Air used for dehydration is heated by burning natural gas...

Air used for dehydration is heated by burning natural gas and mixing the combustion products directly with air. The gas has a heating value of $1050 \mathrm{BTU} / \mathrm{ft}^3$ at $70^{\circ} \mathrm{F}$ and $1 \mathrm{~atm}$ pressure. Assume the gas is $98 \%$ methane and $2 \%$ nitrogen. (a) Calculate the quantity of natural gas in $\mathrm{ft}^3$ at $70 \mathrm{EF}$ and $1 \mathrm{~atm}$. needed to supply the heating requirements for a dryer that uses $1500 \mathrm{lb}$ dry air per hour at $170^{\circ} \mathrm{F}$ and $1 \mathrm{~atm}$. Assume the products of combustion will have the same specific heat as dry air, of $0.24 \mathrm{BTU} /\left(\mathrm{lb} \cong{ }^{\circ} \mathrm{F}\right)$. (b) If the air used to mix with the combustion gases is completely dry, what will be the humidity of the air mixture entering the dryer.

Air used for dehydration is heated by burning natural gas and mixing the combustion products directly with air. The gas has a heating value of $1050 \mathrm{BTU} / \mathrm{ft}^3$ at $70^{\circ} \mathrm{F}$ and $1 \mathrm{~atm}$ pressure. Assume the gas is $98 \%$ methane and $2 \%$ nitrogen.
(a) Calculate the quantity of natural gas in $\mathrm{ft}^3$ at $70 \mathrm{EF}$ and $1 \mathrm{~atm}$. needed to supply the heating requirements for a dryer that uses $1500 \mathrm{lb}$ dry air per hour at $170^{\circ} \mathrm{F}$ and $1 \mathrm{~atm}$. Assume the products of combustion will have the same specific heat as dry air, of $0.24 \mathrm{BTU} /\left(\mathrm{lb} \cong{ }^{\circ} \mathrm{F}\right)$.
(b) If the air used to mix with the combustion gases is completely dry, what will be the humidity of the air mixture entering the dryer.

Key Concepts

Heating Value

The heating value is a measure of the energy content in a fuel, defined as the amount of heat released during the complete combustion of a specific volume or mass of the fuel. In energy calculations, knowing the heating value allows one to determine how much fuel is needed to supply a given amount of heat energy.

Combustion Process and Fuel Composition

This concept involves the burning of fuels such as methane, where the fuel composition (including any inert components) plays a crucial role in the combustion process. Understanding the combustion reaction, including the stoichiometry and the production of combustion products, is essential to perform energy balances and predict the outcome of the combustion process.

Energy Balance in Combustion Systems

An energy balance is used to equate the energy input from the fuel with the energy required for a process, such as heating air in a dryer. This conservation of energy principle is applied by comparing the energy provided by the fuel (using its heating value) to the energy absorbed by the working fluid (determined by its mass flow rate and specific heat capacity).

Specific Heat Capacity

The specific heat capacity of a substance is the amount of heat energy required to raise the temperature of a unit mass by one degree. In thermal calculations, such as heating air for a process, the specific heat capacity is used to determine the total energy needed to achieve a desired temperature change.

Humidity of Air Mixtures

This concept involves the determination of the moisture content in an air mixture when different air streams, such as combustion products and dry air, are combined. Understanding how humidity changes upon mixing is important in processes like dehydration where moisture levels in air are critical to the operation and efficiency of the system.

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