Nocturnal cooling of earth and atmosphere

Sun is the primary source of energy for all living things on earth. Sunlight is needed for photosynthesis by the leaves of the plants, which in turn produces food in the presence of few other ingredients. The heat from the sun evaporates water, forming clouds and rain, creating a water cycle. The land surface gets heated up due to sunlight, causing the atmosphere to become warmer and more liveable for most creatures. A fraction of the energy gained by various parts of the earth’s surface is transferred to the atmosphere.

Air in the atmosphere is a mixture of gases, predominantly oxygen and nitrogen, with other trace gases. Air is often loaded with a dynamic distribution of dust or solid suspended particles and water in liquid, vapour, and solid phases. Air which does not contain a significant amount of solid and liquid particles is called dry air. Certain gases in dry air can potentially absorb the energy transferred back by the earth’s surface, making the atmosphere we live in habitable. If the earth and its atmosphere retain the heat from the sun continuously, the temperature will rise till it becomes unbearable. Certain gases in the atmosphere, especially carbon dioxide, have this property. We call this greenhouse gas.

But what happens in the absence of sunlight? The darker parts of the earth no longer get heated up. The heat from the earth’s interior (a few meters below the earth’s surface) will reach the earth’s surface. The surface, in turn, will try to transfer the heat accumulated during the daytime to colder surroundings, which are the surrounding atmosphere and the deep dark space. The heat reaching from the interior to the surface is called conduction. The surface, in turn, transfers heat to the surrounding air in the form of convection, and a part of the energy will be radiated by the earth’s surface.

The radiated component is quite complex. Part of the energy released by the surface gets absorbed by greenhouse gases in the atmosphere. These are carbon dioxide, water vapour, clouds, methane, etc. The remaining part will escape the atmosphere to reach the colder space. Under clear dry sky conditions, heat convection to the surroundings becomes negligible. The energy stored from the deeper soil layers will conduct to the surface, which in turn gets radiated to the cold space. The balance between this conduction and radiation helps us to understand how quickly the earth’s surface gets colder at night, also known as nocturnal cooling.

Under suitable environmental conditions, people worldwide have used nocturnal cooling for the mass production of ice, even when the surrounding atmosphere is warmer! Tetsu Tamura, a Japanese meteorologist, in his published work [1], describes how soil conduction and clear sky radiation contribute to the faster rate of surface cooling. This work was published more than a century ago and is considered a classic example of a conduction–radiation problem in heat transfer.

[1] S. Tetsu Tamura, (1905), Mathematical Theory of the Nocturnal Cooling of the Atmosphere, Monthly Weather Review, Vol. 33, pp. 138-147.

Thermal Protection System

Rub your palms together, and you will feel the heat generated between them. This frictional heat often keeps us warm during cold winter nights. So what happens if you rub your palms faster? You will feel more heat. Imagine that you could rub your palm at 7500 m/s! Your palm can catch fire at this speed. Rockets which are used to put satellites in orbit or other heavenly objects like Moon, Jupiter, etc., are typically launched or re-entered through our atmosphere travelling at incredible speeds. The outer surface of the rocket and the surrounding air from the atmosphere act as two palms.

The extreme heat generated by friction is called aerodynamic heating. The generated heat is so high that aluminium (often used for building the space vehicle) melts and gets removed from the main body. A thermal protection system (TPS) is needed to protect the space vehicle, which can withstand extreme heat and yet does not allow the heat to penetrate the interior of the vehicle.

Heat penetrates through a solid material through conduction. If the conductivity of solid material is very high (true for aluminium and other metals), they can quickly transfer the heat to the other side. A good TPS should have low thermal conductivity to prevent the heat from penetrating inside. At a high heat rate, the vehicle’s temperature can also be very high (exceeding 1500 deg C), at which most materials melt. A good TPS should also be made from a material having a very high melting point.

However, in space, mass is a premium. Every mass added to the vehicle’s design will reduce the mass of scientific payloads such as sensors and instruments. As a trade-off, during the re-entry, a small part (layer) of the TPS material is allowed to melt. This serves two purposes: Firstly, melting involves latent heat (the amount of heat absorbed by the material to change its phase from solid to liquid). As latent heat is usually very high for most substances, part of TPS gets removed upon melting, carrying significant heat away from the vehicle. This ensures that less heat remains for conduction. The removed TPS material now allows a fresh layer of TPS to absorb the heat, and the process continues till the entire TPS material is removed by this process. The other purpose is that since melted TPS material gets detached from the remaining solid part, the melt layer gets removed from the vehicle, thereby reducing its overall weight.

To summarize, more TPS material results in an increased non-scientific payload of the vehicle. While lesser TPS material could result in the entire TPS getting melted off, exposing the base material (an alloy of aluminium) to the harsh environment. So the thickness of TPS should be designed considering the above constraints.

In a recent paper co-authored with Prof. Katte [1], we presented a one-dimensional transient heat conduction model involving phase change at the boundary to simulate the performance of TPS as a function of time. The model considers the outer surface of TPS exposed to extreme heat, while the other surface shielding the base material is insulated. The simulations are done until the TPS base reaches a predefined temperature in non-dimensional form.

Reference:

S. R. Kannan and S. S. Katte, (2018), Numerical Investigation and Correlations for Heat Diffusion through Planar Ablative Thermal Protection Systems, Thermal Science & Engineering Progress, 7, 279-287.