A furnace wall is made of three materials (I, II and III) of equal thickness and having thermal conductivity k1 k2 and k3 respectively. The steady state temperature profile inside each material is shown in the figure. Thermal conductivities of the materials will vary as <img src="/images/question-image/metallurgical-engineering/miscellaneous-in-metallurgy/1684344480-M2-B-19-18.PNG" title="Miscellaneous in Metallurgy mcq question image" alt="Miscellaneous in Metallurgy mcq question image">

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 profiles is as shown below, then the material with the lowest thermal conductivity is

A

M1

B

M2

C

M3

D

M4

Thin layer of material B (of total amount m) is plated on the end faces of two long rods of material A. These are then joined together on the plated side (see the figure below) and heated to a high temperature. Assuming the diffusion coefficient of B in A is D, the composition profile CB along the rod axis x after a time t is described by

A

$${C_B} = \frac{m}{{2\sqrt {\pi Dt} }}\exp \left$$

B

$${C_B} = \frac{m}{{2\sqrt {\pi Dt} }}erf\left$$

C

$${C_B} = \frac{m}{{2\sqrt {\pi Dt} }}\left$$

D

$${C_B} = \frac{m}{{2\sqrt {\pi Dt} }}t$$

The diffusion couple shown below is made from two A-B alloys. The initial compositions of the two alloys are indicated in the diagram. The centreline is at x = 0. The couple is held at an elevated temperature for 40 hours. Diffusivity; D = 3 × 10^-11 m^-2 s^-1. Assume the diffusion couple to be infinitely long.

Which of the parameters give the composition profile in the following form?
$$C\left( {x,t} \right) + {c_1} + {c_2}\,erf\left( {\frac{1}{{2\sqrt {Dt} }}} \right)$$

A

c1 = 0.45, c2 = 0.05

B

c1 = 0.5, c2 = 0.4

C

c1 = -0.05, c2 = 0.45

D

c1 = 0.1, c2 = 0.9

Walls of a cubical oven are of thickness l, and they are made of material of thermal conductivity k. The temperature inside the oven is 100°C and the inside heat transfer co-efficient is 3k/l. If the wall temperature on the outside is held at 25°C, what is the inside wall temperature in degree centigrade?

A

35.5

B

43.75

C

81.25

D

48.25

An elliptical dislocation loop is gliding on plane ABCD of a single crystal of BCC material as shown in the following figure. It is gliding along the burger vector 'b'. Identify the correct statement.

P. Plane ABCD belongs to the family of (110).
Q. Burger vector 'b' belong to direction.
R. Dislocation has the edge character at point x and the screw character at point z.
S. Dislocation has the screw character at point x

A

P, Q

B

Q, R

C

P, R

D

P, S

A composite wall is made of two layers of thickness δ1 and δ2 having thermal conductivities k and 2k and equal surface area normal to the direction of heat flow. The outer surface of composite wall are at 100 degree Celsius and 200 degree Celsius. The minimum surface temperature at the junction is 150 degree Celsius. What will be the ratio of wall thickness?

A

1:1

B

2:1

C

1:2

D

2:3

From a 2 m × 1.2m sheet, squares are Cut out from each of the four comers as shown in the figure and then the sides are bent to form an open box. The maximum possible volume (in m³) of the box is

A

0.14

B

0.26

C

0.54

D

0.82

A furnace wall consists of two layers. The inside layer of 450 mm is made of light weight bricks of thermal conductivity IW/m.K and outside layer of 900 mm is made of refractory of thermal conductivity 2W/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 . . . . . . . . K.

A

1000

B

850

C

700

D

600

An alloy of overall composition, X_B = 0.7 was equilibrated at temperature T₁. Microstructural analysis showed two phases, (α and β, and that the phase fraction of β was 0.75. Given that the equilibrium composition of β at Ti is 0.9 as shown in the phase diagram below, the maximum solubility of B in α (in mole fraction) at this temperature is . . . . . . . .

A

0.05

B

0.10

C

0.50

D

0.85

A furnace is made of a refractory brick wall of thickness 0.5 metre and thermal conductivity 0.7 W/m.°K For the same temperature drop and heat loss, this refractory wall can be replaced by a layer of diatomaceous earth of thermal conductivity 0.14 W/m.K and thickness __________ metre.

A

0.01

B

0.1

C

0.25

D

0.5