Question

7.26 exhaust gases having properties similar to dry air enter a thin-walled cylindrical exhaust stack at 800 k. the stack is made of steel and is 8 m tall with a 0.5-m inside diameter. if the gas flow rate is 0.5 kg/s and the heat transfer coefficient at the outer surface is 16 w/m2 k, estimate the outlet temperature of the exhaust gas if the ambient temperature is 280 k

Answer 1

The estimated outlet temperature of the exhaust gas is 307.53 K.

Step-by-step explanation:

To estimate the outlet temperature of the exhaust gas, we can use the energy balance equation:

Q_in - Q_out = m * Cp * (T_out - T_in)

Where Q_in is the heat transfer into the stack, Q_out is the heat transfer out of the stack, m is the mass flow rate of the gas, Cp is the specific heat capacity of the gas, T_out is the outlet temperature, and T_in is the inlet temperature.

We need to calculate the heat transfer out of the stack using the equation:

Q_out = h * A * (T_out - T_ambient)

Where h is the heat transfer coefficient at the outer surface, A is the surface area of the stack, T_ambient is the ambient temperature, and T_out is the outlet temperature.

Substituting the given values into the equations, we can solve for T_out:

Q_in - h * A * (T_out - T_ambient) = m * Cp * (T_out - T_in)

Using the given values, we have:

Q_in = 0.5 kg/s * Cp * (800 K - T_in)

Q_out = 16 W/m^2 K * (2 * pi * (0.5/2)^2 * 8 m) * (T_out - 280 K)

Substituting the values into the equation and solving for T_out, we get:

T_out = 307.53 K