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

Answer 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 = ?

Answer:

Exit Temperature of cold air = Tc₂ = 302 °C

Step-by-step 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.