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In a certain double pipe heat exchanger, hot water flows at a rate of 50,000 kg/h and gets cooled from 95 degree to 65 degree. At the same time 50,000 kg/h of cooling water at 30 degree Celsius enters the heat exchanger. The flow conditions are such that the overall heat transfers are required and the effectiveness, assuming the two streams are in parallel flow. Assume for both streams cp=4.2 kg/h.?
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In a certain double pipe heat exchanger, hot water flows at a rate of ...
Calculation of Heat Transfer in Double Pipe Heat Exchanger
Given:
Hot water flow rate = 50,000 kg/h
Cooling water flow rate = 50,000 kg/h
Inlet temperature of hot water (Thi) = 95°C
Outlet temperature of hot water (Tho) = 65°C
Inlet temperature of cooling water (Tci) = 30°C
Specific heat of both streams (cp) = 4.2 kg/h
Overall Heat Transfer Coefficient (U)
The overall heat transfer coefficient (U) is given by the equation:
1/U = (1/hi) + (1/ho) + (1/ro)
Where,
hi = inside heat transfer coefficient
ho = outside heat transfer coefficient
ro = thermal resistance of the wall
Assuming that the two streams are in parallel flow, the inside heat transfer coefficient (hi) and outside heat transfer coefficient (ho) are given by the equations:
hi = (Nu * k) / d
ho = (Nuo * ko) / do
Where,
Nu = Nusselt number for the inside pipe
Nuo = Nusselt number for the outside pipe
k = thermal conductivity of the fluid inside the pipe
ko = thermal conductivity of the fluid outside the pipe
d = diameter of the inside pipe
do = diameter of the outside pipe
Nusselt Number (Nu)
The Nusselt number (Nu) is given by the equation:
Nu = (hd) / k
Where,
h = convective heat transfer coefficient
d = diameter of the pipe
k = thermal conductivity of the fluid
The convective heat transfer coefficient (h) can be calculated using the Dittus-Boelter equation for turbulent flow:
h = (0.023 * Re^0.8 * Pr^0.4 * k) / d
Where,
Re = Reynolds number
Pr = Prandtl number
Reynolds Number (Re)
The Reynolds number (Re) is given by the equation:
Re = (ρ * V * d) / μ
Where,
ρ = density of the fluid
V = velocity of the fluid
d = diameter of the pipe
μ = viscosity of the fluid
Prandtl Number (Pr)
The Prandtl number (Pr) is given by the equation:
Pr = (cp * μ) / k
Thermal Resistance of the Wall (ro)
The thermal resistance of the wall (ro) is given by the equation:
ro = (ln(do/di)) / (2π * k * L)
Where,
do = diameter of the outside pipe
di = diameter of the inside pipe
L = length of the heat exchanger
Heat Transfer Area (A)
The heat transfer area (A) is given by the equation:
A = (Q / U * ΔTlm)
Where,
Q = heat transferred
ΔTlm = log mean temperature difference
Log Mean Temperature Difference (ΔTlm)
The log mean temperature difference (ΔTlm) is given by the equation:
ΔTlm = (ΔT1 - ΔT2) / ln(ΔT1 / ΔT2)
Where,
ΔT1 = Thi - Tci
ΔT2 = Tho - Tco
Effectiveness (ε)
The effectiveness (ε) is given by the equation:
ε =
Given:
Hot water flow rate = 50,000 kg/h
Cooling water flow rate = 50,000 kg/h
Inlet temperature of hot water (Thi) = 95°C
Outlet temperature of hot water (Tho) = 65°C
Inlet temperature of cooling water (Tci) = 30°C
Specific heat of both streams (cp) = 4.2 kg/h
Overall Heat Transfer Coefficient (U)
The overall heat transfer coefficient (U) is given by the equation:
1/U = (1/hi) + (1/ho) + (1/ro)
Where,
hi = inside heat transfer coefficient
ho = outside heat transfer coefficient
ro = thermal resistance of the wall
Assuming that the two streams are in parallel flow, the inside heat transfer coefficient (hi) and outside heat transfer coefficient (ho) are given by the equations:
hi = (Nu * k) / d
ho = (Nuo * ko) / do
Where,
Nu = Nusselt number for the inside pipe
Nuo = Nusselt number for the outside pipe
k = thermal conductivity of the fluid inside the pipe
ko = thermal conductivity of the fluid outside the pipe
d = diameter of the inside pipe
do = diameter of the outside pipe
Nusselt Number (Nu)
The Nusselt number (Nu) is given by the equation:
Nu = (hd) / k
Where,
h = convective heat transfer coefficient
d = diameter of the pipe
k = thermal conductivity of the fluid
The convective heat transfer coefficient (h) can be calculated using the Dittus-Boelter equation for turbulent flow:
h = (0.023 * Re^0.8 * Pr^0.4 * k) / d
Where,
Re = Reynolds number
Pr = Prandtl number
Reynolds Number (Re)
The Reynolds number (Re) is given by the equation:
Re = (ρ * V * d) / μ
Where,
ρ = density of the fluid
V = velocity of the fluid
d = diameter of the pipe
μ = viscosity of the fluid
Prandtl Number (Pr)
The Prandtl number (Pr) is given by the equation:
Pr = (cp * μ) / k
Thermal Resistance of the Wall (ro)
The thermal resistance of the wall (ro) is given by the equation:
ro = (ln(do/di)) / (2π * k * L)
Where,
do = diameter of the outside pipe
di = diameter of the inside pipe
L = length of the heat exchanger
Heat Transfer Area (A)
The heat transfer area (A) is given by the equation:
A = (Q / U * ΔTlm)
Where,
Q = heat transferred
ΔTlm = log mean temperature difference
Log Mean Temperature Difference (ΔTlm)
The log mean temperature difference (ΔTlm) is given by the equation:
ΔTlm = (ΔT1 - ΔT2) / ln(ΔT1 / ΔT2)
Where,
ΔT1 = Thi - Tci
ΔT2 = Tho - Tco
Effectiveness (ε)
The effectiveness (ε) is given by the equation:
ε =
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In a certain double pipe heat exchanger, hot water flows at a rate of 50,000 kg/h and gets cooled from 95 degree to 65 degree. At the same time 50,000 kg/h of cooling water at 30 degree Celsius enters the heat exchanger. The flow conditions are such that the overall heat transfers are required and the effectiveness, assuming the two streams are in parallel flow. Assume for both streams cp=4.2 kg/h.?
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In a certain double pipe heat exchanger, hot water flows at a rate of 50,000 kg/h and gets cooled from 95 degree to 65 degree. At the same time 50,000 kg/h of cooling water at 30 degree Celsius enters the heat exchanger. The flow conditions are such that the overall heat transfers are required and the effectiveness, assuming the two streams are in parallel flow. Assume for both streams cp=4.2 kg/h.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about In a certain double pipe heat exchanger, hot water flows at a rate of 50,000 kg/h and gets cooled from 95 degree to 65 degree. At the same time 50,000 kg/h of cooling water at 30 degree Celsius enters the heat exchanger. The flow conditions are such that the overall heat transfers are required and the effectiveness, assuming the two streams are in parallel flow. Assume for both streams cp=4.2 kg/h.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a certain double pipe heat exchanger, hot water flows at a rate of 50,000 kg/h and gets cooled from 95 degree to 65 degree. At the same time 50,000 kg/h of cooling water at 30 degree Celsius enters the heat exchanger. The flow conditions are such that the overall heat transfers are required and the effectiveness, assuming the two streams are in parallel flow. Assume for both streams cp=4.2 kg/h.?.
In a certain double pipe heat exchanger, hot water flows at a rate of 50,000 kg/h and gets cooled from 95 degree to 65 degree. At the same time 50,000 kg/h of cooling water at 30 degree Celsius enters the heat exchanger. The flow conditions are such that the overall heat transfers are required and the effectiveness, assuming the two streams are in parallel flow. Assume for both streams cp=4.2 kg/h.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about In a certain double pipe heat exchanger, hot water flows at a rate of 50,000 kg/h and gets cooled from 95 degree to 65 degree. At the same time 50,000 kg/h of cooling water at 30 degree Celsius enters the heat exchanger. The flow conditions are such that the overall heat transfers are required and the effectiveness, assuming the two streams are in parallel flow. Assume for both streams cp=4.2 kg/h.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a certain double pipe heat exchanger, hot water flows at a rate of 50,000 kg/h and gets cooled from 95 degree to 65 degree. At the same time 50,000 kg/h of cooling water at 30 degree Celsius enters the heat exchanger. The flow conditions are such that the overall heat transfers are required and the effectiveness, assuming the two streams are in parallel flow. Assume for both streams cp=4.2 kg/h.?.
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