How to Determine the Exit Temperature of Helium in a Heat Exchanger?

How can we calculate the exit temperature of helium in a heat exchanger?

Given the data of hot water entering the heat exchanger, determine the exit temperature of the helium and its mass flow rate. What equations and formulas can we use to solve this problem?

Calculation Method:

First, we need to use the energy balance equation to find the exit temperature of the helium and its mass flow rate. The equation is given as:

Q = m1 * Cp1 * (T1 - T2) = m2 * Cp2 * (T3 - T4)

Where:

Q = Heat transfer rate (in Watts)

m1 = Mass flow rate of hot water (in kg/s)

Cp1 = Specific heat capacity of hot water (in J/kg.K)

T1 = Inlet temperature of hot water (in °C)

T2 = Outlet temperature of hot water (in °C)

m2 = Mass flow rate of helium (in kg/s)

Cp2 = Specific heat capacity of helium (in J/kg.K)

T3 = Inlet temperature of helium (in °C)

T4 = Outlet temperature of helium (to be determined)

Detailed Calculation Steps:

1. Find the Logarithmic Mean Temperature Difference (ΔTlm) using the equation:

ΔTlm = (T1 - T4) - (T2 - T3) / ln((T1 - T4) / (T2 - T3))

2. Substitute the calculated ΔTlm into the heat transfer rate equation:

Q = U * A * ΔTlm

3. Use the energy balance equation to find m2 by rearranging the equation and substituting known values:

m1 * Cp1 * (T1 - T2) = m2 * Cp2 * (T3 - T4)

4. Solve for T4 by substituting ΔTlm back into the logarithmic mean temperature difference equation

5. Once T4 is determined, substitute it into the energy balance equation to find the mass flow rate of helium, m2

By following these steps and equations, you can accurately calculate the exit temperature of helium in the heat exchanger based on the given data.