Heat and Mass Transfer - Convection
Exam Duration: 45 Mins Total Questions : 25
Which non-dimensional number relates the thermal boundary layer and hydrodynamic boundary layer?
- (a)
Rayleigh number
- (b)
Peelet number
- (c)
Grashof number
- (d)
Prandtl number
Match List I (Non-dimensional number) with List II (Application) and select the correct answer using the codes given below the lists
List I | List II |
P. Grashof number | 1. Mass transfer |
Q. Stanton number | 2. Unsteady state heat conduction |
R. Sherwood number | 3. Free convection |
S. Fourier number | 4. Forced convection |
- (a)
P Q R S 4 3 1 2 - (b)
P Q R S 3 4 1 2 - (c)
P Q R S 4 3 2 1 - (d)
P Q R S 3 4 2 1
For a fluid having Prandtl number equal to unity, how are the hydrodynamic bondary layer thickness \({ \delta }_{ t }\) and the thermal boundary layer thickness \({ \delta }_{ t }\) related?
- (a)
\(\delta ={ \delta }_{ t }\)
- (b)
\(\delta >{ \delta }_{ t }\)
- (c)
\(\delta <{ \delta }_{ t }\)
- (d)
\({ \delta }_{ t }={ \delta }^{ 1/3 }\)
The Nusselt number is related to Reynolds number in laminar and turbulent flows respectivley a
- (a)
Re-1/2 and Re0.8
- (b)
Re1/2 and Re0.8
- (c)
Re-1/2 and Re-0.8
- (d)
Re1/2 and Re-0.8
Heat is lost from a 100 mm diameter steam pipe placed horizontally in ambient at 30"C. If the Nusselt number is 25 and thermal conductivity of air is 0.03 W/m-K, then the heat transfer coefficient will be
- (a)
7.5 W/m2-K
- (b)
16.2 W/m2-K
- (c)
25.2 W/m2-K
- (d)
30 W/m2-K
A 320 cm high vertical pipe at 150"C wall temperature is in a room with still air at 10"C. This pipe supplies heat at the rate of 8 kW into the room air by natural convection.
Assuming laminar flow, the height of the pipe needed to supply 1 kW only is
- (a)
10cm
- (b)
20 cm
- (c)
40 cm
- (d)
80 cm
The average Nusselt number in laminar natural convection from a vertical wall at 180oC with still air at 20 ° C is found to be 48. If the wall temperature becomes 30oC, all other
parameters remaining same, the average Nusselt number will be
- (a)
8
- (b)
16
- (c)
24
- (d)
32
If the viscosity of air is 24.5 x 10-6 N-s/m2 and its specific heat capacity is 1 kJ/kg-K and thermal conductivity is 0.12 W/m-K then,
- (a)
Pr = 0.30
- (b)
Pr = 0.20
- (c)
Pr = 0.15
- (d)
Pr = 0.25
In a thermal boundary region, thickness of thermal boundary layer is \({ \delta }_{ t }\) If air flow over the plate has temperature \({ T }_{ \infty }\) and T(y) = ay - by 2, where a and bare constant.
Which of the following is correct?
- (a)
\({ \delta }_{ t }\) > 0.5, if a=b
- (b)
\({ \delta }_{ t }\) = 0.5,if a=2,b =1
- (c)
\({ \delta }_{ t }\) = 0.5, if a = 1, b = 2
- (d)
\({ \delta }_{ t }\) < 0.5, if a < b
In a thermal boundary region, thickness of thermal boundary layer is \({ \delta }_{ t }\) If air flow over the plate has temperature \({ T }_{ \infty }\) and T(y) = ay - by 2, where a and bare constant.
If \({ T }_{ \infty }\)= 100oC, \({ \delta }_{ t }\) = 0.5 m, then value of a is (If b = 0)
- (a)
200°C/m
- (b)
100°C/m
- (c)
400°C/m
- (d)
300°C/m
The temperature distribution within the thermal boundary layer over a heated isothermal flat plate is given by
\(\cfrac { T-{ T }_{ w } }{ { T }_{ \infty }-{ T }_{ w } } =\cfrac { 3 }{ 2 } \left( \cfrac { y }{ { \delta }_{ t } } \right) -\cfrac { 1 }{ 2 } { \left( \cfrac { y }{ { \delta }_{ t } } \right) }^{ 3 }\)
where, Tw and \({ T }_{ \infty }\) are the temperature of plate and free stream respectively and y is the normal distance measured from the plate. The local Nusselt number based on the thermal boundary layer thickness \({ \delta }_{ t }\) is given by
- (a)
1.33
- (b)
1.50
- (c)
2.0
- (d)
4.64
A straight tube having a diameter of 40 mm carries water with a velocity of 10 m/s .The temperature of the tube surfaceis 45°C and the flowing water is heated from the inlet temperature Ti= 10 oC to an outlet temperature To = 20oC. Physical properties of water at its mean bulk temperature are
v = 1.006 x 10-6 m2/s
K = 59.86 x 10-2 W/m-K
Cp = 4183 J/kg-K; Pr = 0.702
Length of the tube will be
- (a)
9.05 m
- (b)
15.05 m
- (c)
21.05 m
- (d)
27.05 m
Air flows through a 10 cm internal diameter tube at the rate of 75 kg/h. Measurement indicate that at a particular point in the tube, the pressure and temperature of air are 15 bar and 350 K respectively, while the tube wall temperature is 400 K. General non dimensional correlation for turbulent the tube is
Nu = 0.023 Reo.8 PrO.4
where fluid properties are evaluated at the bulk temperature.
Given,\(\mu \) = 1.967 x 10-5 WIm2-K,
K = 0.02792 W/m-K, Pr = 0.713
The value of convective heat transfer coefficient will be
- (a)
7.296 W/m2-K
- (b)
9.76 W/m2-K
- (c)
11.29 W/m2-K
- (d)
None of these
Air flows through a 10 cm internal diameter tube at the rate of 75 kg/h. Measurement indicate that at a particular point in the tube, the pressure and temperature of air are 15 bar and 350 K respectively, while the tube wall temperature is 400 K. General non dimensional correlation for turbulent the tube is
Nu = 0.023 Reo.8 PrO.4
where fluid properties are evaluated at the bulk temperature.
Given, \(\mu \) = 1.967 x 10-5 W/m2-K,
K = 0.02792 W/m-K, Pr = 0.713
The heat transfer rate from one metre length in the region of this point is
- (a)
95.35 W
- (b)
105.35 W
- (c)
150.35 W
- (d)
177.35 W
Air passes through the every face of the plate (Ts = 60oC). For air,
Ta=20oC
\(\rho \) =1.09kg/m3
\(\mu \) = 20.1X120-6N-s/m2
K = 0.027W/m-K
Pr = 0.7
u = 30 m/s
Assume flow is turbulent with NuL = 0.036 \({ Re }_{ L }^{ 0.8 }\) Pr1/3
Value of NuL is=
- (a)
2200
- (b)
2237.8
- (c)
2507
- (d)
2001
ir passes through the every face of the plate (Ts = 60oC). For air,
Ta=20oC
\(\rho \) =1.09kg/m3
\(\mu \) = 20.1X120-6N-s/m2
K = 0.027W/m-K
Pr = 0.7
u = 30 m/s
Assume flow is turbulent with NuL = 0.036 \({ Re }_{ L }^{ 0.8 }\) Pr1/3
Rate of heat transfer from all surface is
- (a)
1.754 kW
- (b)
1754 kW
- (c)
1712W
- (d)
1892W
A flat plate is 2 m long, 0.8 m wide and 3 mm thick. Density of plate is 3000 kg/m3. Specific heat of plate material is 700 J/kg-K. Its initial temperature is 90oC. A stream of air at 30oC is blow over both surfaces of the plate along its width, at a velocity 2 m/s.
Properties of air, \(\rho \) = 1.09 kg/m3, K = 0.028 W/m-K,
Pr = 0.698, \(\mu \) = 2.03 x 10-5 kg/m-s,
Nu = 0.664 (Re)1/2 (Pr)1/3
Rate of heat dissipation from plate
- (a)
586 W
- (b)
586 kW
- (c)
1173 W
- (d)
1173 kW
A flat plate is 2 m long, 0.8 m wide and 3 mm thick. Density of plate is 3000 kg/m3. Specific heat of plate material is 700 J/kg-K. Its initial temperature is 90oC. A stream of air at 30oC is blow over both surfaces of the plate along its width, at a velocity 2 m/s.
Properties of air, \(\rho \) = 1.09 kg/m3, K = 0.028 W/m-K,
Pr = 0.698, \(\mu \) = 2.03 x 10-5 kg/m-s,
Nu = 0.664 (Re)1/2 (Pr)1/3
Initial rate of cooling is
- (a)
0.0058 oCIs
- (b)
0.0058oCIs
- (c)
0.0116 oC/min
- (d)
None of these
Air flows between the space of two concentric pipes as shown in figure. Air is at 2 atm and 200"C and flows with a velocity of 12 m/s. Properties of air
Pr = 0.681, \(\mu \)= 2.57 x 10-5 kg/m-s, K = 0.0386 WIm-K and Cp = 1.025 kJ/kg-K, NUd = 0.023 (Re)0.8 (Pr)O.4. Assume wall temperature is 20°C above the air temperature all along the length of tube .
If D = 5 cm, d = 2 cm, then heat transfer per unit length of tube is
- (a)
140 W/m
- (b)
136.79 W/m
- (c)
171 W/m
- (d)
None of these
Air flows between the space of two concentric pipes as shown in figure . Air is at 2 atm and 200"C and flows with a velocity of 12 m/s. Properties of air
Pr = 0.681, \(\mu \)= 2.57 x 10-5 kg/m-s, K = 0.0386 WIm-K and Cp = 1.025 kJ/kg-K, NUd = 0.023 (Re)0.8 (Pr)O.4. Assume wall temperature is 20°C above the air temperature all along the length of tube .
If D = 5 cm, d = 2 cm, then heat transfer per unit length of tube is
Temperature of air after 4 m length of tube
- (a)
42.15oC
- (b)
242.15oC
- (c)
157.85oC
- (d)
Data is insufficient
Air having temperature 200°C flows over a plate whose surface temperature is 50° C. For plate, L = 10 cm, b = 5 cm, t = 2 cm, K = 10 W/m-K, value of heat transfer coefficient at distance x from leading edge is as h(x)=Coex/L
Here, Co is a constant.
Value of average heat transfer coefficient is
- (a)
\(\bar { h } \)= 1.71, Co:= 2
- (b)
\(\bar { h } \)= 3.43, Co = 1
- (c)
\(\bar { h } \)= 0.85, Co = 0.5
- (d)
None of these
Air having temperature 200°C flows over a plate whose surface temperature is 50° C. For plate, L = 10 cm, b = 5 cm, t = 2 cm, K = 10 W/m-K, value of heat transfer coefficient at distance x from leading edge is as h (x)=Coex/L
Here, Co is a constant.
At steady state, temperature of point P will be (if Co = 15 W/m2-K)
- (a)
5.1oC
- (b)
45oC
- (c)
42.30oC
- (d)
50oC
Properties of air are as follows:
\(\rho \) = 1.02 kg/m3, v = 18 x 10-6 m2/s, Cp = 1.005 kJ,/Kg-K,
\(\mu \) = 20 x 10-6 N-s/m, K = 0.029 W/m-K and
g = 9.8 m/s2, Ts = 100oC, \({ T }_{ \infty }\) = 30oC
Prandtl number is
- (a)
6.93
- (b)
0.00693
- (c)
0.0693
- (d)
0.693
Properties of air are as follows:
\(\rho \) = 1.02 kg/m3, v = 18 x 10-6 m2/s, Cp = 1.005 kJ,/Kg-K,
\(\mu \) = 20 x 10-6 N-s/m, K = 0.029 W/m-K and
g = 9.8 m/s2, Ts = 100oC, \({ T }_{ \infty }\) = 30oC
It Lc = 1m, then Rayleigh number is 4.34 x 1011
- (a)
4.34 x 1011
- (b)
4.34 x 1012
- (c)
4.34 x 108
- (d)
4.34 x 109
Coefficient of volumetric expansion \(\beta \) is
- (a)
\(\beta =-\rho \left( \cfrac { \partial \rho }{ \partial T } \right) \)
- (b)
\(\beta =-\cfrac { 1 }{ \rho } \left( \cfrac { \partial \rho }{ \partial T } \right) _{ T=c }\)
- (c)
\(\beta =-\cfrac { 1 }{ \rho } \left( \cfrac { \partial \rho }{ \partial T } \right) _{ p=c }\)
- (d)
\(\beta =-\cfrac { 1 }{ T } \left( \cfrac { \partial \rho }{ \partial T } \right) _{ p=c }\)