How should I proceed to find a formula $\lambda(t)$ for the thickness of and ice sheet in terms of

  1. The diference $T_{a}(t)-T_w(t)$ of the temperatures of air above the sheet and water below
  2. Thermal conductivity ($k$) and entalphy of fusion ($h$) of ice

Im new to "modelling" this stuff so I haven't made any real progress. All the equations I find online make sense for an ice sheet of area $A$ or take into account the depth of the river/lake or some other factor, but I want to assume that the ice sheet is infinite in extension: an infinite plane with some thickness dividing the space into "water region" and "air region". I wouldn't mind if $T_a$ and $T_w$ are constant (they are regions so huge that their temperatures do not really change).

Please consider explaining some steps that may be obvious in physics. I'm looking for a line of reasoning like "by conservation of energy we should have the following equation _______ which, combined with ______ gives us ______" or something similar. Nothing fancy, only an equation $\lambda(t)=$expression in terms of $k$, $h$ and the temperature difference


  • $\begingroup$ I think you'd also need relative humidity. $\endgroup$
    – zonksoft
    May 9, 2020 at 20:19
  • $\begingroup$ @zonksoft No you don’t $\endgroup$ May 9, 2020 at 20:47
  • $\begingroup$ Are you familiar with Fourier's law of heat conduction? $\endgroup$ May 9, 2020 at 23:16
  • $\begingroup$ I don't know why this thread was closed. It makes perfect sense to me. $\endgroup$ May 9, 2020 at 23:27
  • $\begingroup$ @ChetMiller No, but I am now. I understand the formula and it makes perfect sense $\endgroup$ May 10, 2020 at 14:06


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