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Engineering
Grade 11-12
Heat Exchanger Design (LMTD Method) Cheat Sheet
A printable reference covering LMTD, heat duty, overall heat transfer coefficient, fouling, correction factors, and effectiveness-NTU for grades 11-12.
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Heat exchanger design uses temperature differences, heat transfer area, and fluid properties to predict how much heat can move between hot and cold streams. The LMTD method is one of the main tools engineers use when inlet and outlet temperatures are known or can be estimated. This cheat sheet helps students organize the formulas needed to size a heat exchanger and compare flow arrangements. It is especially useful for solving steady-state design problems in thermal systems.
Key Facts
- The heat duty for a fluid with no phase change is q = m_dot cp (T_out - T_in), using the sign convention that heat gained is positive for the cold fluid.
- For an ideal heat exchanger with no heat loss to the surroundings, q_hot = q_cold in magnitude.
- The basic LMTD design equation is q = U A F DeltaT_lm, where U is overall heat transfer coefficient, A is area, F is correction factor, and DeltaT_lm is log mean temperature difference.
- The log mean temperature difference is DeltaT_lm = (DeltaT_1 - DeltaT_2) / ln(DeltaT_1 / DeltaT_2), where DeltaT_1 and DeltaT_2 are the terminal temperature differences.
- For counterflow, DeltaT_1 = T_h,in - T_c,out and DeltaT_2 = T_h,out - T_c,in.
- For parallel flow, DeltaT_1 = T_h,in - T_c,in and DeltaT_2 = T_h,out - T_c,out.
- Overall thermal resistance can be written as 1 / U = 1 / h_i + R_wall + 1 / h_o + R_f,i + R_f,o for a simplified flat-wall model.
- The effectiveness-NTU method uses effectiveness = q / q_max, q_max = C_min (T_h,in - T_c,in), and NTU = U A / C_min.
Vocabulary
- Heat exchanger
- A device that transfers thermal energy between two fluids without requiring the fluids to mix.
- LMTD
- The log mean temperature difference, which represents the average driving temperature difference across a heat exchanger.
- Overall heat transfer coefficient
- A combined measure of convection, wall conduction, and fouling resistance that controls heat transfer rate per area per temperature difference.
- Fouling
- The buildup of deposits on heat transfer surfaces that increases thermal resistance and lowers heat exchanger performance.
- Correction factor
- A multiplier used with LMTD to account for non-ideal flow arrangements such as shell-and-tube or crossflow designs.
- Effectiveness
- The ratio of actual heat transfer to the maximum possible heat transfer for the same inlet temperatures.
Common Mistakes to Avoid
- Using arithmetic average temperature difference instead of LMTD, which is wrong because the temperature driving force changes nonlinearly along the heat exchanger.
- Mixing up counterflow and parallel-flow terminal differences, which gives the wrong DeltaT_1 and DeltaT_2 and can greatly change the required area.
- Forgetting the correction factor F, which overpredicts heat transfer when the exchanger is not a simple ideal parallel-flow or counterflow unit.
- Ignoring fouling resistance, which makes U too large and causes the calculated heat transfer area to be too small for real operation.
- Using inconsistent units for m_dot, cp, U, and area, which makes q = U A F DeltaT_lm numerically incorrect even if the formula is chosen correctly.
Practice Questions
- 1 A counterflow heat exchanger has T_h,in = 120 C, T_h,out = 70 C, T_c,in = 25 C, and T_c,out = 55 C. Calculate DeltaT_1, DeltaT_2, and DeltaT_lm.
- 2 A heat exchanger transfers 45,000 W with U = 300 W/m^2 C, F = 0.90, and DeltaT_lm = 50 C. What heat transfer area is required?
- 3 Water flows at 0.80 kg/s with cp = 4180 J/kg C and warms from 20 C to 38 C. Calculate the heat gained by the water.
- 4 Why does counterflow usually allow a smaller heat exchanger area than parallel flow for the same inlet temperatures and heat duty?