Page 42 - Fundamentals of The Finite Element Method for Heat and Fluid Flow

SOME BASIC DISCRETE SYSTEMS
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Mould
Metal
Air gap

Figure 2.13 Casting and mould arrangement

Table 2.2 Details of the composite wall

Material Thermal conductivity (W/m C) Thickness (cm)
◦
Aluminium 200 5
Copper 400 15
Steel 50 20

surface of the window are 10 W/m 2 ◦ C and 40 W/m 2 ◦ C respectively. Note that these heat
transfer coefficients include the effect of radiation. If the air gap is not provided, what is the
temperature of the glass inside the room?

Exercise 2.5.7 A simplified model can be applied to describe the steady state temperature
distribution through the core region, muscle region and skin region of the human body.
The core region temperature T c , is the mean operating temperature of the internal organs.
The muscle temperature, T m , is the operating temperature of the muscle layer of the human
body. Muscle is a shell tissue, and can be either resting or actively working. The skin
temperature, T s , is the operating temperature of the surface region of the body consisting of
a subcutaneous fat layer, the dermal layer and finally the epidermal layer. If the metabolic
2
◦
heat rate of a common man is 45 W/m and the skin temperature is 32.6 C, calculate the core
◦
region temperature if the thermal conductivity of the core, muscle and skin are 0.48 W/m C
and the thickness of the layers are 4 cm, 2 cm and 1 cm respectively. Also calculate the
muscle temperature.
Exercise 2.5.8 A composite wall consists of layers of aluminium, copper and steel. The
steel external surface is 350 C, and the external surface of the aluminium is exposed to an
◦
ambient of 25 C with a heat transfer coefficient of 5 W/m 2 ◦ C. Calculate the heat loss and
◦
the interfacial temperature using a three-element model using the data given in Table 2.2.

Exercise 2.5.9 An incompressible fluid flows through a pipe network of circular pipes as
3
shown in Figure 2.14. If 0.1 m /s of fluid enters and leaves the pipe network, using a 4-node