Question

Water (cp = 4 kJ/ kgK) enters a cross-flow heat exchanger (both fluids unmixed) at 15°C and flows at the rate 7.5 kg/s. It cools air (Cp = 1 kJ/kgK) flowing at the rate 10 kg/s from an inlet temperature of 120°C. Assuming the effectiveness (Ɛ) of the heat exchanger = 0.94. What is the outlet temperature of air?

• A. ${108}^{o}C$
• B. ${29}^{o}C$
• C. ${97.2}^{o}C$
• D. ${21.3}^{o}C$

Answer 1

The correct option is D ${21.3}^{o}C$

Thermal capacity rates for hot and cold fluids,

$C_c=m_c{c}_c=7.5\times 4=30kJ/sK$

$C_h=m_h{c}_h=10\times 1=10kJ/sK$

Heat transfer rate,
$Q=ϵC_{min}[t_{h1}-t_{c1}]$

$=0.94\times 10\times [120-15]$

$=987kJ/s$

Energy balance of hot fluid gives,

$Q=m_h{c}_h[T_{h1}-T_{h2}]$

$\Rightarrow 987=10\times 1[120-T_{h2}]$

$\Rightarrow T_{h2}=120-\frac{987}{10}={21.3}^{o}C$