AI for Mechanical Engineering: Heat Transfer

By Jongmok Lee
Industrial AI Lab at KAIST

1. Regression Model for Heat Fins

1.1 Recap: Heat Fins

  • Fins are widely used to increase the rate of heat transfer from a wall$,$
    • The selection of a suitable fin geometry requires a compromise among the cost, weight, and etc.
    • The heat transfer effectiveness and efficiency is determined by these fin geometries
      • ex) $\eta_f = \frac{\tanh \sqrt{\bar{h}PL^2/KA}}{\sqrt{\bar{h}PL^2/KA}}$ for fin of rectangular cross section (length $L$ and thickness $t$)
    • However, for complex, geometry, FDM calculation is required to obtain heat transfer efficiency and effectiveness
      • Build regression model that predicts efficiency and effectiveness using fin geometries
  • Train regession model to predict heat transfer performance using fin parameters
  • Inputs: fin parameters:
    • Outer diameter of tube $(D_o)$
    • Fin spacing $(\delta)$
    • Fin thickness $(t)$
    • Thermal conductivity of the material $(k)$
    • Convective heat transfer coefficient $(h)$
  • Outputs: heat fin performances:
    • Efficiency $(\eta)$
    • Effectiveness $(\epsilon)$
  • In order to dimensionally balance the equation, the input variables are convected into non-dimensional forms subsequently decreasing the number of input variables
    • $\delta^* = \frac{\delta}{D_o}$
    • $t^* = \frac{t}{D_o}$
    • $M = \frac{h}{8k}L_{exp}$
  • $\eta = f_1(\delta^*, t^*, M)$
  • $\epsilon = f_2(\delta^*, t^*, M)$