Understanding the Calculation of the Surface Area of a Heat Exchanger

Calculating the surface area of a heat exchanger is essential for efficient thermal design. This process determines the heat transfer capacity and overall performance.

This article explores detailed formulas, common values, and real-world examples for precise surface area calculation. Engineers will gain expert insights into optimizing heat exchanger design.

• Calculate the surface area of a shell and tube heat exchanger with given flow rates and temperatures.
• Determine the required surface area for a plate heat exchanger handling specific heat duties.
• Estimate the surface area for a double-pipe heat exchanger with known heat transfer coefficients.
• Calculate surface area based on overall heat transfer rate and temperature difference in a condenser.

Common Values and Parameters in Heat Exchanger Surface Area Calculation

Fundamental Formulas for Calculating Heat Exchanger Surface Area

The surface area of a heat exchanger is primarily calculated using the heat transfer equation:

Q = U × A × ΔT_lm

Where:

• Q = Heat duty (W)
• U = Overall heat transfer coefficient (W/m²·K)
• A = Heat transfer surface area (m²)
• ΔT_lm = Log mean temperature difference (K)

Rearranging to solve for surface area:

A = Q / (U × ΔT_lm)

Log Mean Temperature Difference (LMTD)

The LMTD accounts for the temperature variation between hot and cold fluids along the heat exchanger length. It is calculated as:

ΔT_lm = (ΔT₁ – ΔT₂) / ln(ΔT₁ / ΔT₂)

Where:

• ΔT₁ = Temperature difference at one end (T_hot,in – T_cold,out)
• ΔT₂ = Temperature difference at the other end (T_hot,out – T_cold,in)

Overall Heat Transfer Coefficient (U)

The overall heat transfer coefficient combines individual resistances from convection, conduction, and fouling:

1 / U = 1 / h₁ + R_w + 1 / h₂ + R_f

Where:

• h₁ = Convective heat transfer coefficient on hot fluid side (W/m²·K)
• h₂ = Convective heat transfer coefficient on cold fluid side (W/m²·K)
• R_w = Thermal resistance of the wall (m²·K/W)
• R_f = Fouling resistance (m²·K/W)

The wall resistance for a flat wall or tube wall is calculated by:

R_w = δ / k

Where:

• δ = Wall thickness (m)
• k = Thermal conductivity of wall material (W/m·K)

Heat Duty (Q)

Heat duty can be calculated from fluid properties and temperature change:

Q = ṁ × c_p × (T_in – T_out)

Where:

• ṁ = Mass flow rate (kg/s)
• c_p = Specific heat capacity (J/kg·K)
• T_in, T_out = Fluid inlet and outlet temperatures (K or °C)

Effectiveness-NTU Method (Alternative Approach)

When outlet temperatures are unknown, the effectiveness-NTU method is used to estimate heat exchanger performance and surface area.

Effectiveness (ε) is defined as:

ε = Q / Q_max

Where Q_max is the maximum possible heat transfer:

Q_max = C_min × (T_hot,in – T_cold,in)

Here, C_min is the minimum heat capacity rate between hot and cold fluids.

The Number of Transfer Units (NTU) is related to surface area:

NTU = U × A / C_min

By knowing ε and NTU relations (available in standard charts or equations depending on heat exchanger type), surface area A can be calculated.

Real-World Application Examples

Example 1: Shell and Tube Heat Exchanger for Cooling Water

A shell and tube heat exchanger is used to cool 2 kg/s of oil from 120 °C to 80 °C using water entering at 30 °C and leaving at 50 °C. The specific heat capacity of oil is 2200 J/kg·K, and water is 4180 J/kg·K. The overall heat transfer coefficient is estimated as 500 W/m²·K. Calculate the required surface area.

Step 1: Calculate heat duty Q

Q = ṁ × c_p × (T_in – T_out)

Q = 2 × 2200 × (120 – 80) = 2 × 2200 × 40 = 176,000 W

Step 2: Calculate temperature differences

ΔT₁ = T_hot,in – T_cold,out = 120 – 50 = 70 °C

ΔT₂ = T_hot,out – T_cold,in = 80 – 30 = 50 °C

Step 3: Calculate LMTD

ΔT_lm = (70 – 50) / ln(70 / 50) = 20 / ln(1.4) ≈ 20 / 0.3365 ≈ 59.44 °C

Step 4: Calculate surface area A

A = Q / (U × ΔT_lm) = 176,000 / (500 × 59.44) ≈ 176,000 / 29,720 ≈ 5.92 m²

Result: The required heat transfer surface area is approximately 5.92 m².

Example 2: Plate Heat Exchanger for Heating Process Fluid

A plate heat exchanger heats 1.5 kg/s of process fluid from 40 °C to 90 °C using steam condensing at 120 °C. The specific heat capacity of the process fluid is 3500 J/kg·K. The overall heat transfer coefficient is 800 W/m²·K. Calculate the surface area required.

Step 1: Calculate heat duty Q

Q = ṁ × c_p × (T_out – T_in)

Q = 1.5 × 3500 × (90 – 40) = 1.5 × 3500 × 50 = 262,500 W

Step 2: Calculate temperature differences

ΔT₁ = T_hot,in – T_cold,out = 120 – 90 = 30 °C

ΔT₂ = T_hot,out – T_cold,in = 100 (assumed steam condensate temp) – 40 = 60 °C

Step 3: Calculate LMTD

ΔT_lm = (60 – 30) / ln(60 / 30) = 30 / ln(2) ≈ 30 / 0.693 ≈ 43.29 °C

Step 4: Calculate surface area A

A = Q / (U × ΔT_lm) = 262,500 / (800 × 43.29) ≈ 262,500 / 34,632 ≈ 7.58 m²

Result: The required surface area for the plate heat exchanger is approximately 7.58 m².

Additional Considerations for Accurate Surface Area Calculation

• Fouling Factors: Over time, fouling deposits reduce heat transfer efficiency. Incorporate fouling resistance (R_f) in U calculation to ensure realistic sizing.
• Material Thermal Conductivity: Wall material impacts heat transfer resistance. Metals like copper and aluminum have high conductivity, reducing R_w.
• Flow Arrangement: Counterflow, parallel flow, and crossflow configurations affect LMTD and effectiveness, influencing surface area.
• Pressure Drop Constraints: Larger surface areas may increase pressure drop; balance thermal and hydraulic design.
• Safety Margins: Include design margins to accommodate operational variability and future fouling.

References and Further Reading

• Heat Exchanger Design – CHEResources
• Heat Exchanger Fundamentals – eFunda
• Heat Exchanger – Thermal Fluids Central
• Heat Exchanger Design – Engineering Toolbox