Heat Transfer Miscellaneous
 Cold water flowing at 0.1 kg/s is heated from 20°C to 70°C in a counter flow type heat exchange by a hot water stream flowing at 0.1 kg/s and entering at 90°C. The specific heat of water is 4200 J/(kgK) and density is 1000 kg/m^{3} . If the overall heat transfer coefficient U for the heat exchange is 2000 W/(m^{2} K), the required heat exchange area (in m^{2} ) is

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C_{h} = C_{c} = 0.1 × 4200 = 420 J/s
C_{c} (T_{c1} – T_{c2}) = C_{h} (T_{h1} – T_{h2}) (70 – 20) = 90° T_{h2}
LMTD = θ_{1} = θ_{2} (∵ θ_{1} = θ_{2})
C_{c} (T_{c2} – T_{c1}) = UA(LMTD)
or A = 0.525 m^{2}.Correct Option: B
C_{h} = C_{c} = 0.1 × 4200 = 420 J/s
C_{c} (T_{c1} – T_{c2}) = C_{h} (T_{h1} – T_{h2}) (70 – 20) = 90° T_{h2}
LMTD = θ_{1} = θ_{2} (∵ θ_{1} = θ_{2})
C_{c} (T_{c2} – T_{c1}) = UA(LMTD)
or A = 0.525 m^{2}.
 In a concentric counter flow heat exchange, water flows through the inner tube at 25°C and leaves at 42°C. The engine oil enters at 100°C and flows in the annular flow passage. The exit temperature of the engine oil is 50°C. Mass flow rate of water and the engine oil are 1.5 kg/s and 1 kg/s, respectively. The specific heat of water and oil are 4178 J/kgK and 2130 J/kgK, respectively. The effectiveness of this heat exchange is

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T_{c,i} = 25°C;
T_{c,o} = 42°C;
m_{c} = 1.5 kg/s;
C_{c} = 4.178 kJ/kg.k
T_{h,i} = 100°C;
T_{h,o} = 50°C;
m_{h} = 1 kg/s;
C_{h} = 2.130 kJ/kg.k
m_{c}C_{c} = 1.5 × 4.178
= 6.267 kW/°C = C_{max}
m_{h}C_{h} = 1 × 2.130
= 2.130 kW/°C = C_{min}effectiveness = ε = C_{h}(T_{h,i}  T_{h,o}) C_{min}(T_{h,i}  T_{c,i}) = 100  50 = 0.666 100  25 Correct Option: A
T_{c,i} = 25°C;
T_{c,o} = 42°C;
m_{c} = 1.5 kg/s;
C_{c} = 4.178 kJ/kg.k
T_{h,i} = 100°C;
T_{h,o} = 50°C;
m_{h} = 1 kg/s;
C_{h} = 2.130 kJ/kg.k
m_{c}C_{c} = 1.5 × 4.178
= 6.267 kW/°C = C_{max}
m_{h}C_{h} = 1 × 2.130
= 2.130 kW/°C = C_{min}effectiveness = ε = C_{h}(T_{h,i}  T_{h,o}) C_{min}(T_{h,i}  T_{c,i}) = 100  50 = 0.666 100  25
 The heat transfer process between body and its ambient is governed by an Intemal Conductive Resistance (ICR) and an External Convective Resistance (ECR). The body can be considered to be a lumped heat capacity system is

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Lumped heat capacity can be applied when Bi < 0.1
B_{i} hl/k, for desired condition i.e. Bi < 0
k > h, ICR is smallCorrect Option: D
Lumped heat capacity can be applied when Bi < 0.1
B_{i} hl/k, for desired condition i.e. Bi < 0
k > h, ICR is small
 Biot number signifies

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Biot number = R_{conduction}/R_{convective}
Correct Option: D
Biot number = R_{conduction}/R_{convective}
 When the fluid velocity is doubled the thermal time constant of a thermometer used of measuring the fluid temperature reduces by a factor of 2 (T/F)

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It is not necessary that h would become a half if velocity becomes double.
Correct Option: D
It is not necessary that h would become a half if velocity becomes double.