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Topic · Mechanical Engineering

Heat Transfer and Mathematical Modeling

Heat Transfer and Mathematical Modeling is a research topic within Mechanical Engineering. Science Explorer counts 3.5k research works in it since 1951. 9.9% of them reached the world's top 10% most cited for their field and year.

This cluster of papers covers a wide range of topics in mechanical engineering and materials science, including ultrasonic treatment, polymer adsorption, finite element method, thermal protection, nanoparticle synthesis, elasticity theory, heat transfer, composite materials, numerical modeling, and aerospace industry.

  • Ultrasonic Treatment
  • Polymer Adsorption
  • Finite Element Method
  • Thermal Protection
  • Nanoparticle Synthesis
  • Elasticity Theory
  • Heat Transfer
  • Composite Materials
  • Numerical Modeling
  • Aerospace Industry
Research works
3.5k
fractional, since 1951
In the world top 10%
345
per year above
Top-10% rate
9.9%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
-2%
the tick is no change
Largest producer
Russia
58% of the 10 largest, 2022-now
Heat Transfer and Mathematical Modeling

Which countries lead Heat Transfer and Mathematical Modeling research?

By volume, Russia and Ukraine publish the most (438 and 143 works in 2022-now).

By volume, 2022-now

  1. 1 Russia 438 works
  2. 2 Ukraine 143 works
  3. 3 United States 43 works
  4. 4 Uzbekistan 30 works
  5. 5 China 25 works
  6. 6 Kazakhstan 25 works
  7. 7 Azerbaijan 15 works
  8. 8 Belarus 14 works
  9. 9 India 10 works
  10. 10 Poland 10 works

How concentrated that is

The same countries as shares of everything the list above accounts for. A node where two countries do two thirds of the work and one spread evenly across twelve read alike as a ranking and not at all alike here.

Russia: 58.1%Ukraine: 19.0%United States: 5.8%Uzbekistan: 4.0%6 others listed: 13.1%58%largest
Russia438 · 58.1%Ukraine143 · 19.0%United States43 · 5.8%Uzbekistan30 · 4.0%6 others listed99 · 13.1%

Shares of the rows listed above, not of the whole node.

Which institutions lead Heat Transfer and Mathematical Modeling research?

By volume in 2022-now, Russian Academy of Sciences publishes the most Heat Transfer and Mathematical Modeling research, followed by Moscow Aviation Institute and National Academy of Sciences of Ukraine.

By volume, 2022-now

  1. 1 Russian Academy of SciencesRussia 78 works
  2. 2 Moscow Aviation InstituteRussia 68 works
  3. 3 National Academy of Sciences of UkraineUkraine 31 works
  4. 4 Bauman Moscow State Technical UniversityRussia 17 works
  5. 5 Weatherford CollegeUnited States 16 works
  6. 6 Lomonosov Moscow State UniversityRussia 16 works
  7. 7 Samara State Technical UniversityRussia 14 works
  8. 8 National Aerospace University – Kharkiv Aviation InstituteUkraine 11 works
  9. 9 State University "Kyiv Aviation Institute"Ukraine 9 works
  10. 10 Oles Honchar Dnipro National UniversityUkraine 9 works

Who are the leading researchers in Heat Transfer and Mathematical Modeling?

The most-cited researchers publishing on Heat Transfer and Mathematical Modeling include Richard Bellman.

  1. 1 Richard Bellman United States 80k citations

Ranked by citations received across their whole record, among researchers with at least three works on this topic.

What are the most cited papers in Heat Transfer and Mathematical Modeling?

The most cited paper in Heat Transfer and Mathematical Modeling is "Perturbation Methods" (A. H. Nayfeh, Vimal Singh, 1978), with 4,699 citations. Next come "Simple microfluids" (1,239) and "Canonical transformations depending on a small parameter" (1,005).

Most cited papers
#PaperReleasedCitations
1 Perturbation Methods A. H. Nayfeh, Vimal Singh · IEEE Transactions on Systems Man and Cybernetics May 1978 4,699
2 Simple microfluids A. Cemal Eringen · International Journal of Engineering Science May 1964 1,239
3 Canonical transformations depending on a small parameter Andr� Deprit · Celestial Mechanics and Dynamical Astronomy Mar 1969 1,005
4 Stress Distribution in Bonded Dissimilar Materials With Cracks F. Erdoğan · Journal of Applied Mechanics Jun 1965 648
5 Dynamic Problems of Thermoelasticity Witold Nowacki, P. H. Francis, R. B. Hetnarski et al. · Journal of Applied Mechanics Jun 1977 645
All 100 most cited papers, with filters and sorting

Where is Heat Transfer and Mathematical Modeling research done?

The largest centres of Heat Transfer and Mathematical Modeling research in 2022-now are Moscow (Russia), Kyiv (Ukraine), Saint Petersburg (Russia) and Kharkiv (Ukraine). Among places with at least 20 works in it, it is an unusually large share of all research in Samara, Kharkiv and Moscow.

Largest cities, 2022-now

  1. 1 MoscowRussia 200 works
  2. 2 KyivUkraine 49 works
  3. 3 Saint PetersburgRussia 28 works
  4. 4 KharkivUkraine 24 works
  5. 5 SamaraRussia 22 works
  6. 6 Kazan’Russia 19 works
  7. 7 LvivUkraine 17 works
  8. 8 TashkentUzbekistan 16 works
  9. 9 WeatherfordUnited States 16 works
  10. 10 AlmatyKazakhstan 15 works

Where it is the local speciality

  1. SamaraRU · 22.0 works63×
  2. KharkivUA · 24.0 works29×
  3. MoscowRU · 199.9 works24×
  4. KyivUA · 49.5 works21×
← less than its size predicts1×more →

Location quotient: how much more of its research is in Heat Transfer and Mathematical Modeling than the world average.

See Heat Transfer and Mathematical Modeling on the map

Where is the best place to study Heat Transfer and Mathematical Modeling?

Among universities, judged by research, Moscow Aviation Institute, Weatherford College and National Aerospace University – Kharkiv Aviation Institute score highest, combining excellence, specialisation, size, growth and international reach. Research strength is one signal when choosing where to study; it does not measure teaching.

0%10%20%30%mean 7.4875%fractional works in this field (log) →share of work in the world top 10% →Moscow Aviation Inst…Weatherford CollegeNational Aerospace U…Lomonosov Moscow Sta…
above the meannear itbelow it

One dot per university in the first ten of the table below, at the default weights. The upper left is the interesting corner: small places doing unusually strong work.

Excellenceshare of its work in the world top 10%, 2022-now and all time averaged
40%
Specialisationhow much of its work is in this field, counted up to 10× the world share
10%
Sizeits output in this field, on a log scale
30%
Growthoutput growth, counted from -20% to +20%
10%
Internationalshare of its work with a co-author abroad
10%
Each slider sets a weight; the share it gets of the score is beside it.
#UniversityScoreTop 10%SpecialisationWorksGrowth
1Moscow Aviation InstituteRussia 80.525.4%594.9×68 +39.4%
2Weatherford CollegeUnited States 30.58.4%16.4×16 +183.3%
3National Aerospace University – Kharkiv Aviation InstituteUkraine 27.96.9%266.5×11 +175.0%
4Lomonosov Moscow State UniversityRussia 22.44.6%25.1×16 -19.3%
5Oles Honchar Dnipro National UniversityUkraine 16.811.1%151.3×9 +5.5%
6State University "Kyiv Aviation Institute"Ukraine 11.90.8%83.2×9 +64.9%
7Bauman Moscow State Technical UniversityRussia 11.82.4%124.3×17 -67.1%
8Samara State Technical UniversityRussia 11.70.3%237.7×14 +1.8%

Universities only. The score blends excellence (40%), size (30%), specialisation (10%), growth (10%), international reach (10%), 2022-now; growth compares 2018-21 with 2022-25 and counts up to +20%, since a jump from a small base is mostly noise.

Every institution in Heat Transfer and Mathematical Modeling, country by country

Is Heat Transfer and Mathematical Modeling research growing?

Output in 2022-2025 was 2% lower than in 2018-2021, peaking in 2025.

still counting19801990200020102020
grewheldshrank

The same series as a ribbon: one cell per year, darker for more. The line above answers how much; this answers when.

Its share of all research

Growing output can still be a shrinking share: all of science grows. This is Heat Transfer and Mathematical Modeling as a percentage of every work published that year, 0.0020% in 2024.

still counting0.0050%0.010%Heat Transfer and Mathematical Modeling0.0039% in 202519801990200020102020

Fractional works of Heat Transfer and Mathematical Modeling over all fractional works that year. How the balance of science has shifted.

How much of it reaches the world top 10%

Year by year.

still counting5%10%15%Heat Transfer and Mathematical Modeling9.7% in 2025200020102020

Of each year's works in it, the share that reached the world's 10% most cited for their field and year. A field is the world for its own topics, so there is no other line to hold it against.

Which topics inside it are moving

Growth and decline on one axis around a shared zero. Two lists side by side hide the thing that matters: whether the growth dwarfs the decline, or the other way round.

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