Conduction, Convection and Radiation - Heat Transfer - Chemical Engineering Previous Year Questions

1

2007 · Chemical Engineering · Heat Transfer · Conduction, Convection and Radiation

Chemical Engineering (CH) 2007

The Grashof Number is

A

thermal diffusivity/mass diffusivity

B

inertial force/surface tension force

C

sensible heat/latent heat

D

buoyancy force/viscous force

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2

2007 · Chemical Engineering · Heat Transfer · Conduction, Convection and Radiation

Chemical Engineering (CH) 2007

For the two long concentric cylinders with surface areas \( A_1 \) and \( A_2 \), the view factor \( F_{22} \) is given by

A

0

B

1

C

1 - A_1 / A_2

D

A_1 / A_2

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3

2007 · Chemical Engineering · Heat Transfer · Conduction, Convection and Radiation

Chemical Engineering (CH) 2007

The composite wall of an oven consists of three materials A, B and C. Under steady state operating conditions, the outer surface temperature \( T_{so} \) is 20 °C, the inner surface temperature \( T_{si} \) is 600 °C and the oven air temperature is \( T_\infty = 800 \) °C. For the following data
thermal conductivities \( k_A = 20 \) W/(m·K) and \( k_C = 50 \) W/(m·K),
thickness \( L_A = 0.3 \) m, \( L_B = 0.15 \) m and \( L_C = 0.15 \) m,
inner-wall heat transfer coefficient \( h = 25 \) W/(m²·K),
the thermal conductivity \( k_B \) (W/(m·K)) of the material B, is calculated as

A

35

B

1.53

C

0.66

D

0.03

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4

2007 · Chemical Engineering · Heat Transfer · Conduction, Convection and Radiation

Chemical Engineering (CH) 2007

Water enters a thin walled tube (L=1 m, D =3 mm) at an inlet temperature of 97°C and mass flow rate 0.015 kg/s. The tube wall is maintained at a constant temperature of 27°C. Given the following data for water
Density, \( \rho = 1000 \) kg/m³
Viscosity, \( \mu = 489 \times 10^{-6} \) Ns/m²
Specific heat \( C_p = 4184 \) J/kgK
Inside heat transfer coefficient h =12978 W/(m²·K),
the outlet temperature of water in °C is,

A

28

B

37

C

62

D

96

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5

2007 · Chemical Engineering · Heat Transfer · Conduction, Convection and Radiation

Chemical Engineering (CH) 2007

Consider a liquid stored in a container exposed to its saturated vapor at constant temperature \( T_{sat} \). The bottom surface of the container is maintained at a constant temperature \( T_s < T_{sat} \) while its side walls are insulated. The thermal conductivity \( k_l \) of the liquid, its latent heat of vaporisation \( \lambda \) and density \( \rho \), are known. Assuming a linear temperature distribution in the liquid, the expression for the growth of the liquid layer \( \delta \) as a function of time t is given by

A

\(\delta(t) = \left[ \frac{4k_l (T_{sat} - T_s)}{\rho_l \lambda} t \right]^{1/2}\)

B

\(\delta(t) = \left[ \frac{k_l (T_{sat} - T_s)}{2\rho_l \lambda} t \right]^{1/2}\)

C

\(\delta(t) = \left[ \frac{2k_l (T_{sat} - T_s)}{\rho_l \lambda} t \right]^{1/2}\)

D

\(\delta(t) = \left[ \frac{k_l (T_{sat} - T_s)}{\rho_l \lambda} t \right]^{1/2}\)

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6

2008 · Chemical Engineering · Heat Transfer · Conduction, Convection and Radiation

Chemical Engineering (CH) 2008

Q.15 Transient three-dimensional heat conduction is governed by ONE of the following differential equations (\( \alpha \) - thermal diffusivity, \( k \) - thermal conductivity and \( \psi \) - volumetric rate of heat generation)

A

\(\frac{1}{\alpha} \frac{\partial T}{\partial t} = \nabla T + \psi k \)

B

\(\frac{1}{\alpha} \frac{\partial T}{\partial t} = \nabla T + \frac{\psi}{k} \)

C

\(\frac{1}{\alpha} \frac{\partial T}{\partial t} = \nabla^2 T + \psi k \)

D

\(\frac{1}{\alpha} \frac{\partial T}{\partial t} = \nabla^2 T + \frac{\psi}{k} \)

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7

2008 · Chemical Engineering · Heat Transfer · Conduction, Convection and Radiation

Chemical Engineering (CH) 2008

Two plates of equal thickness (t) and cross-sectional area, are joined together to form a composite as shown in the figure. If the thermal conductivities of the plates are k and 2k then, the effective thermal conductivity of the composite is

A

3k/2

B

4k/3

C

3k/4

D

2k/3

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8

2008 · Chemical Engineering · Heat Transfer · Conduction, Convection and Radiation

Chemical Engineering (CH) 2008

A metallic ball (ρ = 2700 kg/m³ and C_p = 0.9 kJ/kg °C) of diameter 7.5 cm is allowed to cool in air at 25°C. When the temperature of the ball is 125°C, it is found to cool at the rate of 4°C per minute. If thermal gradients inside the ball are neglected, the heat transfer coefficient (in W/m² °C) is

A

2.034

B

20.34

C

81.36

D

203.4

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9

2008 · Chemical Engineering · Heat Transfer · Conduction, Convection and Radiation

Chemical Engineering (CH) 2008

Hot liquid is flowing at a velocity of 2 m/s through a metallic pipe having an inner diameter of 3.5 cm and length 20 m. The temperature at the inlet of the pipe is 90°C. Following data is given for liquid at 90°C
Density = 950 kg/m³;
Specific heat = 4.23 kJ/kg °C;
Viscosity = 2.55 x 10⁻³ kg/m.s;
Thermal conductivity = 0.685 W/m °C
The heat transfer coefficient (in W/m² °C) inside the tube is

A

222.22

B

111.11

C

22.22

D

11.11

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10

2008 · Chemical Engineering · Heat Transfer · Conduction, Convection and Radiation

Chemical Engineering (CH) 2008

The temperature profile for heat transfer from one fluid to another separated by a solid wall is

A

[Image: (A) Temperature profile with solid wall between warm and cold fluids, curve drops sharply near wall]

B

[Image: (B) Temperature profile with solid wall between warm and cold fluids, curve drops sharply near wall]

C

[Image: (C) Temperature profile with solid wall between warm and cold fluids, curve drops sharply near wall]

D

[Image: (D) Temperature profile with solid wall between warm and cold fluids, curve drops sharply near wall]

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11

2009 · Chemical Engineering · Heat Transfer · Conduction, Convection and Radiation

Chemical Engineering (CH) 2009

During the transient convective cooling of a solid object, Biot number \( \rightarrow 0 \) indicates

A

uniform temperature throughout the object

B

negligible convection at the surface of the object

C

significant thermal resistance within the object

D

significant temperature gradient within the object

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12

2009 · Chemical Engineering · Heat Transfer · Conduction, Convection and Radiation

Chemical Engineering (CH) 2009

The Prandtl number of a fluid is the ratio of

A

thermal diffusivity to momentum diffusivity

B

momentum diffusivity to thermal diffusivity

C

conductive resistance to convective resistance

D

thermal diffusivity to kinematic viscosity

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13

2009 · Chemical Engineering · Heat Transfer · Conduction, Convection and Radiation

Chemical Engineering (CH) 2009

A well-insulated hemispherical furnace (radius = 1 m) is shown below:

The self-view factor of radiation for the curved surface 2 is

A

1/4

B

1/2

C

2/3

D

3/4

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14

2009 · Chemical Engineering · Heat Transfer · Conduction, Convection and Radiation

Chemical Engineering (CH) 2009

For the composite wall shown below (Case 1), the steady state interface temperature is 180 °C. If the thickness of layer P is doubled (Case 2), then the rate of heat transfer (assuming 1-D conduction) is reduced by

A

20%

B

40%

C

50%

D

70%

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15

2009 · Chemical Engineering · Heat Transfer · Conduction, Convection and Radiation

Chemical Engineering (CH) 2009

The maximum temperature in the slab occurs at \( x \) equal to

A

0

B

\(L/4 \)

C

\(L/2 \)

D

\(L \)

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16

2009 · Chemical Engineering · Heat Transfer · Conduction, Convection and Radiation

Chemical Engineering (CH) 2009

The heat flux at \( x = L \) is

A

0

B

\(S L/4 \)

C

\(S L/2 \)

D

\(S L \)

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17

2010 · Chemical Engineering · Heat Transfer · Conduction, Convection and Radiation

Chemical Engineering (CH) 2010

The ratio of Nusselt number to Biot number is

A

Conductive resistance of fluid / conductive resistance of solid

B

Conductive resistance of fluid / convective resistance of fluid

C

Conductive resistance of solid / conductive resistance of fluid

D

Unity

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18

2010 · Chemical Engineering · Heat Transfer · Conduction, Convection and Radiation

Chemical Engineering (CH) 2010

The ratio of the thermal boundary layer thickness to the concentration boundary layer thickness is proportional to

A

Nu

B

Le

C

Sh

D

Pr

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19

2010 · Chemical Engineering · Heat Transfer · Conduction, Convection and Radiation

Chemical Engineering (CH) 2010

The figure below shows steady state temperature profiles for one dimensional heat transfer within a solid slab for the following cases:
P: uniform heat generation with left surface perfectly insulated
Q: uniform heat generation with right surface perfectly insulated
R: uniform heat consumption with left surface perfectly insulated
S: uniform heat consumption with right surface perfectly insulated
Match the profiles with appropriate cases.

A

P – I, Q – III, R – II, S – IV

B

P – II, Q – III, R – I, S – IV

C

P – I, Q – IV, R – II, S – III

D

P – II, Q – IV, R – I, S – III

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20

2010 · Chemical Engineering · Heat Transfer · Conduction, Convection and Radiation

Chemical Engineering (CH) 2010

The view factor matrix for two infinitely long co-axial cylinders, shown in the figure below, is

A

\(\begin{bmatrix} 0 & 1 \\ 0.5 & 0.5 \end{bmatrix} \)

B

\(\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix} \)

C

\(\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} \)

D

\(\begin{bmatrix} 0.5 & 0.5 \\ 0 & 1 \end{bmatrix} \)

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