Respuesta :
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
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
[tex]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[/tex]
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.
