Category: Writing

1. For the two-dimensional body shown in Figure P13–34, determine the temperature distribution. Let the left and right ends have constant temperatures of 200 C and 100 C, respectively. Let K
xx
= K
yy
= 5 W/(m C). The body is insulated along the top and bottom.
2. For the two-dimensional body shown in Figure P13–35, determine the temperature distribution. The top and bottom sides are insulated. The right side is subjected to heat transfer by convection. Let K
xx
= K
yy
= 10 W/(m C).

A 200-mm-thick concrete bridge deck is embedded with heating
cables as shown in Figure P13–33. If the ambient temperature under the deck is
10
0
C with h = 10 W/(m
2
– C) and the ambient air temperature above the
deck is 10 C with h = 10 W/(m
2
– C), what is the temperature
distribution in the slab? The heating cables are line sources generating heat
of Q = 50 W/m. The thermal conductivity of the concrete is 1:2 W/m-C. Use
symmetry in your model.

For the square two-dimensional body shown in Figure P13–32,
determine the temperature distribution. Let K
xx
= K
yy
=
10 W/(m C) and h = 10 W/(m
2
C). The top face is maintained at 100 C,
the left face is maintained at 0 C, and the other two faces are exposed to a
free-stream temperature of 0 C. Also, plot the temperature contours on the
body.

A 10-in.-thick concrete bridge deck is embedded with heating
cables, as shown in Figure P13–30. If the lower surface is at 0 F, the rate of
heat generation (assumed to be the same in each cable) is 100 Btu/(h-in.) and
the top surface of the concrete is at 35 F. The thermal conductivity of the
concrete is 0.500 Btu/(h-ft-F). What is the temperature distribution in the
slab? Use symmetry in your model.

1. For the one-dimensional flow through the porous media
shown in Figure P14–1, determine the potentials at one-third and two-thirds of
the length. Also determine the velocities in each element. Let A = 0:2 m
2
.
2. For the one-dimensional flow through the porous medium
shown in Figure P14–2 with fluid flux at the right end, determine the
potentials at the third points. Also determine the velocities in each element.
Let A =2 m
2
.

1. The buried pipeline in Figure P13–29 transports oil with
an average temperature of 60 F. The pipe is located 15 ft below the surface of
the earth. The thermal conductivity of the earth is 0.6 Btu/(h-ft-F). The
surface of the earth is 50 F. Determine the temperature distribution in the
earth.
2. For the circular body with holes shown in Figure P13–31,
determine the temperature distribution. The inside surfaces of the holes have
temperatures of 150 C. The outside of the circular body has a temperature of 30
C. Let K
xx
= K
yy
= 10 W/(m C).

Air is flowing at a rate of 10lb/h inside a round tube with
a diameter of 1.5 in. and length of 10 in., similar to Figure 13–32 on page
644. The initial temperature of the air entering the tube is 50F. The wall of
the tube has a uniform constant temperature of 200F. The specific heat of the
air is 0.24 Btu/(lb-F), the convection coefficient between the air and the
inner wall of the tube is 3.0 Btu/h-ft
2
– F), and the thermal
conductivity is 0.017 Btu/h-ft
2
– F). Determine the temperature of
the air along the length of the tube and the heat flow at the inlet and outlet
of the tube.

1. The cross section of a tall chimney shown in Figure
P13–27 has an inside surface temperature of 330 F and an exterior temperature
of 130 F. The thermal conductivity is K = 0:5 Btu/(h-ft-F). Determine the
temperature distribution within the chimney per unit length.
2. The square duct shown in Figure P13–28 carries hot gases
such that its surface temperature is 570 F. The duct is insulated by a layer of
circular fiberglass that has a thermal conductivity of K = 0:020 Btu/(h-ft-F).
The outside surface temperature of
the fiberglass is maintained at 110 F. Determine the
temperature distribution within the fiberglass.

The hitch shown in Figure P13–47 (detailed dimensions shown
in Figure P11–22) is unloaded but has an applied temperature of 200 F to the
front end and an applied temperature of 10 F to the rear surface. Determine the
temperature distribution throughout the hitch. The rest of the surfaces are
exposed to ambient temperature of 70F with h = 2 Btu/h-ft
2
– F.