Design, fabricate, and experimentally validate a shell-and-tube heat exchanger, comparing results with LMTD and NTU-effectiveness analytical methods.
Design, fabricate, and experimentally validate a shell-and-tube heat exchanger, comparing results with LMTD and NTU-effectiveness analytical methods. This comprehensive guide covers everything from design through implementation, testing, and deployment.
Heat transfer rate: Q = U × A × LMTD. U = overall heat transfer coefficient (W/m²K). A = heat transfer area. LMTD (Log Mean Temperature Difference): ΔT_LMTD = (ΔT1 - ΔT2) / ln(ΔT1/ΔT2) where ΔT1 and ΔT2 are temperature differences at each end of the exchanger. For parallel flow: both fluids enter same end. For counter-flow: fluids enter opposite ends — counter-flow gives higher LMTD for same temperatures, thus requiring less area. Counter-flow is thermodynamically superior.
10 components required for this project.
| # | Component | Purpose | Qty |
|---|---|---|---|
| 1 | Copper tubes (8mm OD, 0.5mm wall, 500mm) | Inner tubes for hot fluid | x10 |
| 2 | PVC pipe (50mm ID, 500mm) | Shell for cold fluid | x1 |
| 3 | End caps with tube sheet (machined) | Tube bundle headers | x2 |
| 4 | Centrifugal pumps (12V, 5 L/min) | Hot and cold fluid circulation | x2 |
| 5 | DS18B20 Temperature Sensors | Inlet/outlet temperature measurement | x8 |
| 6 | Flow Meters (paddle wheel, 0–10 L/min) | Flow rate measurement | x2 |
| 7 | Arduino Mega + LCD | Data acquisition and display | x1 |
| 8 | Water heater element (1kW) | Hot fluid heating | x1 |
| 9 | Thermostat controller | Hot fluid temperature control | x1 |
| 10 | Pressure gauges (0–2 bar) | Pressure drop measurement | x2 |
Follow these 5 steps carefully.
Heat transfer rate: Q = U × A × LMTD. U = overall heat transfer coefficient (W/m²K). A = heat transfer area. LMTD (Log Mean Temperature Difference): ΔT_LMTD = (ΔT1 - ΔT2) / ln(ΔT1/ΔT2) where ΔT1 and ΔT2 are temperature differences at each end of the exchanger. For parallel flow: both fluids enter same end. For counter-flow: fluids enter opposite ends — counter-flow gives higher LMTD for same temperatures, thus requiring less area. Counter-flow is thermodynamically superior.
Design target: cool hot water from 70°C to 45°C using cold water at 20°C inlet, mass flow 0.05 kg/s each. Heat duty: Q = m_dot × Cp × ΔT = 0.05 × 4186 × 25 = 5232 W. Cold water outlet: T_cold_out = 20 + 5232/(0.05×4186) = 45°C. Counter-flow LMTD: ΔT1 = 70-45 = 25°C, ΔT2 = 45-20 = 25°C → LMTD = 25°C (uniform — special case). Required area: A = Q/(U×LMTD). For water-water, U ≈ 1000 W/m²K → A = 5232/(1000×25) = 0.21 m². With 10 tubes × 8mm OD × 500mm: A = 10 × π × 0.008 × 0.5 = 0.126 m². Need to recalculate or increase tube count/length.
Drill tube sheet (both end caps) with precise hole pattern for 10 tubes. Braze copper tubes into tube sheets (use silver solder, not soft solder — higher temperature resistance). Silver brazing: heat joint area to 700°C (cherry red), apply flux, touch silver solder wire — capillary action draws solder into joint. Test each joint: pressurize tube bundle to 5 bar with compressed air, submerge in water — look for bubbles. Install baffles inside shell (every 100mm) to direct shell-side flow across tubes (increases turbulence, improves U).
Set steady-state conditions: run both pumps, heat hot fluid to 70°C, wait 10 minutes for temperatures to stabilize. Record: hot fluid inlet temp (T_hi), hot fluid outlet temp (T_ho), cold fluid inlet temp (T_ci), cold fluid outlet temp (T_co), hot flow rate (m_h), cold flow rate (m_c). Calculate actual Q from each stream: Q_h = m_h × Cp × (T_hi - T_ho), Q_c = m_c × Cp × (T_co - T_ci). Energy balance error = (Q_h - Q_c) / Q_h should be < 5% (heat losses to environment account for discrepancy).
Calculate experimental U: Q = U × A × LMTD → U_exp = Q/(A × LMTD). Compare with theoretical U using Dittus-Boelter correlation: Nu = 0.023 × Re^0.8 × Pr^0.4 → h_inside = Nu × k / D. Shell-side h_outside from shell-side Re and Nu correlation. U_theoretical = 1/(1/h_i + wall_resistance + 1/h_o). Compare U_exp with U_theoretical. Discrepancy analysis: fouling factor (scale buildup on tube surfaces reduces U), measurement errors, non-uniform flow distribution. NTU-effectiveness method provides alternative calculation.
Core code for heat_exchanger_daq.ino:
#include <OneWire.h> #include <DallasTemperature.h> // DS18B20 sensors on different pins OneWire ow1(2); DallasTemperature T_hi(&ow1); // Hot inlet OneWire ow2(3); DallasTemperature T_ho(&ow2); // Hot outlet OneWire ow3(4); DallasTemperature T_ci(&ow3); // Cold inlet OneWire ow4(5); DallasTemperature T_co(&ow4); // Cold outlet #define FLOW_HOT A0 // Pulse from flow meter #define FLOW_COLD A1 float readFlowLPM(int pin) { // Frequency to flow: 5500 pulses/L → measure pulse frequency // Simplified: count pulses in 1 second long count = 0; unsigned long start = millis(); while(millis() - start < 1000) if(digitalRead(pin)) { count++; while(digitalRead(pin)); } return count / 5500.0 * 60; // L/min } void loop() { T_hi.requestTemperatures(); T_ho.requestTemperatures(); T_ci.requestTemperatures(); T_co.requestTemperatures(); float Thi = T_hi.getTempCByIndex(0), Tho = T_ho.getTempCByIndex(0); float Tci = T_ci.getTempCByIndex(0), Tco = T_co.getTempCByIndex(0); float mh = readFlowLPM(FLOW_HOT) / 60000 * 1000; // kg/s (assuming water density) float mc = readFlowLPM(FLOW_COLD) / 60000 * 1000; float Qh = mh * 4186 * (Thi - Tho); // W float Qc = mc * 4186 * (Tco - Tci); float LMTD = ((Thi-Tco) - (Tho-Tci)) / log((Thi-Tco)/(Tho-Tci)); float U_exp = Qh / (10 * 3.14159 * 0.008 * 0.5 * LMTD); // 10 tubes, 8mm OD, 500mm Serial.print("Qh="); Serial.print(Qh); Serial.print("W LMTD="); Serial.print(LMTD); Serial.print("°C U="); Serial.print(U_exp); Serial.println(" W/m²K"); delay(5000); }Test Heat Exchanger Design and Testing by verifying each subsystem individually before full integration.
Verify power voltages, check ground connections, use serial monitor for debug.
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