6. For the circular tube of equal length and diameter shown in figure below, the view factor F₁₃ is 0.17. The view factor F₁₂ in this case will be
   

1. 1. 0.17

   
   
   

   2. 0.21

   
   
   

   3. 0.79

   
   
   

   4. 0.83

   
   
   

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1. View Hint View Answer Discuss in Forum

   1	= 2
   r1

   
   

   and	r3	= 0.5
   	l

   
   F₁₃ = 0.17,
   F₁₁ = 0,
   F₁₁ + F₁₂ + F₁₃ = 1
   ∴ F₁₂ = 1 – F₁₃
   = 1 – 0 – 17 = 0.83

   Correct Option: D

   1	= 2
   r1

   
   

   and	r3	= 0.5
   	l

   
   F₁₃ = 0.17,
   F₁₁ = 0,
   F₁₁ + F₁₂ + F₁₃ = 1
   ∴ F₁₂ = 1 – F₁₃
   = 1 – 0 – 17 = 0.83

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7. The properties of mercury at 300 K are: Density = 13529 kg/m³, cp = 0.1393 kJ/kgK, dynamic viscosity = 0.1523 × 10^–2 Ns/m² and thermal conductivity = 8.540 W/mK. The Prandtl number of the mercury at 300 K is

1. 1. 0.0248

   
   
   

   2. 2.48

   
   
   

   3. 24.8

   
   
   

   4. 248

   
   
   

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1. View Hint View Answer Discuss in Forum

   Prandtl number =	μCp
   	K

   
   

   = 0.1523 × 10-2	Ns	×	0.1393 × 1000	kJ	= 0.0248
   	m²		8.54/mK	kgK

   Correct Option: A

   Prandtl number =	μCp
   	K

   
   

   = 0.1523 × 10-2	Ns	×	0.1393 × 1000	kJ	= 0.0248
   	m²		8.54/mK	kgK

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8. A coolant fluid at 30°C flows over a heated flat plate maintained at a constant temperature of 100°C. The boundary layer temperature distribution at a given location on the plate may be approximated as T = 30 + 70 expt(-y) where y(in m) is the distance normal to the plate and fis in °C. If thermal conductivity of the fluid is 1.0 W/mK, the local convective heat transfer coefficient (in W/m²K) at that location will be

1. 1. 0.2

   
   
   

   2. 1

   
   
   

   3. 5

   
   
   

   4. 10

   
   
   

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1. View Hint View Answer Discuss in Forum

   Under steady state conditions
   Heat transfer by conduction = Heat transfer by convection
   

   ∴ -kA	dT	= h AΔT
   	dy

   
   

   or -k	dT	= h ΔT
   	dy

   
   

   or -k	dT	(30 + 70e-y) = h (100 - 30°)
   	dy

   
   

   or -k	δ	(- 70e-y) = h × 70
   	δy

   
   or – k
   ∴ -k (– 70 e⁰) = 70h
   or 70 k = 70 h
   But k = 1
   ∴ h = 1W/m²k
   Alternately
   

   hAΔ = kA	dT
   	dy

   
   or h(100 – 30) = k × (100 – 30)
   or h = k = 1 W/m²K

   Correct Option: B

   Under steady state conditions
   Heat transfer by conduction = Heat transfer by convection
   

   ∴ -kA	dT	= h AΔT
   	dy

   
   

   or -k	dT	= h ΔT
   	dy

   
   

   or -k	dT	(30 + 70e-y) = h (100 - 30°)
   	dy

   
   

   or -k	δ	(- 70e-y) = h × 70
   	δy

   
   or – k
   ∴ -k (– 70 e⁰) = 70h
   or 70 k = 70 h
   But k = 1
   ∴ h = 1W/m²k
   Alternately
   

   hAΔ = kA	dT
   	dy

   
   or h(100 – 30) = k × (100 – 30)
   or h = k = 1 W/m²K

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9. The location of maximum temperature within the plate from its left face is

1. 1. 15 mm

   
   
   

   2. 10 mm

   
   
   

   3. 5 mm

   
   
   

   4. 0 mm

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   

   d²T	+	q0	= 0
   dx²		K

   
   

   ∴ T =	- 1	q0	x² + C1x + C2......(i)
   	2	K

   
   At x = 0, T = 433 K
   ∴ C² = 433
   At x = 20 × 10^–3 m, T = 393 K.
   ∴ C¹ = 200
   For maximum temperature,
   

   dT	= 0
   dx

   
   

   ∴	q0x	+ C1 = 0
   	K

   
   x = 5 × 10^–3 = 5 mm

   Correct Option: C

   
   

   d²T	+	q0	= 0
   dx²		K

   
   

   ∴ T =	- 1	q0	x² + C1x + C2......(i)
   	2	K

   
   At x = 0, T = 433 K
   ∴ C² = 433
   At x = 20 × 10^–3 m, T = 393 K.
   ∴ C¹ = 200
   For maximum temperature,
   

   dT	= 0
   dx

   
   

   ∴	q0x	+ C1 = 0
   	K

   
   x = 5 × 10^–3 = 5 mm

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10. A 10 mm diameter electrical conductor is covered by an insulation of 2 mm thickness. The conductivity of the insulation is 0.08 W/mK and the convection coefficient at the insulation surface is 10 W/m²K. Addition of further insulation of the same material will

1. 1. increase heat loss continuously

   
   
   

   2. decrease heat loss continuously

   
   
   

   3. increase heat loss to a maximum and then decrease heat loss

   
   
   

   4. decrease heat loss to a minimum and then increase heat loss

   
   
   

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1. View Hint View Answer Discuss in Forum

   r_c = 8mm
   ∴ the heat lost increases to maximum and then decreases.

   Correct Option: C

   r_c = 8mm
   ∴ the heat lost increases to maximum and then decreases.

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