Take a 25mm cube of frozen distilled water with a mass of 15g. Tilt your head back until you can't see the internet and balance the cube on your forehead. During fusion, temperature of the ice and thus temperature difference remains constant, 37 ºC - 0 ºC. So heat rate is constant, if you assume a constant heat transfer coefficient h. Therefore, total energy transferred is equal to 0.0015 kg times enthalpy of fusion (J/kg) of water equal to h (W/m2.K) times superficial area A of the ice mass times temperature difference (37 ºC = 37 K) times time t. From this, you get time t. For the mass of 0.0015 kg you get the volume V with density of ice at 0 ºC (slightly less than 1,000 kg/m3). The question is then what it is the area A, which in our case is 375mm squared. I have taken a typical value of heat transfer to ambient by natural convection and thermal radiation h = 10 W/m2K which means the ice cube should melt completely in 76 minutes and 33 seconds assuming you stay perfectly still and facing away from the internet. If it melts quicker than this, your temperature is elevated.
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