Mechanical - Heat and Mass Transfer - Convection

**1.
Air at 20C at atmospheric pressure flows over a flat plate at a velocity of 3
m/s. if the plate is 1 m wide and 80C, calculate the following at x = 300 mm.**

**1. Hydrodynamic boundary layer thickness, **

**2. Thermal boundary layer thickness, **

**3. Local friction coefficient, **

**4. Average friction coefficient, **

**5. ****Local
heat transfer coefficient **

**6. ****Average
heat transfer coefficient, **

**7. ****Heat
transfer. **

**Given: **Fluid
temperature T¥** **=
20°C , Velocity U = 3 m/s

Wide
W = 1 m

Surface temperature T_{w} = 80°C

Distance x = 300 mm = 0.3 m

**Solution: **We
know

**6. Average heat transfer coefficient
(h):**

h =2 ´h_{x} =2 ´6.20

h =12.41 W / m^{2}K

**7. Heat transfer:**

We know that,

Q =h A(T_{w}
-T_{¥})

= 12.41´(1 ´0.3) (80-20) Q = 23.38 Watts

2. **Air at 40**°**C is flows over a flat plate of 0.9 m at a velocity
of 3 m/s. Calculate the following:**

**1. ****Overall
drag coefficient **

**2. ****Average
shear stress, **

**3. ****Compare
the average shear stress with local shear stress (shear stress at the trailing
edge) **

**Given:**

**Fluid temperature T**¥** = 40**°**C**

**Length L = 0.9 m**

**Velocity
U = 3 m/s.**

**Solution:**

Properties of air at 40°C:

*r*=1.128 Kg/m^{3}

*n*=
16.96 ´10^{-6} m^{2} / s Pr =0.699

K =
26.56 ´10^{-3} W/mK

**3. Air at 20 ^{o}C flows over a flat
plate at 60^{o}C with a free stream velocity of 6 m/s. Determine the
value of the average convective heat transfer coefficient up to a length of 1 m
in the flow direction.**

in the flow direction. (AU2013)

Given:

Fluid temperature T_{inf} = 20^{o}C

Plate temperature Tw = 60^{o}C

Velocity U = 6 m/s

Length L = 1 m

To find: Average heat transfer coefficient

Solution: We know

Local nusselt number} NU_{x} =4.65 W/m^{2}K Average heat transfer coefficient}
h = 2 ´h_{x} =2 ´4.65

h =9.31 W/m^{2}K

**4. Engine oil flows through a 50 mm
diameter tube at an average temperature of 147**°**C.**

**The flow velocity is 80
cm/s. Calculate the average heat transfer coefficient if the tube wall is
maintained at a temperature of 200**°**C
and it is 2 m long.**

**Given:**

Diameter D
= 50 mm = 0.050 m

Average temperature T_{m}= 147°C

Velocity U= 80 cm/s = 0.80 m/s

Tube wall temperature T_{w}= 200°C

Length L= 2m

**To find: **Average
heat transfer coefficient (h)

**Solution: **Properties
of engine oil at 147°C

*r*=
816 Kg/m^{3} *n*= 7 ´10^{-6} m^{2} / s Pr = 116

K = 133.8 ´10^{-3} W/mK

We know

**5. A thin 100 cm long
and 10 cm wide horizontal plate is maintained at a uniform temperature of 150**°**C in a large tank full of water at 75**°**C. Estimate the rate of heat to be supplied to the
plate to maintain constant plate temperature as heat is dissipated from either
side of plate.**

Gr =
3.41´10^{9}

Gr
Pr = 3.41´10^{9} ´1.55

Gr Pr = 5.29 ´10^{9}

Gr Pr value is in between 8 ´10^{6} and 10^{11}

i.e., 8 ´10^{6}<
G r Pr < 10^{11}

**For horizontal plate, upper surface
heated:**

Nusselt number Nu = 0.15 (Gr Pr)^{0.333}

Þ Nu =
0.15 [5.29 ´10^{9} ]^{0.333}^{+}

Þ Nu =
259.41

We know that,

Lower surface heated, heat transfer coefficient h_{1}
= 994.6 W/m^{2}K

Total heat transfer Q = (h_{u} + h_{1})
´A ´DT

= (h_{u}
+ h_{1}) ´W ´L ´(T_{w}
- T¥)

=
(3543.6 + 994.6) ´0.10 ´(150
–75) Q = 34036.5 W

6. **For a particular
engine, the underside of the crank case can be idealized as a flat plat** **measuring
80 cm **´**20 cm. The engine runs
at 80 km/hr and the crank case is cooled by air flowing past it at the same
speed. Calculate the loss of heat from the crank case surface of temperature 75**°**C to the ambient air temperature 25**°**C. Assume the boundary layer becomes turbulent from
the loading edge itself.**

**Given: **Area
A = 80 cm** **´20 cm

= 1600 cm^{2} = 0.16m^{2}

Velocity U = 80 Km/hr

_{=}80 ´10 ^{3 } / m
3600s

=22.22 m/s

Surface temperature T_{w} =75 C°
Ambient air temperature T_{¥} =25 C°

Flow is turbulent from the leading edge, flow is
fully turbulent.

**To find:**

h_{x} =53.85
W/m^{2}K

Local heat transfer coefficient} h_{x} =
53.85 W/m^{2}K

For turbulent flow, flat plate

Average heat transfer
coefficient} h = 1.24 h_{x} h = 1.24 ´53.85

h = 66.78 W/m^{2}K
We know,

Heat loss Q = h A (T_{w}
- T¥) = 66.78 ´0.16 (75 –25)

Q = 534.2 watts.

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