The key was to view a steak as “a fluid-saturated poroelastic medium.” Why didn’t we think of that?
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There’s a certain art to cooking a steak: eyeing up the best cut of meat, watching the changes in color, feeling for when it’s done just right. But there’s a science to it, too: the temperature, the surface area, the resting time. A team of researchers from across the U.S. recently took that latter idea to an extreme, publishing a paper entitled “a mathematical model for meat cooking” that reimagines cooking a steak in the kitchen as a series of complicated equations.

It might not sound like the most thrilling of pastimes, but mathematicians have modeled the cooking of a steak before. However, Hala Nelson—an associate professor of applied mathematics at James Madison University (JMU) and the lead author of the study—and her team explain that these previous studies have failed to create anything beyond a relatively inaccurate one-dimensional model. “The math for cooking a steak is pretty complicated because of the nature of the meat tissue and the changes that occur within the steak and its protein matrix while cooking,” Nelson told me via email.

Medium rare beef steak on wooden board. Top view
Credit: LarisaBlinova/Getty Images

Instead, her team’s work was able to result in a more useful two-dimensional recreation by treating meat—as the paper explains—“as a fluid-saturated poroelastic medium composed of a solid matrix (polymer) and fluid.” No one said it was appetizing, but apparently it works—offering, among other things, an easy way for computers to determine how much a cut of steak will shrink when it’s cooked.

The actual mathematics—which are based on Flory-Rehner theory (of course!)—may be a bit wonky for most people to wrap their head around. “As the temperature increases during cooking, a pressure gradient builds and induces fluid motion and deformation of the solid matrix, which also contributes to the motion of the fluid. The model accounts for temperature distribution, fluid velocity field, moisture content, surface evaporation, and shrinkage during the cooking process,” the paper says in its introduction. Later, the authors conclude, “We demonstrate reasonable agreement with empirical data. The model captures the swelling of moisture in the steak center and the drying out at the surface that is observed during a steak cooking process.”

But Nelson explains that plenty of practical applications exist. “Tracking meat temperature and moisture level is very important for both food safety and flavor, and our model captures both at all times of the cooking process,” she said. “For chefs looking to perfect their steaks, we can play around with our model and compare different ways of cooking steak: double-sided cooking, pan-cooking, oven-cooking, etc., and eventually find the best way to cook a steak, optimizing conditions that produce the best moisture level and temperature.”

And yet, when asked about what the future may hold for this kind of research, Nelson noted that the applications can go well beyond food. “We started this project because my colleague at JMU, John Webb, is a mathematician who is an awesome cook, and he was wondering whether we could model mathematically the perfect way to cook a steak,” she tells me. “This work started as a fun project with four undergraduate students; however, it is a good mathematical model for any poroelastic medium saturated in fluid where changes happen due to a heating process.”

But getting back to meat, the researchers also believe that, with enough computing power and resources, they could “easily” extend their model into an even more enlightening three-dimensional computer recreation of a steak in the future. At that point, I can only assume they’ll be looking to create a three-dimensional computer model of a human to eat it.