General Mechanical

General Mechanical

Radiation to ambient and convection with heat transfer coefficient of temperature do not match

    • denischebakov
      Subscriber

      Good time of day,

      I have a problem setting the surface-to-ambient radiation boundary conditions for the thermal analysis of a 2D model. It seems that I have misunderstandings in fundamental theory. In my world, the surface-to-ambient radiation satisfies the Stefan-Boltzmann law: q = σε(T^4-Ta^4), where T and Ta are nodal and ambient temperatures in Kelvin, respectively. Thus, it must be the same as setting the convection q = α(T)*(T-Ta), where α(T) = σε(T^2+Ta^2)(T+Ta), following the difference of squares formula.

      I tried to check it with a simple APDL model (the script is attached). I created a rectangle and set the constant temperatures of 500 °C for the left and right borders, radiation for the bottom, and convection with α(T) table for the top. I computed all in °C, so I used the temperature offset of 273 for radiation and calculated α(T) as σε((T+273)^2+(Ta+273)^2)(T+Ta+2*273). The RAD keyword does not seem to work in my case, so I used RDSF with a space node with the ambient temperature of 20 °C for setting the radiation to ambient.

      The results are presented in the following image, and they are different for the top and the bottom, and I do not understand why. I tried to compute all in Kelvin and change the position of a space node, but nothing changed.

    • Ashish Khemka
      Ansys Employee
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