The stream of air and gasoline vapour, in the ratio of 14:1 by mass, enters a gasoline engine at a temperature of 30 degree C and leaves as combustion products at a temperature of 790 degree C.The engine has a specific fuel consumption of 0.3kg/kWh . the net heat transfer rate from the fuel-air stream to the jacket cooling water and to the surroundings is 35kW.The shaft power delivered by the engine is 26 kW. Compute the increase in the specific enthalpy of the fuel-air stream , assuming the changes in kinetic energy and in elevation to be negligible.

To determine the increase in specific enthalpy of the fuel-air stream in the gasoline engine, we can use the principles of thermodynamics, particularly focusing on the energy balance around the system. We will analyze the inputs and outputs of energy to find the specific enthalpy change.

Understanding the System

In this scenario, we have a gasoline engine where air and gasoline vapor mix in a specific ratio, combust, and produce work. The key parameters provided are:

• Fuel-air mass ratio: 14:1
• Inlet temperature: 30 °C
• Outlet temperature: 790 °C
• Specific fuel consumption: 0.3 kg/kWh
• Shaft power output: 26 kW
• Net heat transfer rate: 35 kW

Energy Balance Equation

We can apply the first law of thermodynamics, which states that the energy input to the system minus the energy output equals the change in internal energy (or enthalpy in this case) of the system. The equation can be expressed as:

Q_in - Q_out = ΔH

Where:

• Q_in is the heat added to the system (from combustion).
• Q_out is the heat lost to the surroundings and cooling water.
• ΔH is the change in specific enthalpy of the fuel-air stream.

Calculating the Inputs and Outputs

First, we need to calculate the heat input from the fuel. The specific fuel consumption tells us how much fuel is used to generate power:

Fuel consumption rate (kg/s) = Specific fuel consumption (kg/kWh) × Power output (kW)

Substituting the values:

Fuel consumption rate = 0.3 kg/kWh × 26 kW = 7.8 kg/h = 0.00217 kg/s

Next, we need to calculate the heat released during combustion. The heat of combustion for gasoline is approximately 44 MJ/kg. Therefore, the heat input can be calculated as:

Q_in = Fuel consumption rate × Heat of combustion

Q_in = 0.00217 kg/s × 44,000 kJ/kg = 95.48 kW

Now, we can calculate the total heat output:

Q_out = Net heat transfer rate + Shaft power output

Q_out = 35 kW + 26 kW = 61 kW

Finding the Change in Specific Enthalpy

Now we can substitute the values into the energy balance equation:

ΔH = Q_in - Q_out

ΔH = 95.48 kW - 61 kW = 34.48 kW

This value represents the total change in enthalpy for the fuel-air stream. To find the specific enthalpy change per unit mass of the fuel-air mixture, we need to consider the mass flow rate of the fuel-air mixture.

Calculating the Mass Flow Rate of the Fuel-Air Mixture

The total mass flow rate of the fuel-air mixture can be calculated using the fuel-air ratio:

Total mass flow rate = Fuel mass flow rate + Air mass flow rate

Given the fuel-air ratio of 14:1, for every 1 kg of fuel, there are 14 kg of air. Thus, the total mass flow rate is:

Fuel mass flow rate = 0.00217 kg/s

Air mass flow rate = 14 × 0.00217 kg/s = 0.03038 kg/s

Total mass flow rate = 0.00217 kg/s + 0.03038 kg/s = 0.03255 kg/s

Specific Enthalpy Change

Finally, we can calculate the specific enthalpy change:

Specific enthalpy change (Δh) = ΔH / Total mass flow rate

Δh = 34.48 kW / 0.03255 kg/s = 1060.6 kJ/kg

This result indicates that the increase in specific enthalpy of the fuel-air stream is approximately 1060.6 kJ/kg. This value reflects the energy added to the fuel-air mixture as it undergoes combustion and transforms into work and heat.