Thermal Engg Lab (ME-306) - Unit 4 Short Notes

ME-306: Thermal Engineering Lab - UNIT 4 Short Notes

(Based on Generic Blueprint - Assumed Theme: Heat Exchanger Performance Studies)

4.0 UNIT OVERVIEW & LEARNING OBJECTIVES

• Purpose: To experimentally determine the performance of a heat exchanger (typically parallel flow and counter flow), calculate the Overall Heat Transfer Coefficient (U), and validate theoretical LMTD and Effectiveness-NTU methods.

• Key Skills:

  • Safe operation of a shell-and-tube or concentric tube heat exchanger test rig.

  • Precise measurement of inlet/outlet temperatures and flow rates of hot and cold fluids.

  • Achieving and identifying steady-state conditions.

  • Calculating U and comparing with theoretical values.

  • Plotting performance curves (e.g., ε vs. NTU).

  • Comprehensive technical report writing and viva preparation.

4.1 THEORETICAL FOUNDATION & GOVERNING EQUATIONS

• Fundamental Law: First Law of Thermodynamics for a control volume (steady flow energy equation).

  • Heat lost by hot fluid = Heat gained by cold fluid (assuming no losses).

$$ Q_h = \dot{m}_h C_{p,h} (T_{h,in} - T_{h,out}) = Q_c = \dot{m}_c C_{p,c} (T_{c,out} - T_{c,in}) $$

• Basic Conduction Law: Fourier's Law (for wall conduction).

• Convection Law: Newton's Law of Cooling.

$$ Q = U A \Delta T_{lm} $$

• Key Parameters:

  • Log Mean Temperature Difference (LMTD): For constant U and flow rates.

$$ \Delta T_{lm} = \frac{\Delta T_1 - \Delta T_2}{\ln(\Delta T_1 / \Delta T_2)} $$

    where $$\displaystyle \Delta T_1 $$ and $$\displaystyle \Delta T_2 $$ are temperature differences at each end.

*   **Overall Heat Transfer Coefficient (U):** Represents total resistance to heat transfer.

$$ \frac{1}{U A} = \frac{1}{h_h A_h} + \frac{t_w}{k_w A_w} + \frac{1}{h_c A_c} $$

*   **Effectiveness (ε):** Actual heat transfer vs. maximum possible.

$$ \varepsilon = \frac{Q}{Q_{max}} = \frac{\dot{m}_c C_{p,c} (T_{c,out} - T_{c,in})}{\dot{m}_c C_{p,c} (T_{h,in} - T_{c,in})} \quad (\text{for } C_{min} = C_c) $$

*   **NTU Method:** Number of Transfer Units.

$$ NTU = \frac{U A}{C_{min}} $$

    where $$\displaystyle C_{min} = \min(\dot{m}_h C_{p,h}, \dot{m}_c C_{p,c}) $$.

• Dimensionless Numbers (for flow analysis):

  • Reynolds Number (Re): $$\displaystyle \text{Re} = \frac{\rho V D}{\mu} $$ (Indicates laminar/turbulent flow).

  • Prandtl Number (Pr): $$\displaystyle \text{Pr} = \frac{\mu C_p}{k} $$ (Fluid property).

  • Nusselt Number (Nu): $$\displaystyle \text{Nu} = \frac{h D}{k} $$ (Convective heat transfer coefficient).

[!TIP] Exam Focus: Be prepared to derive LMTD for parallel vs. counter-flow configurations. Know the formula for ε for both flow arrangements from the NTU-effectiveness method.

4.2 APPARATUS & INSTRUMENTATION

• Schematic: A typical setup includes:

  1. Test Section: Concentric tube or shell-and-tube heat exchanger.

  2. Hot Fluid Loop: Storage tank, immersion heater, pump, flow control valve, rotameter.

  3. Cold Fluid Loop: Similar to hot loop, often with a constant temperature source (e.g., cooling coil).

  4. Measurement Points: Temperature sensors (Thermocouples/RTDs) at all inlets and outlets. Pressure gauges (optional). Flow meters (Rotameters or measuring cylinder+stopwatch).

  DiagramSEARCH: " concentric tube heat exchanger experimental setup diagram labeled"

• Instrument Specifications & Calibration:

  • Thermocouples/RTDs: Range (0-100°C or higher), accuracy (±0.1°C or 0.5%).

  • Rotameters: Range (LPH), calibration curve (linearity check).

  • Stopwatch & Measuring Cylinder: For manual flow measurement (volumetric method). Least count (0.1 sec, 10 ml).

  • Calibration: Compare instrument readings against a calibrated standard (e.g., standard thermometer). Note calibration certificates.

4.3 EXPERIMENTAL PROCEDURE & OPERATION

• Pre-Experiment Checks:

  1. Check all electrical connections, earthing.

  2. Ensure all valves are closed, fluid levels in storage tanks are adequate.

  3. Verify no leaks in piping.

  4. Note ambient conditions.

• Step-by-Step Operation:

  1. Start cold water pump first. Set a constant flow rate.

  2. Start hot water pump. Set a desired flow rate (can be varied).

  3. Switch ON the heater. Set a constant power input (using variac/controller).

  4. Wait for Steady-State: Monitor all 4 temperature readings. When they fluctuate less than ±0.2°C for 5-10 minutes, steady-state is reached.

  5. Record: T_h_in, T_h_out, T_c_in, T_c_out, flow rates (Q_h, Q_c), heater power input (W).

  6. Vary Parameters: Change either hot/cold flow rate or heater power. Repeat steps 4-5 for at least 4-5 different conditions.

  7. Shutdown: Switch OFF heater, then pumps after cooling.

• Safety Protocols:

  • Wear gloves/face shield near hot surfaces/pipes.

  • Ensure proper grounding for electrical heaters.

  • Do not touch electrical panels with wet hands.

  • Be cautious of pressurized water lines.

[!TIP] Common Pitfall: Not waiting long enough for steady-state leads to erroneous ΔT and Q calculations. Always confirm stability before recording data.

4.4 DATA ACQUISITION & TABULATION

• Observation Table Format:

• Derived Quantities Table (Calculated):

• Note: Record multiple readings (2-3) for each steady-state point to estimate average and random error.

4.5 DATA ANALYSIS & CALCULATIONS

1. Mass Flow Rate: If using volumetric flow (V̇ in m³/s), $$\displaystyle \dot{m} = \rho V̇ $$. Density (ρ) from temperature tables.

2. Heat Transfer Rate: $$\displaystyle Q = \dot{m} C_p \Delta T $$. Use tabulated $$\displaystyle C_p $$ for water at mean temperature.

3. LMTD Calculation: Use formula from 4.1. Identify ΔT₁ and ΔT₂ based on flow arrangement.

4. Experimental U: $$\displaystyle U_{exp} = \frac{Q}{A \Delta T_{lm}} $$. A is heat transfer area (provided/calculated from tube dimensions).

5. NTU & ε:

   • Calculate $$\displaystyle C_h = \dot{m}_h C_{p,h} $$, $$\displaystyle C_c = \dot{m}_c C_{p,c} $$.

   • Identify $$\displaystyle C_{min} $$ and $$\displaystyle C_{max} $$, $$\displaystyle C^* = C_{min}/C_{max} $$.

   • $$\displaystyle NTU = \frac{U_{exp} A}{C_{min}} $$.

   • Use effectiveness formula for the specific flow arrangement (parallel/counter) to find ε_theo from NTU and C*.

   • Compare ε_exp (from Q and Q_max) with ε_theo.

6. Graphical Analysis:

   • Plot Nu vs. Re (if velocity varied) to check flow regime.

   • Plot ε vs. NTU for experimental points and theoretical curve.

4.6 RESULTS, DISCUSSION & ERROR ANALYSIS

• Presentation: Tabulate U_exp, ε_exp, ε_theo. Plot required graphs.

• Discussion Points:

  • U_exp is usually lower than theoretical U_calc (from individual h correlations) due to fouling, imperfect insulation, contact resistance.

  • ε_exp vs. ε_theo: Explain deviation due to heat loss to surroundings, inaccurate U, maldistribution.

  • Counter-flow heat exchanger has higher ε than parallel flow for same NTU and C*.

  • Effect of flow rate: Increasing flow rate generally increases U (higher Re → higher h) but may decrease ε if C_min increases faster than U A.

• Error Analysis:

  • Systematic: Calibration error in thermocouples/rotameters, inaccurate C_p or A.

  • Random: Parallax in reading, fluctuation at "steady-state".

  • Heat Loss: Major source. Affects Q balance (Q_h ≠ Q_c). Insulation minimizes this.

  • Uncertainty Propagation: Use formula for z = f(x,y). E.g., $$\displaystyle \frac{\Delta U}{U} = \sqrt{ \left(\frac{\Delta Q}{Q}\right)^2 + \left(\frac{\Delta A}{A}\right)^2 + \left(\frac{\Delta (\Delta T_{lm})}{\Delta T_{lm}}\right)^2 } $$.

4.7 LAB REPORT FORMAT & VIVA-VOCE PREPARATION

• Standard Report Structure:

  1. Title, Aim, Apparatus (with schematic).

  2. Theory (LMTD, NTU-ε method, formulas).

  3. Procedure (step-by-step, safety).

  4. Observation Tables (raw data).

  5. Calculations (show sample for one set).

  6. Final Results Table & Graphs.

  7. Discussion & Error Analysis.

  8. Conclusion (e.g., "Counter-flow is more effective.").

• Key Viva Questions & Answers:

  • Q: What is the purpose of this experiment?

    A: To determine the overall heat transfer coefficient U and effectiveness ε of a heat exchanger, compare parallel and counter-flow performance, and validate LMTD/NTU methods.

  • Q: How do you ensure steady-state? How do you know it's reached?

    A: By maintaining constant flow rates and heater power. Steady-state is reached when all 4 temperature readings stabilize (change < 0.2°C over 5-10 min).

  • Q: Why is LMTD used instead of simple ΔT?

    A: Because ΔT varies along the length of the heat exchanger. LMTD is an average ΔT that correctly represents the driving force for heat transfer in constant-U conditions.

  • Q: What are the major sources of error?

    A: Heat loss to surroundings, inaccurate flow measurement, thermocouple calibration, assumption of constant C_p and U.

  • Q: Explain the working principle of a rotameter.

    A: A variable area flow meter. Fluid flows up a tapered tube, lifting a float. At equilibrium, float position indicates flow rate on a calibrated scale.

  • Q: What is the significance of the Nusselt number?

    A: It is the dimensionless heat transfer coefficient. Nu = 1 means pure conduction; Nu > 1 indicates convection enhancement. It relates h to conductive heat transfer across the fluid boundary layer.

\boxed{U = \frac{Q}{A \Delta T_{lm}}} \quad \boxed{\varepsilon = \frac{Q}{Q_{max}}} \quad \boxed{NTU = \frac{U A}{C_{min}}}