A photograph on LinkedIn (and elsewhere online [1]) shows watermelons on which someone has placed a stone. The text explains that this is done to make the melons sweeter, among other benefits. Although it is not clear whether or not this is an established farming technique in China or elsewhere (most hits on Google are social media, not reviewed sources), it is an interesting subject to investigate using numbers. The hypothesis we test is the following:
the stone absorbs heat from solar radiation during the day, keeping the melon a little cooler, and gives off heat during the night, keeping the melon warmer.
Modeling watermelons
To keep it simple, soil, melon and stone are represented by a 2D model in Abaqus, a Finite Element Solver we normally use for more complex simulations.
The same boundary condition is used for the exposed surfaces of the soil, melon and stone: a heat transfer coefficient of 20 W/(m2K). The air temperature is 30 °C during the day and 10 °C at night. This is a huge simplification, but it still seems reasonable for a first check to see if there is an effect. Day and night both last 12 hrs.
The solar radiation is modelled as a constant flux at daytime on the exposed surfaces. This, too, is an oversimplification, but if there is a large effect, it will still show. We must remember not to attach too much importance to the exact results. The order of magnitude will be correct, though. The solar radiation depends on the time of day, the absorption/reflection coefficient of the surface and the angle (which depends on the time of day). A surface ‘pointing’ at the sun and maximum absorption receives in the order of 1000 W/m2. We assume the stone absorbs most heat, the melon the least (due to shape and perhaps shiny surface) and the soil somewhere in between: 5/8th of 1000, 3/8th of 1000 and ½ of 1000, including the effect of the changing angle over the day. This is surely inaccurate, but in the right order of magnitude. In the model, therefore, a flux of heat of 625 W/m2 is imposed on the stone, 375 W/m2 on the melon and 500 W/m2 on the soil. For a more accurate calculation, measurements should be done.
Four day-night cycles were simulated to achieve a stable periodic state.
The following values are used for the heat conduction, density and specific heat.
With these numbers, the temperature in stone, melon and soil was simulated by Abaqus. In the figure, only the melon is shown.
There is a visible difference in the resulting temperature. The first graph below shows the calculated temperatures in the top corner of the melon and the bottom center. The main effect is that the stone makes the temperature change at the bottom center slower, both in the morning and in the evening.
The claimed effect (cooler in the daytime, warmer at night) is only clear at the top centre; the temperature under the stone is lower than without a stone. The melon with the stone has a lower temperature at daytime, and a higher temperature in the night, but only in that position. The second graph shows this temperature difference more clearly. A positive value means that the top centre is at a lower temperature than the top corner.
In the bulk of the melon, the difference is very small; in the bottom centre, it does not exceed 0.35 °C.
Cautious conclusion
The stone leads to a larger temperature gradient in the melon; the part that is not covered is not affected, but the part that is under the stone experiences slower heating and also slower cooling. For exact predictions, the analysis should be refined, and the actual material properties should be used.
The next question is how the temperature effect makes the melon sweeter or larger or better shaped. This not evident for a mechanical engineer, and must, for now, be left to the wisdom and experience of the melon-farmer. Or a fruit growing scientist, of course.
[1] for example here: Pet Rocks for Melons - General Gardening - Growing Fruit
