Solution of BLE for External Flows

Q. For laminar flow over a flat plate, the local heat transfer coefficient $h_x$ is known to vary as $x^{-1/2}$, where x is the distance from the leading edge of the plate The ratio of the average coefficient between the leading edge and some location x = L on the plate to the local coefficient at x = L , is

1. 3/2
2. 2
3. 2/3
4. 1/2

Q. Air at ${20}^{o}C$ C and I atm flows over a flat plate at 40 m/s. The plate is 80 cm long and is maintained at ${60}^{o}C$. Properties of air at ${40}^{o}C$ are Pr = 0.7, K = 0.02733 W/mK, $C_p=1.007\frac{kJ}{kgK}\mu =1.906\times {10}^{-5}\frac{kg}{m-s}and\rho =1.128kg/m^3.$
The avergae heat transfer coefficient is ___$Use\overline{Nu}=P{r}^{\frac{1}{3}}(0.036R_e^{0.8}-871)$.

1. $69W/m^{2}K$
2. $62W/m^{2}K$
3. $88W/m^{2}K$
4. $54W/m^{2}K$

Q. For laminar flow over flat plate, the average value of Nusselt Number Nu is prescribed by
$Nu=0.664R{e}^{0.5}P{r}^{0.33}$
Which of the following should be changed independently keeping other parameters same to double the heat transfer coefficient?

1. Specific heat to be increased 9 times
2. Density should be increased 8 times
3. Dynamic viscosity has to be decreased 64 times
4. Plate length should be decreased 16 times

Q. A hot plate of area 0.2 $m^2$ is maintained at a temperature of ${59}^{o}C$ by a 100 W heater when the room temperature is ${20}^{o}C$. The appropriate convection coefficient is 2.512 $(\Delta T{)}^{1/4}W/m^{2}K$. Taking heat transfer from plate is by convection and radiation, the percentage of heat lost by radiation is

1. 27
2. 51
3. 56
4. 49

Q. The Nusselt number is related to Reynolds number in laminar and turbulent flows over a flat plate respectively are

1. $R{e}^{0.5}andR{e}^{0.67}$
2. $R{e}^{0.5}andR{e}^{0.33}$
3. $R{e}^{0.5}andR{e}^{0.8}$
4. $R{e}^{-0.5}andR{e}^{-0.8}$

Q. An uninsulated air conditioning duct of rectangular cross section $1m\times 0.5m$ carrying air at ${20}^{\circ }C$ with a velocity of 20 m/s is exposed to an ambient of ${30}^{\circ }C$. Neglect the effect of duct construction material. For air in range $20-{30}^{\circ }C$, properties are as follows.
Thermal conductivity $=0.025W/mk$
Viscosity $=18\mu Pa-s$
Prandtl numbber $=0.73$
Density $=1.2kg/m^3$
For laminar flow Nusselt number is 3.4 for constant wall temperature and for turbulent flow. The heat transfer in per meter length of the duct is
$\overline{Nu}=0.023R{e}^{0.8}P{r}^{0.33}$

1. 1339 W
2. 1240 W
3. 769 W
4. 5.3 W

Q. Consider the laminar flow of a fluid over a flat plate of length L. maintained at a constant temperature. If the free stream velocity of the fluid is halved and the length of the plate is doubled, the rate of heat transfer between the fluid and the plate

Q. Gas at atmospheric pressure and ${40}^{o}C$ flows with a velocity is 5m/s over a 2m long flat plate whose surface is kept at a uniform temperature of ${120}^{o}C$. The average heat transfer coefficient $\left(inW/m^{2o}C\right)$ over the 2m length of the plate if the properties of gas at mean film temperature are
Kinematic viscosity = $2.107\times {10}^{-5}{m}^2/s,$
Thermal conductivity = 0.03025 W/mK,
Prandtl number = 0.6965.
Average Nussult number = Nu = $0.664R{e}^{0.5}$.
$P{r}^{0.3}....ForLaminarflow$
Average Nussult number = Nu = 0.0375
$R{e}^{0.8}.P{r}^{0.3}....$For turbulent flow

1. 410
2. 3.1
3. 17.68
4. 6.2

Q. Water at ${20}^{o}C$ flows with a velocity of 10m/s over a flat plate which is maintained at ${80}^{o}C$. Find the thermal boundary layer thickness at 1.5m from the leading edge. Viscosity and thermal conductivity of water are $4.5\times {10}^{-4}$ Pa-s and 0.65 W/m-K respectively.

1. 17.4 mm
2. 1.85 mm
3. 12.5 mm
4. 0.91 mm

Q. Caster oil at ${25}^{o}C$ flows at a velocity of 0.1m/s past a flat plate, in a certain process. If the plate is 4.5m long and is maintained at a uniform temperature of ${95}^{o}C$ the thermal boundary layer thickness if the following data is available
$\rho =956.8KG/m^3,\alpha =7.2\times {10}^{-8}{m}^2/s,$
$K=0.213W/mK,v=0.65\times {10}^{-4}{m}^2/s$
Pr = 903,
$\delta$ = Thickness of hydrodynamic boundary layer = 270.4mm

1. 28 mm
2. 900 mm
3. 0.9 mm
4. 99.8 mm

Q. In a certain process, oil at 35°C flows over a flat plate at 6 cm/s. The plate is 6 m long is heated uniformly and maintained at the surface
the temperature of 95°C. What will be the thermal boundary layer thickness at the trailing edge of the plate?
At the mean film temperature, t${}_m$ = 65°C, the relevant fluid properties are
Thermal diffusivity, $\alpha$ = 7.2 x 10${}^{-8}$ m${}^2$/s
Thermal conductivity, k = 0.213 W/mK
Kinematic viscosity, v = 0.65 x 10${}^{-4}$ m${}^2$/s
Density, ρ = 956.8 kg/m${}^3$

1. 3.897 m
2. 0.0417 m
3. 0.4849 m
4. 0.4032 m

Q. Air $\left({20}^{o}C\right)$ is flowing with a Reynolds number of ${10}^6$ over a heated flat plate. The variation of heat transfer coefficient with distance, which is measured from leading edge, is given by,

1. $h\propto x^{-0.2}$
2. $h\propto x^{0.8}$
3. $h\propto x^{-0.8}$
4. $h\propto x^{-0.5}$

Q. It is hotter for the same distance over the top of the fire than it is on the side of it, mainly because

1. convection takes more heat upwards
2. air conducts heat upwards.
3. convection conduction and radiation also contribute significantly to transferring heat upwards.
4. heat is radiated upwards

Q. For thickness of thermal boundary layer to be greater than thickness of hydrodynamic boundary layer, the Prandtle number should be

1. Greater than 1
2. Equal to 1
3. None
4. Less than 1

Q. Which of the following number ratio signifies the type of convection i.e. free convection or forced convection.

1. $\frac{R{e}^2}{Gr}$
2. $\frac{Re}{Gr}$
3. $\frac{Gr}{R{e}^2}$
4. $\frac{Gr}{Re}$

Q. In a laminar flow over plate the thickness of hydrodynamic boundary layer is 2 mm. What will be the thickness of thermal boundary layer? Fluid properties $\mu =4\times {10}^{-4}kg/m-s,k=0.664W/mK,Pr=2.54$

1. 2.54 mm
2. 1.68 mm
3. 1.43 mm
4. 5.08 mm

Q. In case of free convection over a vertical plate, the Nusselt number of laminar and turbulent flow varies respectively with Grashof number as

1. Gr${}^{1/3}$ and Gr ${}^{1/4}$
2. Gr${}^{1/4}$ and Gr ${}^{1/3}$
3. Gr and Gr ${}^{1/4}$
4. Gr${}^{1/2}$ and Gr ${}^{1/3}$

Q.

What is the heat transfer coefficient of air

Q. A fluid of density $978{\text{kg/m}}^3$ is heated in pipe, enters a 20 mm diameter tube with a velocity of 2 m/s at $10{}^{\circ }C$. Convective heat transfer coefficient at outside surface of tube is equal to $10{\text{kW/m}}^2$. The length of tube is 5 meter and properties of water at mean temperature is approximated as following,
$k=0.332\text{WmK}$, $\mu =4\times {10}^{-4}\text{kg/m-s}$, $Pr=2.54$
the value of overall heat transfer coefficient is

1. $4.73{\text{kW/m}}^2\text{K}$
2. $8.73{\text{kW/m}}^2\text{K}$
3. $3.53{\text{kW/m}}^2\text{K}$
4. $1.73{\text{kW/m}}^2\text{K}$

Q. The wall of a building is 5 meters long and 3 meters high. The temperature of the wall is 25°C and the air temperature is 5°C. The heat loss from the wall of the building when the wind is blowing parallel to its surface with a speed of 2 km/hour is
(Assume flow from one side only)
Take , $\rho =1.206kg/m^3,c_p=1005J/kgK$,
$k=0.0252W/mK,v=15.1\times {10}^{-6}{m}^2/s,Pr=0.714$ and the following correlation , $N{u}_x=0.332R{e}_x^{1/2}P{r}^{1/3}$

1. 384 W
2. 512 W
3. 768 W
4. 192 W

Q. Which of the following number ratio signifies the type of convection i.e. free convection or forced convection.

1. $\frac{R{e}^2}{Gr}$
2. $\frac{Gr}{Re}$
3. $\frac{Re}{Gr}$
4. $\frac{Gr}{R{e}^2}$