Kevin Cole

Contact Information:

City Campus (Lincoln)
304 D NH
(402) 472-5857

Professor Emeritus

Academic Degrees

  • Ph.D., 1986 Michigan State University
  • M.S., 1979 University of Minnesota
  • B.S., 1977 Iowa State University

Areas of Research and Professional Interest

  • Analytical Methods
  • Additive Manufacturing
  • Heat Transfer and Mass Diffusion
  • Thermal/fluid sensors
  • Inverse Problems
  • Interpretation of Experimental Data

About Kevin D. Cole

Dr. Cole studies heat and mass transfer through analytical and semi-analytical methods, with application to manufacturing processes, inverse problems, and measurement of thermal properties. Dr. Cole retired from teaching and tie-wearing in 2020 to focus on research and software commercialization. He has current funding from the Department of Energy and the National Science Foundation. He is co-author of a reference book on heat conduction and maintains a website called the Green's Function Library.

He led a team that developed the 
Exact Analytical Conduction Toolbox funded by the National Science Foundation. Dr. Cole is a member of the American Society of Mechanical Engineers (ASME), American Institute of Aeronautics and Astronautics (AIAA), and is a registered professional engineer.

Selected Publications


  • Cole, K. D., Beck, J. V., Haji-Sheikh, A., and Litkouhi, B., Heat Conduction Using Green's Functions, 2nd edition, Taylor and Francis, New York, 2011.


  • Cole, K. D., Rienshe, A., Rao, P. K. "Discrete Green's functions and spectral graph theory for computationally efficient thermal modeling ", Int. J. Heat Mass Transfer, vol. 183, part B, February 2022, 122112.
  • Yavari, R., Riensche, A., Tekerek, E.,  Jacquemetton, L., Halliday, H. Vandever, M., ; Tenequer, A., Perumal, V., Kontsos, A., Smoqi, Z, Cole, K. D., Rao, P. K., "Digitally Twinned Additive Manufacturing: Real-time Detection of Flaws in Laser Powder Bed Fusion by Combining Thermal Simulations with In-Situ Meltpool Sensor Data," Materials & Design, Vol 211, 110167,, 2021.
  • Cole, K. D., "To engineer is human: gender issues in the engineering workplace," Torch Magazine, vol. 92, no. 2, pp. 10-14, 2021.
  • Ҫetin, Barbaros., Kuşcua, Y. F., Ҫetin, Bariş, Tümüklüd, O., Cole, K. D., "Semi-analytical source (SAS) method for 3-D transient heat conduction problems with moving heat source of arbitrary shape," Int. J. Heat Mass Transfer, v. 165,, 2021.
  • Yavari, R., Smoqi, Z., Bevans, B., Kobir, H., Mendoza, H. Song, H., Cole, K. D., Rao, P., Part-scale thermal simulation of laser powder bed fusion using graph theory: effect of thermal history on porosity, microstructure, and recoater-crash, Materials & Design, vol. 204, 109685,, 2021.
  • Yavari, R., Williams, R. J., Riensche, A. Hooper, P. A., Cole, K. D., Jacquemetton, L., Halliday, H., Rao, P., Thermal modeling in metal additive manufacturing using graph theory – application to laser powder bed fusion of a large volume impeller, Additive Manufacturing, Vol. 41, 101956,, 2021.
  • Yavari, R., Williams, R. J., Cole, K. D., Hooper, P. A., and Rao, P., "Thermal Modeling in Metal Additive Manufacturing using Graph Theory: Experimental Validation with In-situ Infrared Thermography Data from Laser Powder Bed Fusion." ASME. J. Manuf. Sci. Eng. doi: 10.1115/1.4047619, 2020.
  • Gaikwad, A., Yavari, M. R., Montazeri, M., Cole, K. D., Bian, L. K., Rao, P. K., "Toward the digital twin of additive manufacturing: Integrating thermal simulations, sensing, and analytics to detect process faults," IISE Transactions,, 2020.
  • Pi, T., Cole, K. D., Zhao, Q., Zhao, W., "Investigation of Numerical Evaluation Improvement for Three-Dimensional Infinite Cylindrical Heat Conduction Problems," J. Heat Transfer, 142(4): 044501,, 2020.
  • Cole, K. D., Yavari, M. R., Rao, P., "Computational heat transfer with spectral graph theory: Quantitative verification," Int. J. Thermal Sciences, Vol. 153, 10638, 2020.

  • Yavari, M. R., Cole, K. D., Rao, P., "Thermal modeling in metal additive manufacturing using graph theory," J. Manufacturing Science and Engineering, 141 (7), 071007 (May 21, 2019) doi: 10.1115/1.4043648, 2019.

  • Cole, K. D., Cetin, B., Demirel, Y., “Semi-analytical source method for reaction-diffusion problems,” J. Heat Transfer, doi:10.1115/1.4038987, 2018.
  • Pi, T., Cole, K. D., Beck, J. V., “Efficient numerical evaluation of exact solutions for 1D and 2D infinite cylindrical heat conduction problems,” J. Heat Transfer, vol. 139, pp 121301.1-10,  2017.
  • Cole, K. D., Cetin, B., “Modeling of Joule Heating and Convective Cooling in a Thick-walled Micro-tube,” Int. J. Thermal Sciences, vol. 119, pp. 24–36, 2017.
  • Cole, K. D, Beck, J. V., Woodbury, K. A. de Monte, F., "Intrinsic verification and a heat conduction database," Int. J. Thermal Sciences, vol. 78, pp. 36 – 47, 2014.
  • Cole, K. D., Cetin, B., and Brettmann, L., "Microchannel heat transfer with slip flow and wall effects," AIAA J. Thermophysics and Heat Transfer, vol 28, No. 3, pp. 455-462, 2014.
  • Tian, T., and Cole, K. D., “Anisotropic Thermal Conductivity Measurements of Carbon-fiber/epoxy Composites," Int. J. Heat Mass Transfer, vol. 55 pp. 6530 – 6537, 2012.
  • Cole, K. D., and Cetin, B., "The Effect of Axial Conduction on Heat Transfer in a Liquid Microchannel Flow," Int. J. Heat Mass Transfer, vol. 54, pp. 2542-2549, 2011.