Question

A house is to be heated by hot water that receives heat from a furnace. Air with an enthalpy of 305 kJ/kg and fuel with an enthalpy of 45360 kJ/kg enters the furnace and the gases leaving have an enthalpy of 608 kJ/kg. There are 17 kg-air per kg-fuel and the water for heating receives 18.3 kW of heat by circulating through the furnace. What is the fuel consumption in kg/hr?

m_f = _____ kg/hr

answer in 3 decimal places

Answer 1

$h_f=45360 \;kJ/kg \\ h_a=305 \;kJ/kg \\ h_g =608 \;kJ/kg \\ Q=18.3 \;kW$

Using conservation of mass:

$m_a+m_f=m_g \\ m_a=21.5m_f \\ 21.5m_f+m_f=m_g \\ 22.5m_f=m_g$

Energy balance:

$E_{in}=E_{out} \\ m_ah_a+ m_fh_f=m_gh_g + Q \\ 21.5m_f \times 305 + m_f \times 45360 = 22.5m_f \times 300 + 18.3 \\ (51917.5 -13680)m_f=18.3 \\ 38237.5m_f=18.3 \\ m_f=4.7858 \times 10^{-4} \; kg/sec \times \frac{1}{1/3600 \;hr} \\ m_f= 4.7858 \times 10^{-4} \times 3600 \;kg/hour \\ m_f=1.7229 \;kg/hr$