Enter the overall heat transfer coefficient (U), heat transfer area (A), and the two terminal temperature differences (ΔT1 and ΔT2) (or any 4 of the 5 fields) into the calculator to determine the heat transfer rate (Q) using the LMTD method.
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Coaxial Heat Exchanger Formula
The following formula is used to calculate the heat transfer rate (heat duty) of a coaxial heat exchanger using the LMTD method.
Q = U * A * LMTD
- Where Q is the heat transfer rate (W)
- A is the total heat transfer area (m²)
- U is the overall heat transfer coefficient (W/(m²·K))
- LMTD is the logarithmic mean temperature difference (K or °C difference): LMTD = (ΔT1 − ΔT2) / ln(ΔT1/ΔT2), where ΔT1 and ΔT2 are the terminal temperature differences
To calculate the heat transfer rate of a coaxial heat exchanger, multiply the overall heat transfer coefficient by the heat transfer area, then multiply by the logarithmic mean temperature difference (LMTD).
What is a coaxial heat exchanger?
A coaxial heat exchanger is a component used in various industries to transfer heat between two fluids. It consists of two concentric tubes, one placed inside the other. The inner tube carries one fluid while the outer annulus carries the other fluid. The fluids may flow in counterflow (often used for higher effectiveness) or in parallel flow. The separation between the tubes allows for the exchange of thermal energy without directly mixing the fluids.
How to calculate coaxial heat exchange?
Example Problem:
The following example outlines how to calculate the heat transfer rate of a coaxial heat exchanger using the LMTD method (counterflow case).
First, determine the area of heat transfer. In this example, the area is 2 m².
Next, determine the inlet and outlet temperatures for both fluids. For this example (counterflow): hot fluid in = 90 °C, hot fluid out = 60 °C, cold fluid in = 30 °C, and cold fluid out = 50 °C.
Next, using the temperatures, calculate the terminal temperature differences and then the LMTD. For counterflow: ΔT1 = Th,in − Tc,out = 90 − 50 = 40 °C, and ΔT2 = Th,out − Tc,in = 60 − 30 = 30 °C. Using the formula linked above, LMTD = (40 − 30) / ln(40/30) ≈ 34.75 °C.
Next, determine the overall heat transfer coefficient. In this example, U = 500 W/(m²·K).
Finally, calculate the heat transfer rate using the formula above:
Q = U * A * LMTD
Q = 500 * 2 * 34.75
Q = 34,750 W (≈ 34.75 kW)
FAQ
What factors can affect the overall heat transfer coefficient in a coaxial heat exchanger?
The overall heat transfer coefficient in a coaxial heat exchanger can be influenced by several factors, including the types of fluids involved, their flow rates, the materials of the tubes, and the presence of any fouling on the tube surfaces. The fluid’s viscosity, temperature, and thermal conductivity also play significant roles in determining the heat transfer efficiency.
How does the flow arrangement (counterflow, parallel flow) affect the performance of a coaxial heat exchanger?
In a coaxial heat exchanger, the counterflow arrangement, where the fluids flow in opposite directions, typically offers higher thermal effectiveness than the parallel flow arrangement, where fluids flow in the same direction. This is because the counterflow arrangement can maintain a larger temperature driving force over more of the exchanger length.
Can the log mean temperature difference (LMTD) method be used for all types of heat exchangers?
The LMTD method is widely used for many heat exchangers operating at steady state with known inlet/outlet temperatures. For multi-pass shell-and-tube and many crossflow configurations, an LMTD correction factor is typically applied. For changing (transient) conditions, or when outlet temperatures are unknown, the effectiveness–NTU method is often more convenient.
