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Heat Exchanger Design Calculator Documentation

Note: This documentation is based on standard chemical engineering principles for heat exchanger design. The actual implementation in the code may vary.

1. Objective

The Heat Exchanger Design Calculator is a tool for the preliminary thermal design of a shell-and-tube heat exchanger. It calculates the required heat transfer area, heat duty, and outlet temperatures based on the Log Mean Temperature Difference (LMTD) method.

2. Design Basis & Methodology

The core of the calculator is the LMTD method for heat exchanger analysis.

Key Formulas:

  1. Heat Duty (Q): The rate of heat transferred from the hot fluid to the cold fluid.

    Q = m_hot * Cp_hot * (T_hot_in - T_hot_out)
Q = m_cold * Cp_cold * (T_cold_out - T_cold_in)

  2. Log Mean Temperature Difference (LMTD): The effective average temperature difference between the two fluids.

    LMTD = (ΔT1 - ΔT2) / ln(ΔT1 / ΔT2)

    Where ΔT1 and ΔT2 are the temperature differences at the two ends of the exchanger. A correction factor (Ft) is applied for multi-pass configurations.

  3. Required Heat Transfer Area (A): The fundamental design equation.

    Q = U * A * LMTD * Ft

    Where U is the Overall Heat Transfer Coefficient.

3. Input Parameters

  • Fluid Properties: Flow rates, specific heats (Cp), and inlet temperatures for both the hot and cold streams.
  • Overall Heat Transfer Coefficient (U): An estimated or known value representing the overall thermal conductivity of the exchanger, including fouling.
  • Exchanger Configuration: To determine the LMTD correction factor (Ft).

4. Output Results

  • Heat Duty (Q): The total heat transferred.
  • Outlet Temperatures: The final temperatures of the hot and cold streams.
  • LMTD: The Log Mean Temperature Difference.
  • Required Heat Transfer Area (A): The surface area needed to achieve the heat duty.

5. Limitations and Assumptions

  • The Overall Heat Transfer Coefficient (U) is a critical input and is often an estimate. Its accuracy directly impacts the calculated area.
  • Assumes constant specific heats and U value across the temperature range.
  • Does not perform pressure drop calculations, which are a critical part of the mechanical design.

6. Example Calculation

Goal: Find the required area for a counter-current heat exchanger to cool a hot water stream.

Given:

  • Hot Fluid (Water): m_hot = 10 kg/s, Cp_hot = 4.18 kJ/kg·K, T_hot_in = 90°C, T_hot_out = 50°C
  • Cold Fluid (Oil): m_cold = 15 kg/s, Cp_cold = 2.1 kJ/kg·K, T_cold_in = 20°C
  • Overall Heat Transfer Coefficient (U): 300 W/m²·K
  • Configuration: Counter-current flow (Ft = 1.0)

Calculation Steps:

  1. Calculate Heat Duty (Q): Q = m_hot * Cp_hot * (T_hot_in - T_hot_out) = 10 kg/s * 4.18 kJ/kg·K * (90 - 50) K = 1672 kW

  2. Calculate Cold Fluid Outlet Temperature (T_cold_out): Q = m_cold * Cp_cold * (T_cold_out - T_cold_in) 1672 kW = 15 kg/s * 2.1 kJ/kg·K * (T_cold_out - 20°C) T_cold_out = (1672 / (15 * 2.1)) + 20 = 53.08 + 20 = 73.08°C

  3. Calculate Log Mean Temperature Difference (LMTD): ΔT1 = T_hot_in - T_cold_out = 90 - 73.08 = 16.92°C ΔT2 = T_hot_out - T_cold_in = 50 - 20 = 30°C LMTD = (ΔT1 - ΔT2) / ln(ΔT1 / ΔT2) = (16.92 - 30) / ln(16.92 / 30) ≈ 22.84°C

  4. Calculate Required Heat Transfer Area (A): Q = U * A * LMTD * Ft 1,672,000 W = 300 W/m²·K * A * 22.84 K * 1.0 A = 1,672,000 / (300 * 22.84) ≈ 244 m²

Result: A heat transfer area of approximately 244 m² is required.

Reference Standards

  • TEMA Standards: Tubular Exchanger Manufacturers Association (9th Edition).
  • ASME Section VIII Div 1: Rules for Construction of Pressure Vessels.
  • API Standard 660: Shell-and-tube Heat Exchangers for General Refinery Services.
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