Kevin Farrell, Principal Engineer, Computational Simulation & Validation

The other day, I was browsing the science and engineering section of my favorite used bookstore, hoping to score a few gems from the semester-end buybacks of university students trying to fill their pockets before leaving town for the summer. The selection was sparse, although typical for the digital age.

Not finding any books specifically on fluid mechanics or heat transfer, my eyes wandered to titles like Geology for Engineers & Environmental Scientists [1] and Physical Geology [2]. In those books, I found many subjects that frequently appear in today's media—water resources, sea-level changes, erosion, volcanoes, seismic waves, fault lines, and plate tectonics. Sure enough, they also covered heat transfer topics such as geothermal energy, heat flow, pressure, and temperature.

What surprised me the most was learning that the center of the Earth is about as hot as the surface of the Sun, at approximately 5000 °C! Figure 1 shows the Earth's mean temperature distribution. Using average values of density, heat capacity, and thermal conductivity to compute the thermal diffusivity of each layer, one can estimate that heat originating at the Earth's center would take roughly a trillion years to reach the surface (about 6.7 million meters away) through conduction alone.

Figure 1. Mean temperature distribution, mean density, thermal conductivity, and heat capacity of the Earth's constituent layers
Figure 1. Mean temperature distribution, mean density, thermal conductivity, and heat capacity of the Earth's constituent layers
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Figure 1. Mean temperature distribution, mean density, thermal conductivity, and heat capacity of the Earth's constituent layers
Figure 1. Mean temperature distribution, mean density, thermal conductivity, and heat capacity of the Earth's constituent layers

Clearly (and thankfully), many other processes are involved. Both solar flux and radioactivity provide heat to the earth's crust. Efficient convection cells are believed to exist in the mantle [2], much like they do in a pot of water heated from below (Figure 2). Despite the hard mantle rocks, heat can flow when stresses are applied over prolonged periods of time. Regions where hot mantle plumes rise toward the surface are associated with high heat flux and volcanic activity, making them prime sites for harvesting geothermal energy. Circulation is maintained by descending currents and lateral flow within the mantle.

Figure 2. Classical Rayleigh-Benard cells in (a) pan heated at the bottom are similar to those (b) conjectured to exist in the Earth's mantle
Figure 2. Classical Rayleigh-Benard cells in (a) pan heated at the bottom are similar to those (b) conjectured to exist in the Earth's mantle
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Figure 2. Classical Rayleigh-Benard cells in (a) pan heated at the bottom are similar to those (b) conjectured to exist in the Earth's mantle
Figure 2. Classical Rayleigh-Benard cells in (a) pan heated at the bottom are similar to those (b) conjectured to exist in the Earth's mantle

The Sun provides heat for our entire solar system. Its diameter is more than 100 times that of the Earth [3]. Scientists estimate the Sun's temperature using spectroscopic data obtained through telescopes. If the Sun's surface temperature is over 5000 °C, common sense suggests that the inside must be a lot hotter. In fact, the Sun is around 15 million °C at its core due to nuclear fusion, which turns hydrogen atoms into helium. Certain areas of the Sun's atmosphere reach temperatures approaching 20 million °C!

And what about the Earth's moon? Its radius is about one-fourth of the Earth's. Surface temperatures on the Moon vary widely (120 °C to -250 °C), because the Moon doesn't have an atmosphere [4] like the Earth. From Earth, we always see the same side of the Moon because its rotational period matches its orbital period around Earth. The proverbial “dark side of the Moon” is hidden and mysterious only in a metaphorical sense; it receives sunlight just as often as the side visible from Earth. Like Earth, the Moon has an iron-rich solid inner core, a liquid outer core, a mantle, and a crust. However, temperature of the Moon's inner core (estimated at 1330 °C to 1430 °C) is about one-fourth that of Earth's core.

Astronomers classify stars, planets, moons, asteroids, and comets as celestial bodies. Our brief look here covered only the first three. These behemoths are characterized by tremendous scales in length, mass, time, and energy that grow even larger when the bodies are grouped in galaxies and nebulae.

Just imagine how a variation of +/-10% in the original design correlations or heat balances might affect Earth. This article could have been either frozen solid or burnt to a crisp. I'm somewhat comforted that, in my day job, my analyses are typically limited to equipment with duties on the order of megawatts.

References

  1. A. E. Kehew, Geology for Engineers and Environmental Scientists, 3rd ed., Pearson Prentice Hall, Upper Saddle River, NJ (2006).
  2. E. A. Hay and A. L. McAlester, Physical Geology, 2nd ed., Prentice-Hall, Englewood Cliffs, NJ (1984).
  3. T. Saunders, How hot is the sun? Our star's staggering temperature, explained, https://www.sciencefocus.com/space/how-hot-is-the-sun (16 May 2026).
  4. US National Aeronautics and Space Administration, Weather on the moon, https://science.nasa.gov/moon/weather-on-the-moon/ (26 May 2026).