Academic Degrees
 Ph.D., Michigan State University
 M.S., University of Minnesota
 B.S., Iowa State University
Areas of Research and Professional Interest
 Additive Manufacturing
 Analytical Methods
 Heat Transfer and Mass Diffusion
 Interpretation of Experimental Data
 Inverse Problems
 Thermal/fluid sensors
Inventions/Patents
 R. Yavari, P. K. Rao, K. D. Cole, Simulating heat flux in additive manufacturing, No. 12,093,614, September 17, 2024.
 J. Severson, P. K. Rao, R. Yavari, K. D. Cole, Thermal modeling of additive manufacturing using graph theory, NO. 17/499,402, 14 April 2022.
 R. Yavari, P. K. Rao, K. D. Cole, Thermal modeling of additive manufacturing using progressive horizontal subsections, No. 17/668,025, 8 Sept 2022.
 R. Yavari, P. Rao, A. Riensche, K. D. Cole, Systems and methods for combining thermal simulations with sensor data to detect flaws and malicous cyber intrusions in additive manufacturing, WO 2023/03884, 16 March 2023.
 K. D. Cole, A. Riensche, P. Rao, Thermal modeling of additive manufacturing, No. WO 2023/076636, 4 May 2023.
About Kevin D. Cole
Dr. Cole studies heat and mass transfer through analytical and semianalytical methods, with application to manufacturing processes, inverse problems, and measurement of thermal properties. He is coauthor 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. He has current funding from the National Institute of Standards and Technology. 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. Dr. Cole retired from teaching and tiewearing in 2020 to focus on research and software commercialization.
Selected Publications
Book:
 Cole, K. D., Beck, J. V., HajiSheikh, A., and Litkouhi, B., Heat Conduction Using Green's Functions, 2nd edition, Taylor and Francis, New York, 2011.
Papers:
 Piercy, N.L., Kulkarni, J.D., Vishnu, A.S., Suryakumar, S., Cole, K.D., Rao, P.K., Rapid thermal modeling of wire arc additive manufacturing process using a meshfree spectral graph theory approach. Int J Adv Manuf Technol (2024). https://doi.org/10.1007/s0017002413994x
 Riensche, R., Bevans, B. D., King, G., Krishnan, A., Cole, K. D., Rao, P. K., Predicting meltpool depth and primary dendritic arm spacing in laser powder bed fusion additive manufacturing using physicsbased machine learning, Materials and Design, v. 237, 112540, 2024.
 Riensche, A., Severson, J., Yavari, R., Piercy, N. L., Cole, K. D., Rao, P. K., Thermal modeling of directed energy deposition additive manufacturing using graph theory, Rapid Prototyping Journal, v. 29, no. 2, pp. 324 – 343, 2023.
 Riensche, R., Bevans, B. D., Smoqi, Z., Yavari, R., Krishnan, A., Gilligan, J., Piercy, N. L., Cole, K. D., Rao, P. K., Feedforward Control of Thermal History in Laser Powder Bed Fusion: Toward Physicsbased Optimization of Processing Parameters, Materials and Design, v. 224, December 2022, 111351, doi.org/10.1016/j.matdes.2022.111351.
 Riensche, R., Severson, J., Yavari, R., Piercy, N. L., Cole, K. D., Rao, P. K., “Thermal Modeling of Directed Energy Deposition Additive Manufacturing using Graph Theory,” Rapid Prototyping Journal, vol. 29, no. 2, pp. 324343, 2022, https://doi.org/10.1108/RPJ0720210184
 Cole, K. D., Riensche, 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, https://doi.org/10.1016/j.ijheatmasstransfer.2021.122112
 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: Realtime Detection of Flaws in Laser Powder Bed Fusion by Combining Thermal Simulations with InSitu Meltpool Sensor Data," Materials & Design, Vol 211, 110167, https://doi.org/10.1016/j.matdes.2021.110167, 2021.
 Cole, K. D., "To engineer is human: gender issues in the engineering workplace," Torch Magazine, vol. 92, no. 2, pp. 1014, 2021.
 Ҫetin, Barbaros., Kuşcua, Y. F., Ҫetin, Bariş, Tümüklüd, O., Cole, K. D., "Semianalytical source (SAS) method for 3D transient heat conduction problems with moving heat source of arbitrary shape," Int. J. Heat Mass Transfer, v. 165, doi.org/10.1016/j.ijheatmasstransfer.2020.120692, 2021.
 Yavari, R., Smoqi, Z., Bevans, B., Kobir, H., Mendoza, H. Song, H., Cole, K. D., Rao, P., Partscale thermal simulation of laser powder bed fusion using graph theory: effect of thermal history on porosity, microstructure, and recoatercrash, Materials & Design, vol. 204, 109685, doi.org/10.1016/j.matdes.2021.109685, 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, doi.org/10.1016/j.addma.2021.101956, 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 Insitu 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, doi.org/10.1080/24725854.2019.1701753, 2020.
 Pi, T., Cole, K. D., Zhao, Q., Zhao, W., "Investigation of Numerical Evaluation Improvement for ThreeDimensional Infinite Cylindrical Heat Conduction Problems," J. Heat Transfer, 142(4): 044501, doi.org/10.1115/1.4045796, 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., “Semianalytical source method for reactiondiffusion 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 121301.110, 2017.
 Cole, K. D., Cetin, B., “Modeling of Joule Heating and Convective Cooling in a Thickwalled Microtube,” 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. 455462, 2014.
 Tian, T., and Cole, K. D., “Anisotropic Thermal Conductivity Measurements of Carbonfiber/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. 25422549, 2011.
Monographs:
 Cole, K. D. and Dolan, K. D., R21B50Z33B00T0 Hollow cylinder with piecewise heating on inner suface, specified temperature on outer surface, and convection cooling at the ends, Exact Analytical Conduction Toolbox, exact.unl.edu, March 14, 2024, https://exact.unl.edu/contents/equation/212
 Samadi, F., Woodbury, K. A., Cole, K. D., R32B0(z5)Z21B00T0 Hollow cylinder of finite length with piecewise heating on outer surface and convection cooling on inner surface, Exact Analytical Conduction Toolbox, exact.unl.edu, February 29, 2024, https://exact.unl.edu/contents/equation/210
 Cole, K. D., R02B5Z00T0 Infinite solid cylinder heated over half of its surface and zero initial temperature, Exact Analytical Conduction Toolbox, Dec. 20, 2023, https://exact.unl.edu/contents/equation/208
 Cole, K. D., R00Z20B5T0 Semiinfinite body with a diskshaped surface heat source, Exact Analytical Conduction Toolbox, Dec. 20, 2023, https://exact.unl.edu/contents/equation/207
 Cole, K. D., R03B0Z33B00T5 Finite cylinder with convective boundaries and piecewise initial condition, Exact Analytical Conduction Toolbox, Nov. 15, 2023, https://exact.unl.edu/contents/equation/206
 Cole, K. D., phi22B10F0T0 Thin cylindrical shell initially at ambient temperature heated at one end and cooled along its circumference, Exact Analytical Conduction Toolbox, Nov. 2, 2023, https://exact.unl.edu/contents/equation/205
 Cole, K. D., R21B00T Hollow cylinder insulated at the minor radius and zero temperature at the major radius with logarithmic initial temperature, Exact Analytical Conduction Toolbox, Oct. 17, 2023, https://exact.unl.edu/contents/equation/204

Cole, K. D., R11B00T1 Hollow cylinder with zero temperature boundaries and uniform initial temperature, Exact Analytical Conduction Toolbox, Oct. 10, 2023, https://exact.unl.edu/contents/equation/203