CANKAYA UNIVERSITY

FACULTY OF ENGINEERING

MECHANICAL ENGINEERING DEPARTMENT

ME 313 HEAT TRANSFER

CHAPTER 7

EXAMPLES

1) Air at 27oC blows over a flat plate with a sharp leading edge at 1.5 m/s. Find the

boundary layer thickness 0.5 m from the leading edge. Check the boundary layer

assumption u>>v at the trailing edge.

2) Calculate the average shear stress and coefficient of friction for the previous example

if the total length L = 0.5 m. Compare wτ with wτ at the trailing edge. At what point on

the surface does wτ = wτ . Finally estimate what fraction of surface can legitimately be

analyzed using boundary layer theory?

3) Air at atmospheric pressure and T∞ = 300 K flows with velocity u∞ = 1.5 m/s along a

plate. Determine the distance from leading edge of plate where transition begins from

laminar to turbulent flow. Calculate the drag force F acting per 1 m width of plate over

the distance from x = 0 to where transition starts.

4) Atmospheric air at 300 K flows with a velocity of u∞ = 5 m/s along a plate L = 1 m

long. The plate has a width w = 0.5 m. The total drag force acting on the plate is

determined to be F = 18×10-3 N. By using Reynolds Colburn analogy estimate average

heat transfer coefficient.

5) Air at 0oC and 1 atm flows at a velocity of 6 m/s across a rectangular plate at a uniform

temperature of 120oC. If the dimension of the plate perpendicular to flow is 2.5 m and

plate in the flow direction is 1 m, find:

a) local heat transfer coefficient at the trailing edge

b) the average heat transfer coefficient for the entire plate

c) convective heat transfer from the plate

6) Air at 20oC and moving at 15 m/s is heated by isothermal steam heated plate at 110oC,

½ m length and ½ m width. Find the average heat transfer coefficient and total heat

transferred. What are h, Δ, and δ at the trailing edge?

7) A plate measuring 42 cm by 42 cm is exposed to uniform heat flux of 1953 W.

Atmospheric air at 27oC flows across the plate at a velocity of 12 m/s. What is the

average surface temperature of plate?

8) Figure given below shows a flat plat, 100 cm in length and 30 cm is width, which is

used as a heating element. Air at 20oC and 1 atm pressure flows over the plate with a

velocity of 6 m/s. The plate has unheated sections at both ends, each 25 cm in length, and

the heated section is maintained at 140oC. Calculate the total heat transfer rate from the

plate to the air.

T∞ = 20oC

U∞ = 6 m/s

100 cm

9) Water at 10oC flows at a velocity of 3 m/s across a plate maintained at a uniform

temperature of 70oC. If the length and width of the plate are 1.2 m and 1 m respectively

determine (a) if transition occurs, if it does, find xc, (b) the average heat transfer

coefficient for the plate and (c) the convective heat transfer from the plate.

10) A flat plate of width 1 m is maintained at a uniform surface temperature of Ts =

150oC by using independently controlled, heat generating rectangular modules of

thickness a = 10 mm and length b = 50 mm. Each module is insulated from its neighbors,

as well as on its back side. Atmospheric air at 25oC flows over the plate at a velocity of

30 m/s. The thermophysical properties of module are k = 5.2 W/m.K, cp = 320 J/kg.K, 3m/kg2300=ρ .

a) find the required power generation, )m/W(q 3 , in a module positioned at a

distance 700 mm from the leading edge?

b) Find the maximum temperature Tmax in the heat generating module?

11) A circular pipe of 25 mm outside diameter is placed in an air stream at 25oC and 1

atm air. The air moves in cross flow over the pipe at 15 m/s while the outer surface of the

pipe is maintained at 100oC. (a) What is the drag force exerted on the pipe per unit length

(b) What is the rate of heat transfer from the pipe per unit length?

V = 15 m/s

25 mm

air

12) Air stream at 27oC moving at 0.3 m/s across 100 W incandescent bulb, glowing at

127oC. If the bulb is approximated by a 60 mm diameter sphere, estimate the heat transfer

rate and the percentage of power

lost

due to convection. (Use correlation: Nu=0.37ReD

0.6)