Heat Transfer Miscellaneous
 A spherical steel ball of 12 mm diameter is initially at 1000 K. It is slowly cooled in a surrounding of 300 K. The heat transfer coefficient between the steel ball and the surroundings is 5 W/m²K. The thermal conductivity of steel is 20 W/mK. The ternperature difference between the centre and the surface of the steel ball is

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Bi = hL = 5 ×0.002 = 0.0005 K 20
For the given condition, Biot number tends to zero, i.e. conduction resistance is far less than convection resistance. Therefore temperature between centre and surface is very small.Correct Option: D
Bi = hL = 5 ×0.002 = 0.0005 K 20
For the given condition, Biot number tends to zero, i.e. conduction resistance is far less than convection resistance. Therefore temperature between centre and surface is very small.
 Water (c = 4.18 kJ/kgK) at 80°C enters a counter flow heat exchanger with a mass flow rate of 0.5 kg/s. Air (c = 1 kJ/kgK) enter at 30°C with a mass flow rate 2.09 kg/s. If the effectiveness of the heat exchanger is 0.8, the LMTD (in °C) is

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ε = C_{h} × (t_{h1}  t_{h2}) C_{min} (t_{h1}  t_{c1}) ∴ 0.8 = 4.18 × 0.5 × (80  t_{h2}) 2.09 × 1 (80  30)
⇒ t_{h2} = 40°C
m_{h}c_{ph} (t_{h1} – t_{h2}) = m_{c} c_{cp} (t_{c2} – t_{c1})
∴ 0.5 × 4.18 × 40 = 2.09 × 1 × (t_{c2} – 30)
⇒ t_{c2} = 70°C
&thet;_{1} = θ_{2} = 10°C
∴ LMTD = 10°CCorrect Option: C
ε = C_{h} × (t_{h1}  t_{h2}) C_{min} (t_{h1}  t_{c1}) ∴ 0.8 = 4.18 × 0.5 × (80  t_{h2}) 2.09 × 1 (80  30)
⇒ t_{h2} = 40°C
m_{h}c_{ph} (t_{h1} – t_{h2}) = m_{c} c_{cp} (t_{c2} – t_{c1})
∴ 0.5 × 4.18 × 40 = 2.09 × 1 × (t_{c2} – 30)
⇒ t_{c2} = 70°C
&thet;_{1} = θ_{2} = 10°C
∴ LMTD = 10°C
 In a condenser of a power plant, the steam condenses at a temperature of 60°C. The cooling water enters at 30°C and leaves at 45°C. The Logarithmic Mean Temperature Difference (LMTD) of the condenser is

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Flow configuration in condenser as shown below.
ΔT_{1} = 30°C (Q_{1})
ΔT_{2} = 15°C (Q_{2})LMTD = ΔT_{1}  ΔT_{2} = 30  15 In ΔT_{1} In 30 ΔT_{2} 15
= 21.6°CCorrect Option: B
Flow configuration in condenser as shown below.
ΔT_{1} = 30°C (Q_{1})
ΔT_{2} = 15°C (Q_{2})LMTD = ΔT_{1}  ΔT_{2} = 30  15 In ΔT_{1} In 30 ΔT_{2} 15
= 21.6°C
 For the same inlet and exit temperatures of the hot and cold fluids, the log mean temperature difference (LMTD) is

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NA
Correct Option: B
NA
 Consider two infinitely long thin concentric tubes of circular cross section as shown in figure. If D_{1} and D_{2} are the diameters of the inner and outer tubes respectively, then the view factor F_{22} is given by

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F_{22} = 1  F_{21} =
= 1  A_{1} = 1  D_{1} A_{2} D_{2} Correct Option: D
F_{22} = 1  F_{21} =
= 1  A_{1} = 1  D_{1} A_{2} D_{2}