Thermomagnetic Garden (21 August 2024)

In my recent foray into horticulture I took interest in growing broccoli and cauliflower but discovered early on that these crops don’t fare too well in summer because of the heat. I mused on the practicability of quenching the temperature around the crops in an open space such as a garden. I thought, if we could enhance convection in the environment ambient to the crops that could have a quenching effect on them.

Googling a bit I came across a phenomenon known as “thermomagnetic convection” that occurs in ferrofluids. With this, the temperature dependence of the magnetic susceptibility of ferrofluids can be used to complement conventional convection by subjecting the fluid to an external magnetic field. Cooler parts of such fluids have a greater magnetic susceptibility and so are attracted to regions of higher magnetic field strength by a so called "Kelvin body force" to displace warm parts of the fluid.

I wondered if this occurrence could be found in matter other than ferrofluids. So I read up on the causes of other types of magnetism viz. diamagnetism and paramagnetism. I discovered that paramagnets have a magnetic susceptibility, 𝜒_m, that has a temperature dependence given by,

where N is the number of molecules per unit volume, m₀ is the molecular magnetic moment, 𝛍₀ is permeability of free space, k is the Boltzmann constant and T is temperature. 

I proceeded to search for data on the composition of  air to see if there’s an abundant paramagnetic constituent which turned out to be oxygen whose concentration in air is around 21%. I jogged my two brain cells into inquiring whether we could actuate this thermomagnetic convection with oxygen around the crop beds to cool off the crops and thus develop what we could call a “thermomagnetic garden”. 

The main challenge would obviously be how to deploy the magnetic field. Having considered a couple of ways to  achieve this I eventually focused on how Ampere’s law;

is instantiated in a direct current (dc) carrying wire lying along the z-axis in cylindrical coordinates:

where H is the magnetic field strength, dl is a differential line element along the closed contour around the wire, I is current in the wire and r is the radial distance from the centre of the wire.

This would mean a higher magnetic field strength occurs closer to the wires allowing them to attract cool oxygen from ambient air and higher altitudes of the atmosphere consequently displacing oxygen heated by the earth’s surface and effectively  augmenting convection. After pondering over a few configurations of the wires I came up with that illustrated in Fig. 1. 

Fig. 1 Thermomagnetic Garden

The diagram should be self-explanatory but, as it shows, a desirable side-effect for the crops is that since carbon dioxide is a diamagnet it would be repelled by a high magnetic field strength from the wires towards the crop beds and elevated heights of the atmosphere.

Looking at Fig. 1 the proposal seems a little too simple to be viable but perhaps experimenting with the aid of appropriate gauges we could see if the desired effect could manifest to the slightest appreciable extent. If the outcome is positive, tuning parameters or changing, say, how we set up the magnetic field could eventually realise a functioning system.