temperature at the interface between the two brick layers.
- Determine the slopes of the temperature profiles T=f(x) in each layer.
Exercise 3
A steel pipe with an outer diameter of 6 cm and an inner diameter of 5 cm is covered with an
insulating layer with 2 cm of thickness. A hot gas flows inside the pipe at a constant temperature
Ta = 330°C. The outer surface of the insulation is in contact with a fluid at Tb = 30 °C and a
coefficient hb = 60 W/m2K.
- Calculate the total heat loss from the pipe over a length of 10 meters.
- Calculate the temperature differences between gaz-ambient air, steel pipe and the ambient air,
and insolation - external air.
kacier = 46 W/mK, kisolant = 0.2 W/mK, ha = 400 W/m2K, hb = 60 W/m2K.