1. Engineering
  2. Mechanical Engineering
  3. problem 4 a simple model of a heat exchanger is...

Question: problem 4 a simple model of a heat exchanger is...

Question details

Problem 4. A simple model of a heat exchanger is shown in Fig. 4. Steam enters the chamber with temperature Tin.1 and mass-flow rate Win and leaves the chamber with temperature Tent...-T, and mass-flow rate wour, 1 win. I =w, . The temperature of the steam in the chamber is Ti, which is equal to the temperature of the outgoing steam. Cold water flow through copper tubes that enter the chamber with temperature Tin2 and mass-flow rate win2. The temperature of the water inside the chamber is T2, which is equal to the temperature of the outgoing hot water. Heat is transferred from the steam to the water through the copper tubes, which have thermal resistance R2, and the hot water leaves the chamber with the same mass- flow rate as the incoming cold water. Thermal insulation Ri surrounds the heat exchanger and provides a thermal barrier with the ambient temperature T (a) Derive the complete mathematical model of the thermal system. (b) Introduce the temperatures Θ,n,,-Tin-l-Ta, Θ.-T,-Z,, Θίη.2 Tin2-Ta and Θ, = T,-T, to the analysis, and expresses the differential equations derived in (a) in terms of these new temperatures (c) Express the linear system of equations derived in (b) in matrix form. (d) Calculate the transfer functions Θ(s) for and Θ.(s) Steam, mass-flow rate Ambient temperature, T Cold water, mass-flow rate Insulation, R Hot water, mass-flow out, 2 Steam chamber temperature, T Water temperature, T Cooler steam, mass-flow rate, Wo,I Fig.4. Thermal system
Solution by an expert tutor
Blurred Solution
This question has been solved
Subscribe to see this solution