How to Find Heat Transfer Area?

The heat transfer area can be found using the fundamental equation: A = Q / (U ΔTm), where you'll need to determine the heat transfer rate (Q), the overall heat transfer coefficient (U), and the appropriate mean temperature difference (ΔTm).

Here's a breakdown of the steps involved in determining the heat transfer area:

1. Determine the Heat Transfer Rate (Q)

• Calculate the heat load: The heat transfer rate (Q) represents the amount of heat that needs to be transferred between the two fluids. This is often the starting point of the design.

• Use the energy balance equation: Determine Q based on energy balances for either the hot or cold fluid, using equations like:

  • Q = ṁ_h c_ph (T_h,in - T_h,out) for the hot fluid
  • Q = ṁ_c c_pc (T_c,out - T_c,in) for the cold fluid

  Where:

  • ṁ is the mass flow rate
  • c_p is the specific heat capacity
  • T_in and T_out are the inlet and outlet temperatures, respectively
  • Subscripts h and c denote hot and cold fluids, respectively.

2. Estimate the Overall Heat Transfer Coefficient (U)

• Preliminary Configuration: Select a preliminary heat exchanger configuration (e.g., shell and tube, plate heat exchanger). The configuration influences the value of U.

• Initial Estimate: Obtain an initial estimate of the overall heat transfer coefficient (U). This can be based on experience with similar fluids and configurations, or by consulting standard tables. Perry's Chemical Engineers' Handbook and other heat transfer textbooks are excellent resources for this. Typical values for U (in W/m²·K) are as follows (these are approximate and highly dependent on specific conditions):

  Fluid Combination	U (W/m2·K)
  Water to Water	800 - 1500
  Water to Oil	100 - 400
  Water to Organic Solvent	200 - 800
  Steam to Water	1000 - 6000
  Steam to Organic Solvent	500 - 1500

• Detailed Calculation (Later): After selecting a preliminary heat exchanger and determining flow rates and physical properties, a more detailed U value will need to be calculated using the following general formula:

  1/U = 1/h_i + R_f,i + t_w/k_w + R_f,o + 1/h_o

  Where:

  • h_i and h_o are the convective heat transfer coefficients on the inside and outside of the tubes (or plates). These depend on the fluid properties, flow rates, and geometry.
  • R_f,i and R_f,o are the fouling factors on the inside and outside of the tubes (or plates).
  • t_w is the wall thickness of the tube (or plate).
  • k_w is the thermal conductivity of the tube (or plate) material.

3. Determine the Mean Temperature Difference (ΔTm)

• Log Mean Temperature Difference (LMTD): For many heat exchangers, especially those with counter-current or parallel flow, the Log Mean Temperature Difference (LMTD) is used:

  ΔTm = (ΔT1 - ΔT2) / ln(ΔT1/ΔT2)

  Where:

  • ΔT1 is the temperature difference between the hot and cold fluids at one end of the heat exchanger.
  • ΔT2 is the temperature difference between the hot and cold fluids at the other end of the heat exchanger.

• Correction Factor (F): For more complex flow arrangements (e.g., multi-pass shell-and-tube exchangers), a correction factor (F) is applied to the LMTD to account for deviations from true counter-current flow. In these cases:

  ΔTm = F * LMTD

  Charts and correlations for F can be found in heat transfer textbooks (e.g., Incropera & DeWitt).

• Arithmetic Mean Temperature Difference (AMTD): For very small temperature differences or when one fluid's temperature remains nearly constant (e.g., a condenser or boiler), the arithmetic mean temperature difference can be used as an approximation:

  ΔTm = (T_h,in + T_h,out)/2 - (T_c,in + T_c,out)/2

4. Calculate the Heat Transfer Area (A)

• Apply the Formula: Once you have values for Q, U, and ΔTm, you can calculate the required heat transfer area using the formula:

  A = Q / (U ΔTm)

• Iterative Process: The calculation of heat transfer area often involves an iterative process. The initial estimate of U may need to be refined based on the calculated area and the resulting heat exchanger dimensions. You might need to adjust the preliminary configuration and recalculate U until a suitable design is achieved.

Example

Let's say you need to cool 5 kg/s of oil from 80°C to 40°C using water entering at 20°C and exiting at 30°C.

1. Q Calculation: Assume the specific heat of the oil is 2.0 kJ/kg·K. Then Q = (5 kg/s) (2.0 kJ/kg·K) (80°C - 40°C) = 400 kW

2. U Estimation: Assume a preliminary design suggests U = 200 W/m²·K (oil to water).

3. ΔTm Calculation: Assuming counter-current flow: ΔT1 = 80°C - 30°C = 50°C, ΔT2 = 40°C - 20°C = 20°C. LMTD = (50-20)/ln(50/20) = 32.7°C

4. A Calculation: A = (400,000 W) / (200 W/m²·K * 32.7°C) = 61.2 m²

Therefore, you would need approximately 61.2 m² of heat transfer area. This result then needs to be checked and refined by selecting a suitable heat exchanger and calculating U more accurately.