Heat transfer - Transport Phenomena and Rate Processes - Metallurgical Engineering Previous Year Questions

1

2007 · Metallurgical Engineering · Transport Phenomena and Rate Processes · Heat transfer

Metallurgical Engineering (MT) 2007

The dimension of thermal conductivity in terms of mass (M), length (L), time (T), and temperature (θ) is

A

\(M L^2 T^{-3} θ^{-1}\)

B

\(M T^{-3} θ^{-1}\)

C

\(L^2 T^{-1}\)

D

\(M L T^{-3} θ^{-1}\)

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2

2009 · Metallurgical Engineering · Transport Phenomena and Rate Processes · Heat transfer

Metallurgical Engineering (MT) 2009

A furnace wall consists of four layers of different materials, M1, M2, M3 and M4. If the layers are of equal thickness and the steady state temperature profile is, as shown below, then the material with the lowest thermal conductivity is

A

M1

B

M2

C

M3

D

M4

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3

2010 · Metallurgical Engineering · Transport Phenomena and Rate Processes · Heat transfer

Metallurgical Engineering (MT) 2010

At steady state and when the inner and outer walls of a long hollow cylinder are kept at two different temperatures, the unidirectional temperature variation along the thickness of the wall is

A

linear

B

parabolic

C

logarithmic

D

constant

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4

2010 · Metallurgical Engineering · Transport Phenomena and Rate Processes · Heat transfer

Metallurgical Engineering (MT) 2010

The temperature of a gas flowing in a long duct as measured by a thermocouple (having an emissivity of 0.5) is 800 K. The internal wall surface of the duct is at a temperature of 500 K. The convective heat transfer coefficient between the gas and the tip of the thermocouple is 100 Wm^-2K^-1. The actual gas temperature is approximately

A

400 K

B

500 K

C

820 K

D

900 K

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5

2011 · Metallurgical Engineering · Transport Phenomena and Rate Processes · Heat transfer

Metallurgical Engineering (MT) 2011

A furnace wall consists of two layers. The inside layer of 450 mm is made of light weight bricks of thermal conductivity 1 W/m.K and the outside layer of 900 mm is made of refractory of thermal conductivity 2 W/m.K. The hot face of the inside layer is at temperature 1300 K and the cold face of the outer layer is at 400 K. The temperature at the interface between the two layers is

A

1000 K

B

850 K

C

700 K

D

600 K

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6

2012 · Metallurgical Engineering · Transport Phenomena and Rate Processes · Heat transfer

Metallurgical Engineering (MT) 2012

How many boundary conditions are required to solve the following equation? \[ \frac{\partial^2 T}{\partial r^2} + \frac{1}{r} \frac{\partial T}{\partial r} = \frac{1}{\alpha} \frac{\partial T}{\partial t} \]

A

Two in r-direction

B

One in r-direction and one for time

C

Two in r-direction and one for time

D

Three in r-direction and one for time

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7

2012 · Metallurgical Engineering · Transport Phenomena and Rate Processes · Heat transfer

Metallurgical Engineering (MT) 2012

Hot metal at 1700 K is poured in a sand mould that is open at the top. Heat loss from the liquid metal takes place by

A

Radiation only

B

Radiation and conduction only

C

Radiation and convection only

D

Radiation, conduction and convection

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8

2013 · Metallurgical Engineering · Transport Phenomena and Rate Processes · Heat transfer

Metallurgical Engineering (MT) 2013

The total number of possible heat transfer mode(s) is __________

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9

2014 · Metallurgical Engineering · Transport Phenomena and Rate Processes · Heat transfer

Metallurgical Engineering (MT) 2014

Consider a steady state heat flux across a rectangular slab composed of two layers of equal width as shown in the figure below. The thermal conductivities are in the ratio of \( \frac{k_1}{k_2} = 10 \). If the first layer experiences a temperature drop \( (T_1 - T_2) \) of 50 K, what is the temperature drop \( (T_2 - T_3) \), in K, across the second layer? ______

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10

2017 · Metallurgical Engineering · Transport Phenomena and Rate Processes · Heat transfer

Metallurgical Engineering (MT) 2017

A continuous cast steel slab, 1 m × 1 m × 0.1 m, at 1298 K cools in air. The initial rate of heat loss (in kW) from the top surface of slab by radiation and convection is __________ (answer up to two decimal places) Given: (i) Ambient temperature = 298 K, (ii) emissivity of steel = 0.8, (iii) convective heat transfer coefficient = 4.6 W.m⁻².K⁻¹, (iv) Stefan-Boltzmann constant (σ) = 5.7×10⁻⁸ W.m⁻².K⁻⁴

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11

2018 · Metallurgical Engineering · Transport Phenomena and Rate Processes · Heat transfer

Metallurgical Engineering (MT) 2018

For a laminar flow of a liquid metal over a flat plate, the thicknesses of the velocity and thermal boundary layers are \(\delta_v\) and \(\delta_t\) respectively. Kinematic viscosity (viscosity/density) of liquid metal is significantly lower than its thermal diffusivity [thermal conductivity / (density × specific heat)]. Based on this information, pick the correct option.
(Note: The temperature of the liquid metal is different from that of the plate).

A

\(\delta_v < \delta_t\)

B

\(\delta_v > \delta_t\)

C

\(\delta_v = \delta_t\)

D

Information insufficient

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12

2018 · Metallurgical Engineering · Transport Phenomena and Rate Processes · Heat transfer

Metallurgical Engineering (MT) 2018

As shown in schematic below, an alloy is cast as a rectangular slab between two thick mould walls that differ in their thermal conductivities. Shrinkage defects are found at a distance L1 from Mould-1 with thermal conductivity \(k_1\) and distance L2 from Mould-2 with thermal conductivity \(k_2\). If the ratio L1:L2 = 3:2, and assuming 1-D heat transfer, the ratio \((k_1/k_2)\) is ______ (to two decimal places)

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13

2018 · Metallurgical Engineering · Transport Phenomena and Rate Processes · Heat transfer

Metallurgical Engineering (MT) 2018

A spherical liquid metal droplet of diameter 1 mm is solidified in a stream of gas at 300 K. Assuming that the metal droplet remains at its melting point of 900 K and neglecting radiative losses, the time to complete the solidification is ______ (in seconds to one decimal place). Given: The enthalpy of fusion for the metal is 4000 kJ kg\(^{-1}\); The gas-droplet convective heat transfer coefficient is 200 W m\(^{-2}\) K\(^{-1}\); Density of liquid metal is 2700 kg m\(^{-3}\).

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14

2019 · Metallurgical Engineering · Transport Phenomena and Rate Processes · Heat transfer

Metallurgical Engineering (MT) 2019

Steady state radial heat conduction through a hollow, infinitely long zirconia cylinder is governed by the following ordinary differential equation:
\(\frac{1}{r} \frac{d}{dr} \left( r k \frac{dT}{dr} \right) = 0\)
Where, \(T\) is the temperature and \(r\) is the radial distance. The inner surface of the hollow cylinder is maintained at 1473 K and the outer surface at 973 K. The rate of heat loss per unit length through the outer surface of the hollow cylinder (in \(W.m^{-1}\), rounded off to the nearest integer) is ______.
Given: Inner radius of cylinder = 0.05 m; outer radius of cylinder = 0.07 m and thermal conductivity of zirconia (\(k\)) = 2 \(W.m^{-1}.K^{-1}\).

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15

2020 · Metallurgical Engineering · Transport Phenomena and Rate Processes · Heat transfer

Metallurgical Engineering (MT) 2020

Two solid spheres X and Y of identical diameter are made of different materials having thermal diffusivities 100 × 10⁻⁶ m²s⁻¹ and 25 × 10⁻⁶ m²s⁻¹ respectively. Both spheres are heated in a furnace maintained at 1000 K. If the center of the sphere X reaches 800 K in 1 hour, time required for the center of sphere Y to reach 800 K is

A

1 hour.

B

2 hours.

C

4 hours.

D

16 hours.

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16

2020 · Metallurgical Engineering · Transport Phenomena and Rate Processes · Heat transfer

Metallurgical Engineering (MT) 2020

Select the correct spectra (shown on a log-log scale in the figures) for emission from a gray surface and a black body, both maintained at 1000 K.

A

B

C

D

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17

2021 · Metallurgical Engineering · Transport Phenomena and Rate Processes · Heat transfer

Metallurgical Engineering (MT) 2021

One-dimensional steady-state temperature distribution in two adjacent refractory blocks (with thermal conductivities, \(k_1\) and \(k_2\)) of unit cross-sectional area are shown below. The temperature \(T_1\) and thermal contact resistance of the interface, respectively, are:

A

200 K, 0.5 K W⁻¹

B

400 K, 1.0 K W⁻¹

C

200 K, 0.25 K W⁻¹

D

500 K, 0.5 K W⁻¹

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18

2021 · Metallurgical Engineering · Transport Phenomena and Rate Processes · Heat transfer

Metallurgical Engineering (MT) 2021

A solid sphere (0.5 m radius) is enclosed within a larger hollow sphere (1 m radius), as shown in Figure. The radiation exchange takes place between the outer surface (surface 1) of the small sphere and the inner surface (surface 2) of the bigger sphere. The value of the view factor, \( F_{22} \) is: ______ (round off to 2 decimal places).
Given: View factor (\( F_{ij} \)) is the fraction of the radiation leaving surface i that is intercepted by surface j.

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19

2022 · Metallurgical Engineering · Transport Phenomena and Rate Processes · Heat transfer

Metallurgical Engineering (MT) 2022

Which of the following statement(s) is(are) TRUE about black body radiation?

A

Among all radiation emitted by an ideal black body at room temperature, the most intense radiation falls in the visible light spectrum

B

The total emissive power of an ideal black body is proportional to the square of its absolute temperature

C

The emissive power of an ideal black body peaks at a wavelength λ which is inversely proportional to its absolute temperature

D

The radiant energy emitted by an ideal black body is greater than that emitted by the non-black body at all temperatures above 0 K

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20

2022 · Metallurgical Engineering · Transport Phenomena and Rate Processes · Heat transfer

Metallurgical Engineering (MT) 2022

A rectangular block made of Material I and Material II of identical cross sections (as shown in the figure) has a temperature (T) of 435 K and 400 K at the bottom and top surfaces, respectively. Assuming purely steady state conductive heat transfer, the temperature at the interface is ______ K (round off to nearest integer).
(Given: The two parts of the block made of Material I and Material II have equal thickness of 25 mm each. The thermal conductivities of Material I and Material II are 50 W·m⁻¹·K⁻¹ and 200 W·m⁻¹·K⁻¹, respectively.)

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