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Anuj Kumar: Alumnus

Degree Program: Applied Mathematics, Ph.D.

Department: Applied Mathematics

Undergraduate Institution: Indian Institute of Technology, Jodhpur, Mechanical Engineering, B.S.

Graduate Institution: Indian Institute of Technology, Bangalore, Mechanical Engineering, M.S.

Advisor: Pascale Garaud

Anuj Kumar, applied mathematics Ph.D. alumnus

“One of the best parts of my research is getting to blend different interdisciplinary concepts together like math, engineering, and physics and collaborate with different researchers across different fields.”

Anuj Kumar was a member of Baskin Engineering’s 25th graduating class, earning a Ph.D. in applied mathematics in June 2023. During his time at UC Santa Cruz, he worked under the guidance of Professor Pascale Garaud conducting research in fluid dynamics. This fall, he will begin a three-year appointment as a visiting assistant professor of math at UC Berkeley.

Describe your journey to the Baskin School of Engineering.
I received both my bachelor’s and master’s degrees in mechanical engineering in India. I was always interested in the subfield of fluid mechanics as it had a lot of mathematical concepts involved. During my master’s program, it became very clear that I was more interested in the mathematical aspects of mechanical engineering, so I decided to pursue an Applied Mathematics Ph.D. program at Baskin Engineering. I moved here five years ago. It’s been a great experience overall. 

Explain the research you’ve been doing during your graduate program.
I work in fluid dynamics, primarily in the area of turbulent flows. Even though we have fluid equations in place, like the Navier–Stokes equations, it’s very hard to solve them when the flow is highly turbulent. My research has two parts to it. The first part involves finding bounds on different mean quantities, such as drag force and heat transfer, in turbulent flows. The second part is about designing flows that have the same characteristics as turbulent flows to show that they can achieve these bound values from the first part.

One of the best things about my research is getting to blend different interdisciplinary concepts together like math, engineering, and physics and collaborate with different researchers across different fields. 

What’s a milestone you’ve reached in your research?
Last year, I was working on a problem related to heat transfer in a fluid medium. The question was how to transfer heat efficiently from a hot surface to a cold surface. This problem has numerous engineering applications including IC engines, air conditioning systems, and heat exchangers. Despite its importance, the optimal flow design for this problem has remained unknown. I came up with a “tree-looking,” 3D-branching flow design and mathematically proved that this flow achieves the maximum value of heat transfer. I plan to move this research forward by implementing these theoretical flow designs into a mechanical apparatus.

What is your favorite memory at Baskin?
I have a couple. One is just being able to do the kind of interdisciplinary research that I really enjoy over the past five years. Another is being able to take a few steps outside of my office and go for a walk in the redwoods. The fresh air and peacefulness would allow me to brainstorm new ideas and think about a problem clearly without distractions.

Now that you’ve graduated with your Ph.D., what’s next for you?
I’m joining the UC Berkeley Math Department faculty as a visiting assistant professor. I start teaching in the fall. I also plan to continue the turbulent flow design research I was doing in my Ph.D. program. 

What advice do you have for prospective applied mathematics graduate program students?
Try not to get stuck too long on one problem. It’s important to know when to take a step back to gain new perspective and insights and help you move forward. Also, don’t forget to enjoy what you’re doing. 

Interview Date: June 21, 2023

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