Double pipe heat exchangers are preferably useful, when%!

Overall heat transfer co-efficient is very high

High viscosity liquid is to be cooled

Requirement of heat transfer area is low

Overall heat transfer co-efficient is very high

A corrosive liquid is to be heated

*$_Multiple effect evaporation is generally recommended, when the?

Corrosive liquids are to be concentrated

Large scale evaporation of liquor is needed

Corrosive liquids are to be concentrated

Evaporation on small scale is to be done

*$_For a counter current heat exchanger with Tih = 80¬¨‚àûC, T¬¨‚àûc = 60¬¨‚àûC, T¬¨‚àûh = 50¬¨‚àûC and Tic = 30¬¨‚àûC, and the temperature difference between the two streams being the same everywhere along Z, the direction of flow of hot fluid. The temperature profile should satisfy?

d¬¨‚â§T/dZ¬¨‚â§ < 0

d¬¨‚â§T/dZ¬¨‚â§ > 0

d¬¨‚â§T/dZ¬¨‚â§ = 0

d¬¨‚â§T/dZ¬¨‚â§ < 0

*$_Which of the following is not used as a medium for high temperature heating??

Liquid metal (e.g. molten sodium)

Fused salts (e.g., an eutectic mixture of 53% KNO‚Äö√á√â, 40% NaNO‚Äö√á√áand 7% NaNO‚Äö√á√â)

*$_In a cooling tower, water becomes cool by?

Vaporisation due to heat loss to air

Is not the same as baffle pitch

Should be less than one fifth the diameter of the shell

Should be less than the inside diameter of the shell

*$_Fouling factor for a heat exchanger is given by (where, U‚Äö√á√Ö = heat transfer co-efficient of dirty surface U‚Äö√á√á = heat transfer co-efficient of clean surface)?

1/U‚Äö√á√á - 1/U‚Äö√á√Ö

U‚Äö√á√Ö - U‚Äö√á√á

1/U‚Äö√á√Ö - 1/U‚Äö√á√á

1/U‚Äö√á√á - 1/U‚Äö√á√Ö

U‚Äö√á√á - U‚Äö√á√Ö

*$_Heat exchangers operating, when the asymptotic range is reached,?

Results in abruptly increased velocity

Provide very large heat transfer co-efficient

Results in making part of the heating surface inactive

Results in abruptly increased velocity

*$_Double pipe heat exchangers are preferably useful, when?

Overall heat transfer co-efficient is very high

High viscosity liquid is to be cooled

Requirement of heat transfer area is low

Overall heat transfer co-efficient is very high

A corrosive liquid is to be heated

*$_Indirect contact heat exchangers are preferred over direct contact heat exchangers, because?

Heat transfer co-efficient are high

There is no risk of contamination

*$_In a forward feed multiple effect, the pressure build up will be?

Highest at the inlet of the last effect

Least at the inlet of the first effect

Least at the outlet of the last effect

Highest at the inlet of the last effect

Highest at the outlet of the last effect

*$_Extremely large or small volumes of fluids are generally best routed through the shell side of a shell and tube heat exchanger, because of the?

Flexibility possible in the baffle arrangement

High heat transfer co-efficient

*$_For a given ambient air temperature with increase in the thickness of insulation of a hot cylinderical pipe, the rate of heat loss from the surface would?

First decrease and then increase

First increase and then decrease

*$_A hollow sphere and a solid sphere of the same material and equal radii are heated to the same temperature. In this case,?

The cooling rate will be the same for the two spheres and hence the two spheres will have equal temperatures at any instant

Both the spheres will emit equal amount of radiation per unit time in the beginning

Both will absorb equal amount of radiation from the surrounding in the beginning

*$_Vent pipes are provided in a condenser to?

Facilitate easy cleaning of tubes

*$_For large heat transfer area requirement, shell and tube heat exchanger is preferred, because it?

Is easy to operate and maintain

*$_The energy radiated from a surface Q at absolute temperature T is related as?

Q ‚Äö√ √π T¬¨‚â•

Q ‚Äö√ √π T¬¨‚â§

Q ‚Äö√ √π T‚Äö√Ö¬•

Q ‚Äö√ √π T¬¨‚â•

*$_Leidenfrost point is a term concerned with the?

Condensation of the saturated vapor on a cold surface

Concentration of a corrosive solution by evaporation

Heat transfer between two highly viscous liquids

Boiling of a liquid on a hot surface

*$_Steam trap is used to?

Condense the steam flowing in the pipeline

Remove water resulting from partial condensation of steam

*$_The thickness of condensate layer in filmwise condensation depends on the?

Liquid flow rate from the surface

*$_In a single evaporator system, the steam economy __________ by creating vacuum in the evaporator.?

May increase or decrease, depends on the vacuum

*$_Bulk of the convective heat transfer resistance from a hot tube surface to the fluid flowing in it, is?

In the central core of the fluid

Uniformly distributed throughout the fluid

Mainly confined to a thin film of fluid near the surface

*$_Air is to be heated by condensing steam. Two heat exchangers are available (i) a shell and tube heat exchanger and (ii) a finned tube heat exchanger. Tube side heat transfer area are equal in both the cases. The recommended arrangement is?

Shell and tube heat exchanger with air inside tubes and steam on shell side

Finned tube heat exchanger with air inside and steam outside

Finned tube heat exchanger with air outside and steam inside

Shell and tube heat exchanger with air inside tubes and steam on shell side

Shell and tube heat exchanger with air on shell side and steam inside tubes

*$_Unsteady state heat conduction occurs, when?

Heat flows in one direction only

Temperature distribution is independent of time

Temperature distribution is dependent on time

Heat flows in one direction only

Three dimensional heat flow is concerned

*$_What is the geometric mean of two heat transfer areas A‚Äö√á√Ö and A‚Äö√á√á ??

‚Äö√ √∂(A‚Äö√á√Ö + A‚Äö√á√á)

‚Äö√ √∂(A‚Äö√á√Ö . A‚Äö√á√á)

‚Äö√ √∂(A‚Äö√á√Ö + A‚Äö√á√á)

1/2 ‚Äö√ √∂(A‚Äö√á√Ö . A‚Äö√á√á)

2 ‚Äö√ √∂(A‚Äö√á√Ö . A‚Äö√á√á)

482 + Mcqs in Heat Transfer in Chemical Engineering Page 2 McqOptions

51.	Double pipe heat exchangers are preferably useful, when%!
A.	High viscosity liquid is to be cooled
B.	Requirement of heat transfer area is low
C.	Overall heat transfer co-efficient is very high
D.	A corrosive liquid is to be heated
Answer» C. Overall heat transfer co-efficient is very high

Discussion

52.	Multiple effect evaporators are commonly used in the manufacture of P. Paper Q. Superphosphate R. Sugar S. Fats%!
A.	P and Q
B.	P and R
C.	P and S
D.	R and S
Answer» D. R and S

Discussion

53.	*$_Multiple effect evaporation is generally recommended, when the?
A.	Large scale evaporation of liquor is needed
B.	Corrosive liquids are to be concentrated
C.	Fuel is cheaply available
D.	Evaporation on small scale is to be done
Answer» B. Corrosive liquids are to be concentrated

Discussion

54.	*$_For a counter current heat exchanger with Tih = 80¬¨‚àûC, T¬¨‚àûc = 60¬¨‚àûC, T¬¨‚àûh = 50¬¨‚àûC and Tic = 30¬¨‚àûC, and the temperature difference between the two streams being the same everywhere along Z, the direction of flow of hot fluid. The temperature profile should satisfy?
A.	d¬¨‚â§T/dZ¬¨‚â§ > 0
B.	d¬¨‚â§T/dZ¬¨‚â§ = 0
C.	d¬¨‚â§T/dZ¬¨‚â§ < 0
D.	dT/dZ = 0
Answer» C. d¬¨‚â§T/dZ¬¨‚â§ < 0

Discussion

55.	*$_Boiling of milk in an open vessel is an example of __________ boiling.?
A.	Film
B.	Sub-cooled
C.	Saturated nucleate
D.	None of these
Answer» B. Sub-cooled

Discussion

56.	*$_All analogy equations connecting friction factor and heat transfer co-efficient apply only to?
A.	Wall or skin friction
B.	Form friction
C.	Both A and B
D.	Turbulent flow
Answer» B. Form friction

Discussion

57.	*$_Multiple effect evaporation accounts for?
A.	Steam economy
B.	Lower operating costs
C.	Investment economy
D.	None of these
Answer» B. Lower operating costs

Discussion

58.	*$_Which of the following is not used as a medium for high temperature heating??
A.	Dowtherm
B.	Mercury
C.	Liquid metal (e.g. molten sodium)
D.	Fused salts (e.g., an eutectic mixture of 53% KNO‚Äö√á√â, 40% NaNO‚Äö√á√áand 7% NaNO‚Äö√á√â)
Answer» C. Liquid metal (e.g. molten sodium)

Discussion

59.	*$_In SI units, fouling factor is expressed in?
A.	m¬¨‚â§¬¨‚àûK/W
B.	W/m¬¨‚â§¬¨‚àûK
C.	m¬¨‚â§¬¨‚àûK
D.	m¬¨‚àûK/W
Answer» B. W/m¬¨‚â§¬¨‚àûK

Discussion

60.	*$_In a cooling tower, water becomes cool by?
A.	Loosing sensible heat
B.	Heat transfer to surroundings
C.	Vaporisation due to heat loss to air
D.	Loosing latent heat
Answer» B. Heat transfer to surroundings

Discussion

61.	*$_Baffle spacing?
A.	Is not the same as baffle pitch
B.	Should be less than one fifth the diameter of the shell
C.	Should be less than the inside diameter of the shell
D.	None of these
Answer» D. None of these

Discussion

62.	*$_Stefan-Boltzman law applies to __________ body.?
A.	Black
B.	White
C.	Grey
D.	Any colour
Answer» B. White

Discussion

63.	*$_Fouling factor for a heat exchanger is given by (where, U‚Äö√á√Ö = heat transfer co-efficient of dirty surface U‚Äö√á√á = heat transfer co-efficient of clean surface)?
A.	U‚Äö√á√Ö - U‚Äö√á√á
B.	1/U‚Äö√á√Ö - 1/U‚Äö√á√á
C.	1/U‚Äö√á√á - 1/U‚Äö√á√Ö
D.	U‚Äö√á√á - U‚Äö√á√Ö
Answer» C. 1/U‚Äö√á√á - 1/U‚Äö√á√Ö

Discussion

64.	*$_Agitated film evaporator is suitable for concentrating __________ liquids.?
A.	Foaming
B.	Viscous
C.	Very thin
D.	Corrosive
Answer» C. Very thin

Discussion

65.	*$_The most conducive surface for dropwise condensation to occur is the __________ surface.?
A.	Coated
B.	Oily
C.	Glazed & polished
D.	Smooth
Answer» C. Glazed & polished

Discussion

66.	*$_Absorptivity and refletivity of a perfect black body are respectively?
A.	1 and 0
B.	0 and 1
C.	1 and ?
D.	0 and 0.5
Answer» B. 0 and 1

Discussion

67.	*$_Heat exchangers operating, when the asymptotic range is reached,?
A.	Provide very large heat transfer co-efficient
B.	Results in making part of the heating surface inactive
C.	Results in abruptly increased velocity
D.	None of these
Answer» C. Results in abruptly increased velocity

Discussion

68.	*$_Which is the best tube arrangement (in a shell and tube heat exchanger) if the fluids are clean and non-fouling??
A.	Square pitch
B.	Triangular pitch
C.	Diagonal square pitch
D.	None of these
Answer» C. Diagonal square pitch

Discussion

69.	*$_Double pipe heat exchangers are preferably useful, when?
A.	High viscosity liquid is to be cooled
B.	Requirement of heat transfer area is low
C.	Overall heat transfer co-efficient is very high
D.	A corrosive liquid is to be heated
Answer» C. Overall heat transfer co-efficient is very high

Discussion

70.	*$_Multiple effect evaporators are commonly used in the manufacture of P. Paper Q. Superphosphate R. Sugar S. Fats?
A.	P and Q
B.	P and R
C.	P and S
D.	R and S
Answer» D. R and S

Discussion

71.	*$_For small temperature difference, the heat transfer rate as per Newton's law of cooling is proportional to (where, ≈í√Æt = excess temperature)?
A.	≈í√Æt
B.	≈í√Æt¬¨‚â§
C.	≈í√Æt¬¨‚â•
D.	‚Äö√ √∂≈í√Æt
Answer» B. ≈í√Æt¬¨‚â§

Discussion

72.	*$_Three solid objects of the same material and of equal mass-a sphere, a cylinder (length = diameter) and a cube are at 500¬¨‚àûC initially. These are dropped in a quenching bath containing a large volume of cooling oil each attaining the bath temperature eventually. The time required for 90% change in temperature is the smallest for?
A.	Cube
B.	Cylinder
C.	Sphere
D.	Equal for all the three
Answer» B. Cylinder

Discussion

73.	*$_Indirect contact heat exchangers are preferred over direct contact heat exchangers, because?
A.	Heat transfer co-efficient are high
B.	There is no risk of contamination
C.	There is no mist formation
D.	Cost of equipment is lower
Answer» C. There is no mist formation

Discussion

74.	*$_In a forward feed multiple effect, the pressure build up will be?
A.	Least at the inlet of the first effect
B.	Least at the outlet of the last effect
C.	Highest at the inlet of the last effect
D.	Highest at the outlet of the last effect
Answer» C. Highest at the inlet of the last effect

Discussion

75.	*$_At what value of Prandtl number, the hydrodynamic and thermal boundary layers of a fluid flowing over a heated plate will be identical??
A.	1
B.	< 1
C.	> 1
D.	None of these
Answer» B. < 1

Discussion

76.	*$_Graetz number is given by?
A.	mCp/kL
B.	kL/mCp
C.	mCp/k≈í¬∫
D.	k≈í¬∫/mCp
Answer» B. kL/mCp

Discussion

77.	*$_Use of transverse baffles in a shell and tube heat exchanger is done to increase the?
A.	Rate of heat transfer
B.	Flow velocity
C.	Turbulence of shell side fluid
D.	All of the above
Answer» E.

Discussion

78.	*$_Extremely large or small volumes of fluids are generally best routed through the shell side of a shell and tube heat exchanger, because of the?
A.	Less corrosion problems
B.	Flexibility possible in the baffle arrangement
C.	Low pressure drop
D.	High heat transfer co-efficient
Answer» C. Low pressure drop

Discussion

79.	*$_For what value of Prandtl number, the Col-burn analogy is valid??
A.	0.06 to 120
B.	0.6 to 120
C.	1 to 103
D.	L to 50
Answer» C. 1 to 103

Discussion

80.	*$_The rate of heat transfer from a vertical plate by natural convection depends upon the temperature differences (≈í√ÆT) between wall and outside bulk. The proportionality is given as?
A.	(≈í√ÆT)1/4
B.	(≈í√ÆT)1/2
C.	(≈í√ÆT)5/4
D.	(≈í√ÆT)3/4
Answer» E.

Discussion

81.	*$_For a given ambient air temperature with increase in the thickness of insulation of a hot cylinderical pipe, the rate of heat loss from the surface would?
A.	Decrease
B.	Increase
C.	First decrease and then increase
D.	First increase and then decrease
Answer» E.

Discussion

82.	*$_A hollow sphere and a solid sphere of the same material and equal radii are heated to the same temperature. In this case,?
A.	The cooling rate will be the same for the two spheres and hence the two spheres will have equal temperatures at any instant
B.	Both the spheres will emit equal amount of radiation per unit time in the beginning
C.	Both will absorb equal amount of radiation from the surrounding in the beginning
D.	Both B & C
Answer» E.

Discussion

83.	*$_What is the absorptivity of a black body??
A.	1
B.	0
C.	0.78
D.	0.95
Answer» B. 0

Discussion

84.	*$_Vent pipes are provided in a condenser to?
A.	Remove non-condensable gases
B.	Purge the condenser
C.	Facilitate easy cleaning of tubes
D.	None of these
Answer» B. Purge the condenser

Discussion

85.	*$_For large heat transfer area requirement, shell and tube heat exchanger is preferred, because it?
A.	Occupies smaller space
B.	Is more economical
C.	Is easy to operate and maintain
D.	All of the above
Answer» E.

Discussion

86.	*$_A composite wall consists of two plates A and B placed in series normal to the flow of heat. The thermal conductivities are kA and kB and the specific heat capacities are CPA and CPB for plates A and B respectively. Plate B has twice the thickness of plate A. At steady state, the temperature difference across plate A is greater than that across plate B, when?
A.	CPA > CPB
B.	CPA < CPB
C.	KA < 0.5kB
D.	KA>2 kB
Answer» D. KA>2 kB

Discussion

87.	*$_The energy radiated from a surface Q at absolute temperature T is related as?
A.	Q ‚Äö√ √π T¬¨‚â§
B.	Q ‚Äö√ √π T‚Äö√Ö¬•
C.	Q ‚Äö√ √π T¬¨‚â•
D.	None of these
Answer» C. Q ‚Äö√ √π T¬¨‚â•

Discussion

88.	*$_Leidenfrost point is a term concerned with the?
A.	Condensation of the saturated vapor on a cold surface
B.	Concentration of a corrosive solution by evaporation
C.	Heat transfer between two highly viscous liquids
D.	Boiling of a liquid on a hot surface
Answer» E.

Discussion

89.	*$_Steam trap is used to?
A.	Condense the steam flowing in the pipeline
B.	Remove water resulting from partial condensation of steam
C.	Stop the supply of steam
D.	None of these
Answer» C. Stop the supply of steam

Discussion

90.	*$_The thickness of condensate layer in filmwise condensation depends on the?
A.	Condensation rate
B.	Surface configuration
C.	Liquid flow rate from the surface
D.	All of the above
Answer» E.

Discussion

91.	*$_A composite flat wall of a furnace is made of two materials 'A' and 'B'. The thermal conductivity of 'A' is twice of that of material 'B', while the thickness of layer of 'A' is half that of B. If the temperature at the two sides of the wall are 400 and 1200¬¨‚àûK, then the temperature drop (in ¬¨‚àûK) across the layer of material 'A' is?
A.	125
B.	133
C.	150
D.	160
Answer» E.

Discussion

92.	*$_In a single evaporator system, the steam economy __________ by creating vacuum in the evaporator.?
A.	Increases
B.	Decreases
C.	Remains constant
D.	May increase or decrease, depends on the vacuum
Answer» B. Decreases

Discussion

93.	*$_Bulk of the convective heat transfer resistance from a hot tube surface to the fluid flowing in it, is?
A.	In the central core of the fluid
B.	Uniformly distributed throughout the fluid
C.	Mainly confined to a thin film of fluid near the surface
D.	None of these
Answer» D. None of these

Discussion

94.	*$_Air is to be heated by condensing steam. Two heat exchangers are available (i) a shell and tube heat exchanger and (ii) a finned tube heat exchanger. Tube side heat transfer area are equal in both the cases. The recommended arrangement is?
A.	Finned tube heat exchanger with air inside and steam outside
B.	Finned tube heat exchanger with air outside and steam inside
C.	Shell and tube heat exchanger with air inside tubes and steam on shell side
D.	Shell and tube heat exchanger with air on shell side and steam inside tubes
Answer» C. Shell and tube heat exchanger with air inside tubes and steam on shell side

Discussion

95.	*$_The variation of thermal conductivity of a metal with temperature is often correlated using an expression of the form K = K‚Äö√á√Ñ + at. where, K is the thermal conductivity and T is the temperature (in ¬¨‚àûK). The units of 'a' in SI system will be?
A.	W/m.k
B.	W/m
C.	W/m.k¬¨‚â§
D.	None, A is just a number
Answer» D. None, A is just a number

Discussion

96.	*$_Heat transfer by __________ may not necessarily require the presence of a medium.?
A.	Conduction
B.	Natural convection
C.	Forced convection
D.	Radiation
Answer» E.

Discussion

97.	*$_Sensible heat of hot industrial flue gases can not be recovered by a/an?
A.	Economiser
B.	Regenerator
C.	Ceramic recuperator
D.	None of these
Answer» E.

Discussion

98.	*$_Unsteady state heat conduction occurs, when?
A.	Temperature distribution is independent of time
B.	Temperature distribution is dependent on time
C.	Heat flows in one direction only
D.	Three dimensional heat flow is concerned
Answer» C. Heat flows in one direction only

Discussion

99.	*$_Prandtl and Reynolds analogy are same, when Prandtl number is?
A.	0.5
B.	1
C.	> 2
D.	1.5
Answer» C. > 2

Discussion

100.	*$_What is the geometric mean of two heat transfer areas A‚Äö√á√Ö and A‚Äö√á√á ??
A.	‚Äö√ √∂(A‚Äö√á√Ö . A‚Äö√á√á)
B.	‚Äö√ √∂(A‚Äö√á√Ö + A‚Äö√á√á)
C.	1/2 ‚Äö√ √∂(A‚Äö√á√Ö . A‚Äö√á√á)
D.	2 ‚Äö√ √∂(A‚Äö√á√Ö . A‚Äö√á√á)
Answer» B. ‚Äö√ √∂(A‚Äö√á√Ö + A‚Äö√á√á)

Discussion

Explore topic-wise MCQs in Chemical Engineering.

Double pipe heat exchangers are preferably useful, when%!

Multiple effect evaporators are commonly used in the manufacture of P. Paper Q. Superphosphate R. Sugar S. Fats%!

*$_Multiple effect evaporation is generally recommended, when the?

*$_Boiling of milk in an open vessel is an example of __________ boiling.?

*$_All analogy equations connecting friction factor and heat transfer co-efficient apply only to?

*$_Multiple effect evaporation accounts for?

*$_Which of the following is not used as a medium for high temperature heating??

*$_In SI units, fouling factor is expressed in?

*$_In a cooling tower, water becomes cool by?

*$_Baffle spacing?

*$_Stefan-Boltzman law applies to __________ body.?

*$_Fouling factor for a heat exchanger is given by (where, U‚Äö√á√Ö = heat transfer co-efficient of dirty surface U‚Äö√á√á = heat transfer co-efficient of clean surface)?

*$_Agitated film evaporator is suitable for concentrating __________ liquids.?

*$_The most conducive surface for dropwise condensation to occur is the __________ surface.?

*$_Absorptivity and refletivity of a perfect black body are respectively?

*$_Heat exchangers operating, when the asymptotic range is reached,?

*$_Which is the best tube arrangement (in a shell and tube heat exchanger) if the fluids are clean and non-fouling??

*$_Double pipe heat exchangers are preferably useful, when?

*$_Multiple effect evaporators are commonly used in the manufacture of P. Paper Q. Superphosphate R. Sugar S. Fats?

*$_For small temperature difference, the heat transfer rate as per Newton's law of cooling is proportional to (where, ≈í√Æt = excess temperature)?

*$_Indirect contact heat exchangers are preferred over direct contact heat exchangers, because?

*$_In a forward feed multiple effect, the pressure build up will be?

*$_At what value of Prandtl number, the hydrodynamic and thermal boundary layers of a fluid flowing over a heated plate will be identical??

*$_Graetz number is given by?

*$_Use of transverse baffles in a shell and tube heat exchanger is done to increase the?

*$_Extremely large or small volumes of fluids are generally best routed through the shell side of a shell and tube heat exchanger, because of the?

*$_For what value of Prandtl number, the Col-burn analogy is valid??

*$_The rate of heat transfer from a vertical plate by natural convection depends upon the temperature differences (≈í√ÆT) between wall and outside bulk. The proportionality is given as?

*$_For a given ambient air temperature with increase in the thickness of insulation of a hot cylinderical pipe, the rate of heat loss from the surface would?

*$_A hollow sphere and a solid sphere of the same material and equal radii are heated to the same temperature. In this case,?

*$_What is the absorptivity of a black body??

*$_Vent pipes are provided in a condenser to?

*$_For large heat transfer area requirement, shell and tube heat exchanger is preferred, because it?

*$_The energy radiated from a surface Q at absolute temperature T is related as?

*$_Leidenfrost point is a term concerned with the?

*$_Steam trap is used to?

*$_The thickness of condensate layer in filmwise condensation depends on the?

*$_In a single evaporator system, the steam economy __________ by creating vacuum in the evaporator.?

*$_Bulk of the convective heat transfer resistance from a hot tube surface to the fluid flowing in it, is?

*$_Air is to be heated by condensing steam. Two heat exchangers are available (i) a shell and tube heat exchanger and (ii) a finned tube heat exchanger. Tube side heat transfer area are equal in both the cases. The recommended arrangement is?

*$_The variation of thermal conductivity of a metal with temperature is often correlated using an expression of the form K = K‚Äö√á√Ñ + at. where, K is the thermal conductivity and T is the temperature (in ¬¨‚àûK). The units of 'a' in SI system will be?

*$_Heat transfer by __________ may not necessarily require the presence of a medium.?

*$_Sensible heat of hot industrial flue gases can not be recovered by a/an?

*$_Unsteady state heat conduction occurs, when?

*$_Prandtl and Reynolds analogy are same, when Prandtl number is?

*$_What is the geometric mean of two heat transfer areas A‚Äö√á√Ö and A‚Äö√á√á ??