An air to air intercooler is a heat exchanger used in turbocharged engines. Suppose that air flows into an engine at 0.02m3/s at a temperatu

Question

An air to air intercooler is a heat exchanger used in turbocharged engines. Suppose that air flows into an engine at 0.02m3/s at a temperature of 450K and then passes through an intercooler after which the air has cooled to 350K. The external air flowing into the intercooler at a rate of 1.0m3/s enters at the ambient temperature of 300K. What is the temperature of the external air after passing through the intercooler

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1 year 2021-07-21T05:47:48+00:00 1 Answers 25 views 0

1. Given Information:

Inlet Temperature of hot air= Th₁ = 450K

Exit Temperature of hot air = Th₂ = 350K

Inlet Temperature of cold air = Tc₁ = 300K

Volume flow rate of hot air = vh = 0.02 m³/s

Volume flow rate of cold air = vc = 1 m³/s

Required Information:

Exit Temperature of cold air= Tc₂ = ?

Exit Temperature of cold air = Tc₂ = 302 °C

Explanation:

In a heat exchanger, the cold air absorbs heat that is lost by the hot air,

Heat absorbed by cold air = Heat lost by hot air

$$m_{c}\cdot c_{p}(T_{c2} -T_{c1} ) = m_{h}\cdot c_{p}(T_{h1} -T_{h2})\\m_{c}(T_{c2} -T_{c1} ) = m_{h}(T_{h1} -T_{h2})\\\rho\dot{v_{c}}(T_{c2} -T_{c1} ) =\rho\dot{v_{h}} (T_{h1} -T_{h2})\\\dot{v_{c}}(T_{c2} -T_{c1} ) =\dot{v_{h}} (T_{h1} -T_{h2})\\1 \cdot(T_{c2} -300 ) =0.02\cdot (450 -350)\\(T_{c2} -300 ) =0.02\cdot (100)\\(T_{c2} -300 ) =2\\T_{c2} =2 + 300 \\T_{c2} = 302$$

Therefore, the exit temperature of the cold air is 302 °C or 575K

Note:

m = ρv

Where ρ is density of air and v is the volume flow rate and m is the mass flow rate.

cp is the specific heat capacity of air.