Chose the correct one with respect to critical radius of insulation

Heat loss decreases with addition of insulation

There is more heat loss i.e. conductive

There occurs a decrease in heat flux

Heat loss increases with addition of insulation

Heat loss decreases with addition of insulation

For insulation to be properly effective in restricting heat transmission, the pipe radius r0 will be

Greater than or equal to critical radius

A plane wall of thickness δ has its surfaces maintained at temperatures T₁ and T₂. The wall is made of a material whose thermal conductivity varies with temperature according to the relation k = k₀ T². Find the expression to work out the steady state heat conduction through the wall?

Q = A k₀ (T₁² – T₂²)/3 δ

Q = 2A k₀ (T₁³ – T₂³)/3 δ

Q = A k₀ (T₁³ – T₂³)/3 δ

Q = A k₀ (T₁² – T₂²)/3 δ

Q = A k₀ (T₁ – T₂)/3 δ

Let us say thermal conductivity of a wall is governed by the relation k = k0 (1 + α t). In that case the temperature at the mid-plane of the heat conducting wall would be

Less than average of the temperature at the wall faces

Av. of the temperature at the wall faces

More than average of the temperature at the wall faces

Less than average of the temperature at the wall faces

Depends upon the temperature difference between the wall faces

With respect to the equation k = k0 (1 +β t) which is true if we put β = 0?

Slope of temperature curve does not change

Slope of temperature curve is constant

Slope of temperature curve does not change

Slope of temperature curve increases

Slope of temperature curve is decreases

The temperatures on the two sides of a plane wall are t1 and t2 and thermal conductivity of the wall material is prescribed by the relationK = k0 e^(-x/δ)Where, k0 is constant and δ is the wall thickness. Find the relation for temperature distribution in the wall?

t 1 – t x / t 1 – t 2 = δ/x

t 1 – t x / t 1 – t 2 = x/δ

69 + Mcqs in Steady State Conduction in Heat Transfer Page 1 McqOptions

1.	A cable of 10 mm outside is to be laid in an atmosphere of 25 degree Celsius (h = 12.5 W/m² degree) and its surface temperature is likely to be 75 degree Celsius due to heat generated within it. How would the heat flow from the cable be affected if it is insulated with rubber having thermal conductivity k = 0.15 W/m degree?
A.	43.80 W per meter length
B.	53.80 W per meter length
C.	63.80 W per meter length
D.	73.80 W per meter length
Answer» C. 63.80 W per meter length

Discussion

2.	The inner and outer surfaces of a furnace wall, 25 cm thick, are at 300 degree Celsius and 30 degree Celsius. Here thermal conductivity is given by the relationK = (1.45 + 0.5 * 10¯⁵ t²) KJ/m hr degWhere, t is the temperature in degree centigrade. Calculate the heat loss per square meter of the wall surface area?
A.	1355.3 kJ/m² hr
B.	2345.8 kJ/m² hr
C.	1745.8 kJ/m² hr
D.	7895.9 kJ/m² hr
Answer» D. 7895.9 kJ/m² hr

Discussion

3.	Chose the correct one with respect to critical radius of insulation
A.	There is more heat loss i.e. conductive
B.	There occurs a decrease in heat flux
C.	Heat loss increases with addition of insulation
D.	Heat loss decreases with addition of insulation
Answer» D. Heat loss decreases with addition of insulation

Discussion

4.	The unit of thermal conductivity doesn’t contain which parameter?
A.	Watt
B.	Pascal
C.	Meter
D.	Kelvin
Answer» C. Meter

Discussion

5.	A pipe of outside diameter₂0 mm is to be insulated with asbestos which has a mean thermal conductivity of 0.1 W/m degree. The local coefficient of convective heat to the surroundings is 5 W/square meter degree. Find the critical radius of insulation for optimum heat transfer from pipe?
A.	10 mm
B.	20 mm
C.	30 mm
D.	40 mm
Answer» C. 30 mm

Discussion

6.	For insulation to be properly effective in restricting heat transmission, the pipe radius r0 will be
A.	Greater than critical radius
B.	Less than critical radius
C.	Equal to critical radius
D.	Greater than or equal to critical radius
Answer» E.

Discussion

7.	The value of critical radius in case of cylindrical hollow object is
A.	2k/h
B.	2h/k
C.	k/h
D.	h/k
Answer» D. h/k

Discussion

8.	A wire of radius 3 mm and 1.25 m length is to be maintained at 60 degree Celsius by insulating it by a material of thermal conductivity 0.175 W/m K. The temperature of surrounding is 20 degree Celsius with heat transfer coefficient 8.5 W/ m² K. Find percentage increase in heat loss due to insulation?
A.	134.46 %
B.	124.23 %
C.	100.00 %
D.	12.55 %
Answer» B. 124.23 %

Discussion

9.	A heat exchanger shell of outside radius 15 cm is to be insulated with glass wool of thermal conductivity 0.0825 W/m degree. The temperature at the surface is 280 degree Celsius and it can be assumed to remain constant after the layer of insulation has been applied to the shell. The convective film coefficient between the outside surface of glass wool and the surrounding air is estimated to be 8 W/m² degree. What is the value of critical radius?
A.	9.31 mm
B.	10.31 mm
C.	11.31 mm
D.	12.31 mm
Answer» C. 11.31 mm

Discussion

10.	“Radiation cannot be affected through vacuum or space devoid of any matter”. True or false
A.	True
B.	False
C.	May be
D.	Can't say
Answer» C. May be

Discussion

11.	A composite slab has two layers having thermal conductivities in the ratio of 1:2. If thickness is same for each layer then the equivalent thermal conductivity of the slab would be
A.	1/3
B.	2/3
C.	2
D.	4/3
Answer» E.

Discussion

12.	The rate of heat conduction through a cylindrical tube is usually expressed as
A.	Per unit length
B.	Per unit area
C.	Only length
D.	Only area
Answer» B. Per unit area

Discussion

13.	Typical examples of heat conduction through cylindrical tubes are not found in
A.	Power plants
B.	Oil refineries
C.	Most process industries
D.	Aircrafts
Answer» E.

Discussion

14.	In case of homogeneous plane wall, there is a linear temperature distribution given by
A.	t = t₁ + (t₂-t₁) δ/x
B.	t = t₂ – (t₂-t₁) x/ δ
C.	t = t₁ + (t₂-t₁) x
D.	t = t₁ + (t₂-t₁) x/ δ
Answer» E.

Discussion

15.	A homogeneous wall of area A and thickness δ has left and right hand surface temperatures of 0 degree Celsius and 40 degree Celsius. Determine the temperature at the center of the wall
A.	10 degree Celsius
B.	20 degree Celsius
C.	30 degree Celsius
D.	40 degree Celsius
Answer» C. 30 degree Celsius

Discussion

16.	Heat is transferred from a hot fluid to a cold one through a plane wall of thickness (δ), surface area (A) and thermal conductivity (k). The thermal resistance is
A.	1/A (1/h₁ + δ/k + 1/h₂)
B.	A (1/h₁ + δ/k + 1/h₂)
C.	1/A (h₁ + δ/k + h₂)
D.	A (1/h₁ + δ/k + 1/h₂)
Answer» B. A (1/h₁ + δ/k + 1/h₂)

Discussion

17.	A plane wall of thickness δ has its surfaces maintained at temperatures T₁ and T₂. The wall is made of a material whose thermal conductivity varies with temperature according to the relation k = k₀ T². Find the expression to work out the steady state heat conduction through the wall?
A.	Q = 2A k₀ (T₁³ – T₂³)/3 δ
B.	Q = A k₀ (T₁³ – T₂³)/3 δ
C.	Q = A k₀ (T₁² – T₂²)/3 δ
D.	Q = A k₀ (T₁ – T₂)/3 δ
Answer» C. Q = A k₀ (T₁² – T₂²)/3 δ

Discussion

18.	Let us say thermal conductivity of a wall is governed by the relation k = k0 (1 + α t). In that case the temperature at the mid-plane of the heat conducting wall would be
A.	Av. of the temperature at the wall faces
B.	More than average of the temperature at the wall faces
C.	Less than average of the temperature at the wall faces
D.	Depends upon the temperature difference between the wall faces
Answer» C. Less than average of the temperature at the wall faces

Discussion

19.	A rod of 3 cm diameter and 20 cm length is maintained at 100 degree Celsius at one end and 10 degree Celsius at the other end. These temperature conditions are attained when there is heat flow rate of 6 W. If cylindrical surface of the rod is completely insulated, determine the thermal conductivity of the rod material
A.	21.87 W/m degree
B.	20.87 W/m degree
C.	19.87 W/m degree
D.	18.87 W/m degree
Answer» E.

Discussion

20.	With variable thermal conductivity, Fourier law of heat conduction through a plane wall can be expressed as
A.	Q = -k0 (1 + β t) A d t/d x
B.	Q = k0 (1 + β t) A d t/d x
C.	Q = – (1 + β t) A d t/d x
D.	Q = (1 + β t) A d t/d x
Answer» B. Q = k0 (1 + β t) A d t/d x

Discussion

21.	A composite wall generally consists of
A.	One homogenous layer
B.	Multiple heterogeneous layers
C.	One heterogeneous layer
D.	Multiple homogenous layers
Answer» C. One heterogeneous layer

Discussion

22.	The rate of convective heat transfer between a solid boundary and adjacent fluid is given by
A.	Q = h A (ts – tf)
B.	Q = h A
C.	Q = (ts – tf)
D.	Q = h (ts – tf)
Answer» B. Q = h A

Discussion

23.	With respect to the equation k = k0 (1 +β t) which is true if we put β = 0?
A.	Slope of temperature curve is constant
B.	Slope of temperature curve does not change
C.	Slope of temperature curve increases
D.	Slope of temperature curve is decreases
Answer» B. Slope of temperature curve does not change

Discussion

24.	For the same material and same temperature difference, the heat flow in terms of shape factor is given by
A.	S k d t
B.	k d t/S
C.	2S k/d t
D.	2S/3
Answer» B. k d t/S

Discussion

25.	The annealing furnace for continuous bar stock is open at the ends and has interior dimensions of 0.6 m * 0.6 m * 1.5 m long with a wall 0.3 m thick all around. Calculate the shape factor for the furnace?
A.	15.24 m
B.	16.34 m
C.	14.54 m
D.	13.76 m
Answer» B. 16.34 m

Discussion

26.	“All the factors relating to geometry of the sections are grouped together into a multiple constant called the shape factor” True or false
A.	True
B.	False
C.	May be
D.	Can't say
Answer» C. May be

Discussion

27.	A spherical vessel of 0.5 m outside diameter is insulated with 0.2 m thickness of insulation of thermal conductivity 0.04 W/m degree. The surface temperature of the vessel is – 195 degree Celsius and outside air is at 10 degree Celsius. Determine heat flow
A.	– 47.93 W
B.	– 57.93 W
C.	– 67.93 W
D.	– 77.93 W
Answer» C. – 67.93 W

Discussion

28.	A spherical vessel of 0.5 m outside diameter is insulated with 0.2 m thickness of insulation of thermal conductivity 0.04 W/m degree. The surface temperature of the vessel is – 195 degree Celsius and outside air is at 10 degree Celsius. Determine heat flow per m² based on inside area
A.	– 63.79 W/m²
B.	– 73.79 W/m²
C.	– 83.79 W/m²
D.	– 93.79 W/m²
Answer» C. – 83.79 W/m²

Discussion

29.	The quantity d t/Q for conduction of heat through a body i.e. spherical in shape is
A.	ln (r2/r1)/2πLk
B.	ln (r2/r1)/πLk
C.	ln (r2/r1)/2Lk
D.	ln (r2/r1)/2πk
Answer» B. ln (r2/r1)/πLk

Discussion

30.	The thermal resistance for heat conduction through a hollow sphere of inner radius r1 and outer radius r2 is
A.	r₂ – r₁/4πk r₁r₂
B.	r₂ /4πk r₁r₂
C.	r₁/4πk r₁r₂
D.	4πk r₁r₂
Answer» B. r₂ /4πk r₁r₂

Discussion

31.	A stainless steel tube with inner diameter₁2 mm, thickness 0.2 mm and length 50n cm is heated electrically. The entire 15 k W of heat energy generated in the tube is transferred through its outer surface. Find the intensity of current flow
A.	52 amps
B.	62 amps
C.	72 amps
D.	82 amps
Answer» B. 62 amps

Discussion

32.	A cylindrical cement tube of radii 0.05 cm and 1.0 cm has a wire embedded into it along its axis. To maintain a steady temperature difference of 120 degree Celsius between the inner and outer surfaces, a current of 5 ampere is made to flow in the wire. Find the amount of heat generated per meter length. Take resistance of wire equal to 0.1 ohm per cm of length
A.	150 W/m length
B.	250 W/m length
C.	350 W/m length
D.	450 W/m length
Answer» C. 350 W/m length

Discussion

33.	The thermal resistance for heat conduction through a spherical wall is
A.	(r₂-r₁)/2πkr₁r₂
B.	(r₂-r₁)/3πkr₁r₂
C.	(r₂-r₁)/πkr₁r₂
D.	(r₂-r₁)/4πkr₁r₂
Answer» E.

Discussion

34.	For steady state and constant value of thermal conductivity, the temperature distribution associated with radial convection through a cylinder is
A.	Linear
B.	Parabolic
C.	Logarithmic
D.	Exponential
Answer» D. Exponential

Discussion

35.	For a prescribed temperature difference, bodies with the same shape factor will allow heat conduction proportional to
A.	k/2
B.	2k
C.	k
D.	k/4
Answer» D. k/4

Discussion

36.	The temperature distribution associated with radial conduction through a sphere is represented by
A.	Parabola
B.	Hyperbola
C.	Linear
D.	Ellipse
Answer» C. Linear

Discussion

37.	The interior of an oven is maintained at a temperature of 850 degree Celsius by means of a suitable control apparatus. The oven walls are 500 mm thick and are fabricated from a material of thermal conductivity 0.3 W/m degree. For an outside wall temperature of 250 degree Celsius, workout the resistance to heat flow
A.	0.667 degree/W
B.	1.667 degree/W
C.	2.667 degree/W
D.	3.667 degree/W
Answer» C. 2.667 degree/W

Discussion

38.	A hot fluid is being conveyed through a long pipe of 4 cm outer diameter and covered with 2 cm thick insulation. It is proposed to reduce the conduction heat loss to the surroundings to one-third of the present rate by further covering with same insulation. Calculate the additional thickness of insulation
A.	11 cm
B.	12 cm
C.	13 cm
D.	14 cm
Answer» C. 13 cm

Discussion

39.	Logarithmic mean area of the cylindrical tube is given as
A.	2πrm
B.	πrml
C.	2πrml
D.	2rml
Answer» D. 2rml

Discussion

40.	Let us assume two walls of same thickness and cross-sectional area having thermal conductivities in the ratio 1/2. Let us say there is same temperature difference across the wall faces, the ratio of heat flow will be
A.	1
B.	1/2
C.	2
D.	4
Answer» C. 2

Discussion

41.	The heat flow equation through a cylinder of inner radius r1 and outer radius r2 is desired to be written in the same form as that for heat flow through a plane wall. For wall thickness (r₂-r₁) the area will be
A.	A1 + A2/2
B.	A1 + A2
C.	A2 – A1/ log e (A2/A1)
D.	A1 + A2/2 log e (A2/A1)
Answer» B. A1 + A2

Discussion

42.	The following data pertains to a hollow cylinder and a hollow sphere made of same material and having the same temperature drop over the wall thicknessInside radius = 0.1 m and outside surface area = 1 square meterIf the outside radius for both the geometrics is same, calculate the ratio of heat flow in the cylinder to that of sphere?
A.	0.056
B.	2.345
C.	1.756
D.	3.543
Answer» D. 3.543

Discussion

43.	A cylinder of radius r and made of material of thermal conductivity k 1 is surrounded by a cylindrical shell of inner radius r and outer radius 2r. This outer shell is made of a material of thermal conductivity k 2. Net conductivity would be
A.	k 1 + 3 k 2/4
B.	k 1 + k 2/4
C.	k 1 + 3k 2
D.	k 1 + k 2
Answer» B. k 1 + k 2/4

Discussion

44.	“If β is less than zero, then with respect to the relation k = k0 (1 + β t), conductivity depends on surface area”. True or false
A.	True
B.	False
C.	May be
D.	Can't say
Answer» C. May be

Discussion

45.	The temperature distribution in a large thin plate with uniform surface temperature will be(Assume steady state condition)
A.	Logarithmic
B.	Hyperbolic
C.	Parabolic
D.	Linear
Answer» E.

Discussion

46.	The temperatures on the two sides of a plane wall are t1 and t2 and thermal conductivity of the wall material is prescribed by the relationK = k0 e^(-x/δ)Where, k0 is constant and δ is the wall thickness. Find the relation for temperature distribution in the wall?
A.	t 1 – t x / t 1 – t 2 = x
B.	t 1 – t x / t 1 – t 2 = δ
C.	t 1 – t x / t 1 – t 2 = δ/x
D.	t 1 – t x / t 1 – t 2 = x/δ
Answer» E.

Discussion

47.	Shape factor for cylinder is
A.	6 π l/log e (r₂/r₁)
B.	4 π l/log e (r₂/r₁)
C.	π l/log e (r₂/r₁)
D.	2 π l/log e (r₂/r₁)
Answer» E.

Discussion

48.	A composite wall of a furnace has two layers of equal thickness having thermal conductivities in the ratio 2:3. What is the ratio of temperature drop across the two layers?
A.	2:3
B.	3:2
C.	1:2
D.	log e 2 : log e 3
Answer» C. 1:2

Discussion

49.	Shape factor for sphere is
A.	4 π r₁ r₂
B.	4 π r₁ r₂/r₂ – r₁
C.	4 π /r₂ – r₁
D.	r₁ r₂/r₂ – r₁
Answer» C. 4 π /r₂ – r₁

Discussion

50.	Shape factor for plane wall is equal to
A.	A/δ
B.	2A/δ
C.	3A/δ
D.	4A/δ
Answer» B. 2A/δ

Discussion

Explore topic-wise MCQs in Heat Transfer.

Chose the correct one with respect to critical radius of insulation

The unit of thermal conductivity doesn’t contain which parameter?

A pipe of outside diameter₂0 mm is to be insulated with asbestos which has a mean thermal conductivity of 0.1 W/m degree. The local coefficient of convective heat to the surroundings is 5 W/square meter degree. Find the critical radius of insulation for optimum heat transfer from pipe?

For insulation to be properly effective in restricting heat transmission, the pipe radius r0 will be

The value of critical radius in case of cylindrical hollow object is

“Radiation cannot be affected through vacuum or space devoid of any matter”. True or false

A composite slab has two layers having thermal conductivities in the ratio of 1:2. If thickness is same for each layer then the equivalent thermal conductivity of the slab would be

The rate of heat conduction through a cylindrical tube is usually expressed as

Typical examples of heat conduction through cylindrical tubes are not found in

In case of homogeneous plane wall, there is a linear temperature distribution given by

A homogeneous wall of area A and thickness δ has left and right hand surface temperatures of 0 degree Celsius and 40 degree Celsius. Determine the temperature at the center of the wall

Heat is transferred from a hot fluid to a cold one through a plane wall of thickness (δ), surface area (A) and thermal conductivity (k). The thermal resistance is

A plane wall of thickness δ has its surfaces maintained at temperatures T₁ and T₂. The wall is made of a material whose thermal conductivity varies with temperature according to the relation k = k₀ T². Find the expression to work out the steady state heat conduction through the wall?

Let us say thermal conductivity of a wall is governed by the relation k = k0 (1 + α t). In that case the temperature at the mid-plane of the heat conducting wall would be

With variable thermal conductivity, Fourier law of heat conduction through a plane wall can be expressed as

A composite wall generally consists of

The rate of convective heat transfer between a solid boundary and adjacent fluid is given by

With respect to the equation k = k0 (1 +β t) which is true if we put β = 0?

For the same material and same temperature difference, the heat flow in terms of shape factor is given by

The annealing furnace for continuous bar stock is open at the ends and has interior dimensions of 0.6 m * 0.6 m * 1.5 m long with a wall 0.3 m thick all around. Calculate the shape factor for the furnace?

“All the factors relating to geometry of the sections are grouped together into a multiple constant called the shape factor” True or false

A spherical vessel of 0.5 m outside diameter is insulated with 0.2 m thickness of insulation of thermal conductivity 0.04 W/m degree. The surface temperature of the vessel is – 195 degree Celsius and outside air is at 10 degree Celsius. Determine heat flow

A spherical vessel of 0.5 m outside diameter is insulated with 0.2 m thickness of insulation of thermal conductivity 0.04 W/m degree. The surface temperature of the vessel is – 195 degree Celsius and outside air is at 10 degree Celsius. Determine heat flow per m² based on inside area

The quantity d t/Q for conduction of heat through a body i.e. spherical in shape is

The thermal resistance for heat conduction through a hollow sphere of inner radius r1 and outer radius r2 is

A stainless steel tube with inner diameter₁2 mm, thickness 0.2 mm and length 50n cm is heated electrically. The entire 15 k W of heat energy generated in the tube is transferred through its outer surface. Find the intensity of current flow

The thermal resistance for heat conduction through a spherical wall is

For steady state and constant value of thermal conductivity, the temperature distribution associated with radial convection through a cylinder is

For a prescribed temperature difference, bodies with the same shape factor will allow heat conduction proportional to

The temperature distribution associated with radial conduction through a sphere is represented by

Logarithmic mean area of the cylindrical tube is given as

Let us assume two walls of same thickness and cross-sectional area having thermal conductivities in the ratio 1/2. Let us say there is same temperature difference across the wall faces, the ratio of heat flow will be

The heat flow equation through a cylinder of inner radius r1 and outer radius r2 is desired to be written in the same form as that for heat flow through a plane wall. For wall thickness (r₂-r₁) the area will be

A cylinder of radius r and made of material of thermal conductivity k 1 is surrounded by a cylindrical shell of inner radius r and outer radius 2r. This outer shell is made of a material of thermal conductivity k 2. Net conductivity would be

“If β is less than zero, then with respect to the relation k = k0 (1 + β t), conductivity depends on surface area”. True or false

The temperature distribution in a large thin plate with uniform surface temperature will be(Assume steady state condition)

The temperatures on the two sides of a plane wall are t1 and t2 and thermal conductivity of the wall material is prescribed by the relationK = k0 e^(-x/δ)Where, k0 is constant and δ is the wall thickness. Find the relation for temperature distribution in the wall?

Shape factor for cylinder is

A composite wall of a furnace has two layers of equal thickness having thermal conductivities in the ratio 2:3. What is the ratio of temperature drop across the two layers?

Shape factor for sphere is

Shape factor for plane wall is equal to