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How do you calculate net heat transfer?

Published in Heat Transfer 4 mins read

Net heat transfer (Q) is calculated by summing all heat transfers into and out of a system. Essentially, you add up all the heat added to the system and subtract all the heat removed from the system.

Here's a more detailed breakdown:

Understanding Heat Transfer

Heat transfer occurs through three primary mechanisms:

  • Conduction: Heat transfer through a material via direct contact.
  • Convection: Heat transfer through the movement of fluids (liquids or gases).
  • Radiation: Heat transfer through electromagnetic waves.

Each of these mechanisms can contribute to either adding heat to the system or removing heat from it.

Calculating Net Heat Transfer (Q)

  1. Identify all heat transfer processes: Determine all instances where heat is entering or leaving the system due to conduction, convection, or radiation.

  2. Calculate the heat transfer for each process: Use the appropriate formulas for each type of heat transfer. Here are some common examples:

    • Conduction: Q = k A (ΔT / d), where:
      • Q is the heat transfer rate
      • k is the thermal conductivity of the material
      • A is the area of heat transfer
      • ΔT is the temperature difference
      • d is the thickness of the material
    • Convection: Q = h A (Ts - Tf), where:
      • Q is the heat transfer rate
      • h is the convection heat transfer coefficient
      • A is the area of heat transfer
      • Ts is the surface temperature
      • Tf is the fluid temperature
    • Radiation: Q = ε σ A * (T4hot - T4cold), where:
      • Q is the heat transfer rate
      • ε is the emissivity of the surface
      • σ is the Stefan-Boltzmann constant (5.67 x 10-8 W/m2K4)
      • A is the area of heat transfer
      • Thot is the temperature of the hot object (in Kelvin)
      • Tcold is the temperature of the cold object (in Kelvin)

  3. Assign Signs: Give a positive sign (+) to heat entering the system and a negative sign (-) to heat leaving the system.

  4. Sum all Heat Transfers: Add up all the individual heat transfer values, taking into account their signs. This gives you the net heat transfer (Q):

    Qnet = Q1 + Q2 + Q3 + ... + Qn

    Where Q1, Q2, etc., represent the individual heat transfer values for each process.

Example

Imagine a room where:

  • A heater adds 500 J of heat via convection. (Q1 = +500 J)
  • Heat is lost through a window by conduction at a rate of 200 J. (Q2 = -200 J)
  • The walls radiate heat outwards at a rate of 100 J. (Q3 = -100 J)

The net heat transfer would be:

Qnet = +500 J + (-200 J) + (-100 J) = +200 J

This means the room is gaining 200 J of heat overall.

The First Law of Thermodynamics and Net Heat Transfer

As the reference states, the first law of thermodynamics is often expressed as:

ΔU = Q - W

Where:

  • ΔU is the change in internal energy of the system.
  • Q is the net heat transfer.
  • W is the net work done by the system (positive if work is done by the system; negative if work is done on the system).

This equation highlights the relationship between net heat transfer, work done, and the change in a system's internal energy.

In summary, to calculate net heat transfer, you must identify and quantify all heat transfer processes into and out of the system, assigning appropriate signs, and summing them together.

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