Heat flux, or heat transfer per rate unit area, is a useful quantity in applications such as determining the transfer of energy from a fuel plate to working fluid, such as in a pressurized water reactor.
Measure the system parameters. Include uniform thickness of the material through which heat is flowing, and call it wall thickness, d. Include thermal conductivity, k, of this material. Measure (or estimate from system design parameters) the hot temperature (such as that of a heat source), Thot. Measure cold temperature (such as that of a working fluid), Tcold.
Calculate heat transfer rate, Q. Q is measured in units of energy per unit time, such as BTU/hr or Watts. For a wall of uniform thickness d, with a thermal conductivity of k, an area of A, a hot temperature, Thot, and cold temperature, Tcold, solve Q with the following equation: Q = k*A(Thot - Tcold)/d. For example, using iron with a k = 79.5 (Watts/m K), a wall 1 cm thick, analyzed over 1 square meter, and Thot - Tcold = 111C (or degrees K, equivalently), Q = 882,450 Watts
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Remove units of area, A, to get heat flux, Q". Divide Q by the area, A, you used to solve for Q since Q" = Q/A. For example, the heat flux Q" in the step above is 882,450 Watts/1m^2 = 882,450 Watts/m^2. Note that you needed to include the area in the original Q calculation to cancel out the meter unit in the value of k.