Question

Air is heated as it flows subsonically through a 10 cm×10 cm square duct. The properties of air at the inlet are maintained at Ma₁ =0.6,P₁ =350kPa, and T₁ =420 K at all times. Disregarding frictional losses, determine the highest rate of heat transfer to the air in the duct without affecting the inlet conditions.

Answer 1

To determine the highest rate of heat transfer to the air in the duct, we can use the formula Q = mcAT. By finding the mass of air using the ideal gas law equation PV = mRT and dividing Q by the time for air turnover, we can calculate the highest rate of heat transfer.

Step-by-step explanation:

The highest rate of heat transfer to the air in the duct can be determined using the formula Q = mcAT, where Q is the heat transfer, m is the mass of air, c is the specific heat of air, and AT is the change in temperature. We are given that AT = 10.0°C, and the specific heat of air is approximately 1000 J/kg.°C. However, we need to find the mass of air before we can calculate Q.

To find the mass of air, we can use the ideal gas law equation PV = mRT, where P is the pressure, V is the volume, m is the mass, R is the gas constant, and T is the temperature. Rearranging the equation, we have m = PV/RT. The volume of the duct is 10 cm x 10 cm x length of the duct. We can convert the volume to cubic meters and use the given pressure and temperature to calculate the mass of air.

Finally, we can calculate the highest rate of heat transfer Q/t by dividing Q by the time for air turnover.