Dr. Jay I. Frankel


Department Head, R. Myers Endowed Professor
Ph.D., Virginia Polytechnic Institute and State University, 1986 M.S.M.E., Virginia Polytechnic Institute and State University, 1982 B.S.M.E., University of Maryland, 1980 (Magna Cum Laude)
Tel: (575) 6462335
Email: jfrankel@nmsu.edu
Office: Jett Hall, Room 104


Research Interests:
Heat Transfer in Hypersonics, Slug Calorimentry and ThinFilm Gauges, Inverse Heat Transfer Problems, Thermal Measurements, Calibration Mathematics, Uncertainty Analysis, Sensitivity Analysis, Parameter Estimation, Applied Mathematics, Vibrations
Memberships and Services:
 AIAA Thermophysics Technical Committee (20182021)
 AIAA Special Awards, AIAA TN (May 2018): For “recognizing your work in engineering analysis and the development of CIEM”
 AIAA Technical Chair Thermophysics Conference, AIAA Aerospace Science Meeting (ASM) Nashville, TN January 2012.
 AIAA Thermophysics Technical Committee (20092012)
 AIAA TCThermophysics Liaison to TCGround Testing (20092012)
 Guest Professor, Ocean University of China, Qingdao, China (20092012)
 AIAA General H.H. Arnold Award, AIAA TN (2010): General H. H. Arnold Award is granted for outstanding contributions in the advancement of thermal analysis in harsh rocket environments and high speed propulsion systems.
 Distinguished Visiting Scientist and Faculty, Oak Ridge National Laboratory (ORNL) (July 07–Jan 08)
 AIAA Associate Fellow, American Institute of Aeronautics and Astronautics (2005)
 AIAA Thermophysics Technical Committee (20032006)
 AIAA Thermophysics Technical Committee (20002003)
 Fellow, Computational Mechanics, Wessex Institute of Technology, Southampton, UK (2000)
Journal and Proposal Reviewer:
 Journal of Computational and Applied Mathematics
 AlAA Journal of Thermophysics and Heat Transfer
 Journal of Engineering Mathematics
 ASME Journal of Heat Transfer
 ASME Journal of Fluids Engineering
 Numerical Heat Transfer
 International Journal for Numerical Methods in Engineering
 International Journal for Numerical Methods in Fluids
 International Journal of Heat and Mass Transfer
 Applied Mathematics and Computation
 Canadian Journal of Physics
 Journal of Physics A: Mathematical and Theoretical
 Journal of Physics D: Applied Physics
 Physica A
 Applied Scientific Research
 Ain Shams Engineering Journal
 Inverse Problems in Science and Engineering
 Engineering Analysis with Boundary Elements
 International Journal of Heat and Fluid Flow
 Aerospace Science and Technology
 Korean Mathematical Society
 Korean Journal of Computational and Applied Mathematics
 Acta Mechanica
 Acta Astronauntica
 Inverse Problems
 Journal of Thermophysics
 International Journal of Thermal Sciences
 Journal of Enhanced Heat Transfer
 Heat Transfer Engineering (an international journal)
 Experiments in Fluids
 Mathematical Modelling and Analysis (Baltics)
 Computer Methods in Applied Mechanics and Engineering
 Advances in Engineering Software
 Chemical Engineering Communications
 Smart Materials and Structures
 Sensors
 ASTM BooksInstitute of Physics (Book chapter reviews)
 National Science Foundation
 Department of Energy
 City University of Hong Kong
 The National Academies
 Czech Science Foundation
Intellectual Property:
 Frankel, J.I., Keyhani, M., Arimilli, R.V., and J. Wu “Ratebased sensors for advance realtime analysis and diagnostics”, U.S. Patent No. 7539587, May 26, 2009.
Research Projects (Partial Listing):
 “New Paradigms for Inverse Heat Conduction Problems: Creative analytics and experiments utilizing advanced technologies“, PI/PD: J.I. Frankel, National Science Foundation, CBET1703442, Amount Received: $302,314, Duration: 1 Aug. 2017 31 July 2021.
 “A High Temperature, High Heat Flux Electrical Heater Test Facility for Rapid Evaluation of Surface Thermal Conditions, Alternative Sensing and Cross Calibration”, PI: J.I. Frankel, subcontracted from University of Dayton Research Institute, Amount Received: $208,784, Duration: 1 January 2018 31 December 2020.
 “Total Heat Transfer Calibration in Multilayer Plates”, PI/PD: J.I. Frankel, CoPi: M. Keyhani, MBDAFrance, Amount Received: $208,259 (186,780 Euro), Award Period: Sept. 1, 2015 March 1, 2019.
 “A Novel Calibration Method for Estimating Transient Surface Heat Flux under Hypersonic Heating Conditions for Global Reach Vehicles”, PI/PD J.I. Frankel, and CoPi: M. Keyhani, Air Force Research Laboratory (WP), Contract Number: FA865013C2326, Amount Received: $374,181, Award Period: Dec. 1, 2012Dec 10, 2017. Plus supplement of 14K for UG support.
 “Transformative Calibration Method for Prediction of Surface Heat Flux”, PI/PD J.I. Frankel, CoPi: M. Keyhani, National Science Foundation (CBET1234419), Amount Received: $249,915, Award Period: Aug. 15, 2012August 14, 2016.
 “EAGER: Experimental Verification to a Transformative Calibration Method”, PI/PD J.I. Frankel, CoPi: M. Keyhani, National Science Foundation (CBET1137625 Combustion, Fire and Plasma Systems), Amount Received: $57,503: Breakdown: $48,500 (CBET), with supplement $9,003 (OISE1148763); Award Period: Aug. 1, 2011July 31, 2012.
 “EAGER: Application of Calibration Convolution Integrals to Diffusion Transport”, PI/PD J.I. Frankel, CoPi: M. Keyhani, National Science Foundation (CBET1153476), Amount Requested: $28,954, Award Period: September 1, 2011August 31, 2012.
 “Heating rate sensor and analytic tools for the prediction of surface heat flux and temperature of TPS via indepth sensor data”, PI/PD J.I. Frankel, CoPi: M. Keyhani, NASA (Contract Number: NNX10AN35A), Amount Budgeted: $1,059,300.00 (Amounts Awarded: NASA: $522,286, UTK cost share: $537,014), Award Period: August 1, 2010July 31, 2014.
 “Time Derivative of Temperature Sensor Development for Advanced Thermal Science Applications” Aerospace Testing Alliance, Contract Number: 0916FRANKEL, Amount Awarded: $45,000, Award Period: 2/1/0912/31/09.
 “RateBased Sensor Development for Advancing Heat Transfer Measurements” (PI/PD J.I. Frankel, CoPI’s: M. Keyhani, R. Arimilli, and J. Wu), National Science Foundation, CBET0601236, Amount: $114,855, Award Period: April 15, 2006September 15, 2007.
 “Inverse Process Analysis for the Acquisition of Thermophysical Property Data” (PI/PD J.I. Frankel (UTK), CoPI’s: A. Sabau (ORNL), W. Porter (ORNL), Department of Energy (DEFC0701ID14249), Amount Awarded: $750,000 (UTK: $345,000, ORNL, $405,000), Award Period: October 1, 2001September 30, 2004.
 “A New Unified Space/Time Treatment for Solving Direct and Thermal Design Problems in Radiative and Conductive Transport”, National Science Foundation (CTS9619192) and Sandia National Laboratories, Amount Awarded: $170,150 (NSFCTS: $95,150 SNL: $75,000), Award Period: Nov. 1, 1997October 31, 2001 (includes NSFREU supplement of $5,000).
Research (Archival) Papers
 Frankel, J.I., Geraets, R.T.P. (Oxford), McGilvray, M. (Oxford) and H.C. Chen (Rheem), “Alternative Data Reduction Equation for Shock Tunnel Experiments Using Diamond Slug Calorimetry”, AIAA J. Thermophysics and Heat Transfer (under “minor” revision).
 Frankel, J.I., and K. Ekici, “Revisiting Slug Calorimeters for Hypersonics”, Aerospace Science and Technology Journal, (accepted, 3/2020).
 Ekici, K., Djeddi, R., Li, H., Hang, and J.I. Frankel, “Modeling Periodic and Nonperiodic Response of Dynamical Systems Using an Efficient ChebyshevBased TimeSpectral Approach” J. Computational Physics, (accepted 5/2020).
 Frankel, J.I. and H.C. Chen, “Analytical Developments and Experimental Validation of a Thermocouple Model through an Experimentally Acquired Impulse Response Function”, Int. J. Heat and Mass Transfer, Vol. 141 (2019), pp. 13011314. doi: 10.1016/j.ijheatmasstransfer.2019.05.098
 Frankel, J.I., and H.C. Chen, “Heat Flux Data Reduction using a Preconditioner Test Function for Thin Film Analysis”, AIAA J. Thermophysics and Heat Transfer (in press). http://arc.aiaa.org/doi/abs/10.2514/1.T5744
 Chen, H.C., and J.I. Frankel, “Estimating the Thermal Effusivity for Coaxial Thermocouple Using a Quantified Aluminum Nitride Heater”, AIAA J. Thermophysics and Heat Transfer (in press) https://doi.org/10.2514/1.T5743
 Chen, H.C., Frankel, J.I. and M. Keyhani, “TwoProbe Calibration Integral Equation Method for Nonlinear Inverse Heat Conduction Problem of Surface Temperature Estimation”, Numerical Heat Transfer, Part B, (minor revision due Jan 2020).
 Frankel, J.I., Chen, H.C., and K. Mathew, “DesigntoValidation of a New Heat Flux Source with Uncertainty Analysis”, AIAA J. Thermophysics and Heat Transfer, Vol. 33, No. 2 (2019), pp. 517535.http://arc.aiaa.org/doi/abs/10.2514/1.T5519.
 Myrick, J.A., Keyhani, M, and J.I. Frankel, “Calibration of a Plate Sensor for Determination of Total Heat Transfer into a Surface with a Spatially Varying Heat Flux”, Experimental Thermal and Fluid Science Vol. 97 (2018), pp 145159. doi: 10.1016/j.expthermflusci.2018.04.005
 Chen, H.C., Frankel, J.I. and M. Keyhani, “TwoProbe Calibration Integral Equation Method for Nonlinear Inverse Heat Conduction Problem of Surface Heat Flux Estimation”, Int. J. Heat Mass Transfer, Vol. 121 (2018), pp. 24626, doi: 10.1016/j.ijheatmasstransfer.2017.12.072
 Chen, H.C., Frankel, J.I. and M. Keyhani, “Nonlinear Inverse Heat Conduction Problem of Surface Temperature Estimation by the Calibration Integral Equation Method”, Numerical Heat Transfer, Part B Vol. 73, Issue 5 (2018) pp. 263291 doi.org/10.1080/10407790.2018.1464316
 Chen, H.C., Frankel, J.I. and M. Keyhani, “Nonlinear Inverse Heat Conduction: Digitally Filtered Space Marching with PhasePlane and CrossCorrelation Analysis”, Numerical Heat Transfer, Part B, Vol. 72, Issue 2, (2017), pp. 109129. doi: 10.1080/10407790.2017.1347004.
 Chen, YY, Frankel, J.I. and M. Keyhani, “A New Front Surface Heat Flux Calibration Method for 1D Nonlinear Thermal System with a TimeVarying Back Boundary Condition”, J. Engineering Mathematics, Vol. 105, Issue 1 (2017) pp. 157187. doi: 10.1007/s1066501698880.
 Myrick, J.A., Keyhani, M, and J.I. Frankel, “Determination of Surface Heat Flux and Temperature Using InDepth Temperature Data – Experimental Verification”, Int. J. Heat and Mass Transfer, Vol. 111, (2017), pp. 982998, doi.org/10.1016/j.ijheatmasstransfer.2017.04.029.
 Frankel, J.I. and M. Keyhani, “Response Function Formulation for Calibration Integral Equation Method: Concept”, Journal of Engineering Mathematics, Vol. 110, Issue 1 (2018), pp. 7595. DOI: 10.1007/s1066501799328.
 Frankel, J.I., Chen, H.C., and M. Keyhani, “New Step Response Formulation for Inverse Heat Conduction”, AIAA J.Thermophysics and Heat Transfer, Vol. 31, No. 4 (2017), pp. 989996 http://arc.aiaa.org/doi/abs/10.2514/1.T5067.
 Frankel, J.I., and M. Keyhani, “Cross Correlation and Inverse Heat Conduction by a Calibration Method”, AIAA J.Thermophysics and Heat Transfer, Vol. 31, No. 3 (2017), pp. 746756 http://arc.aiaa.org/doi/abs/10.2514/1.T5059.
 Myrick, J.A., Keyhani, M, and J.I. Frankel, “Inverse Prediction of Temperature through Time Rescaling of High Temperature Experimental Data”, Journal of Thermal Science and Engineering Applications, Vol.8, No. 4 (2016) 041005 (12 pages) doi: 10.1115/1.4034093.
 Chen, YY., Keyhani, M. and J.I. Frankel, “A New Thermophysical Property Estimation Approach based on Calibration Equations and Rescaling Principle”, Journal of Thermal Science and Engineering Applications, Vol. 8, No. 2 (2015) pp. 021013021023, doi: 10.1115/1.4032179.
 Frankel, J.I. and M. Keyhani, “Inverse Ablation Analysis and the Calibration Integral Equation Method”, AIAA J.Thermophysics and Heat Transfer, Vol. 31, No. 1 (2017), pp. 1019. doi: 10.2514/1.T4625.
 Chen, YY., Frankel, J.I., and M. Keyhani, “A Nonlinear, Rescaling Based Inverse Heat Conduction Calibration Method and Optimal Regularization Parameter Strategy”, AIAA J. Thermophysics and Heat Transfer, Vol. 30, No. 1 (2016), pp.6788 (doi: 10.2514/1.T4572).
 Chen, H.C., J.I. Frankel, and M. Keyhani, “TwoDimensional Formulation for Inverse Heat Conduction Problems by the Calibration Integral Equation Method”, Applied Mathematical Modeling, Volume 40, Issues 13–14, (2016), pp. 6588–6603 (doi:10.1016/j.apm.2016.02.003).
 Frankel, J.I. and D. Bottländer, “Acoustic Interferometry and the Calibration Integral Equation Method for Inverse Heat Conduction”, AIAA J. Thermophysics and Heat Transfer, Vol. 29, No. 4 (2015), pp. 862869
 Löhle, S. (Univ. Stuttgart) and J.I. Frankel, “Physical Insight into System Identification Parameters Applied to Inverse Heat Conduction Problems”, AIAA J. Thermophysics and Heat Transfer, Vol. 29, No. 3 (2015), pp 467472, doi: 10.2514/1.T4431.
 Frankel, J.I. and M. Keyhani, “Calibration Integral Equation Method for TwoProbe Inverse Heat Conduction” AIAA J. Thermophysics and Heat Transfer, Vol. 28, No. 3 (2014) pp. 548553. doi: 10.2514/1.T4374.
 Frankel, J.I., M. Keyhani, “PhasePlane Analysis and CrossCorrelation for Estimating Optimal Regularization Parameters in Inverse Heat Conduction Problems”, AIAA J. Thermophysics and Heat Transfer, Vol. 28, No. 3 (2014) pp. 542548. (doi: 10.2514/1.T4357).
 Chen, Y.Y., Frankel, J.I., and M. Keyhani, “A New Nonlinear Surface Heat Flux Calibration Method based on Kirchhoff Transformation and Rescaling Principles”, Inverse Problems in Sciences and Engineering, Vol. 22, #8 (2014), pp. 13941421. (http://dx.doi.org/10.1080/17415977.2014.880906).
 Frankel, J.I., and M. Keyhani, “Theoretical Development of a New Surface Heat Flux Calibration Method for ThinFilm Resistive Temperature Gauges and CoAxial Thermocouples”, Shock Waves, Vol. 23, Issue 2, pp 177188 (2013). doi: 10.1007/s0019301204183
 Frankel, J.I. and M. Keyhani, “Nonlinear Inverse Calibration Heat Conduction through Property Physics”, AIAA J. Thermophysics and Heat Transfer, Vol. 28, No. 2, pp. 203217 (2014)
 Elkins, B., M. Keyhani, and J.I. Frankel, “Surface Heat Flux Prediction Through PhysicsBased Calibration Part 2: Experimental Verification, AIAA Journal of Thermophysics and Heat Transfer, Vol. 27, No. 2 , pp. 206216 (2013).doi: 10.2514/1.T3918
 Frankel, J.I., M. Keyhani, and B. Elkins, “Surface Heat Flux Prediction through PhysicsBased Calibration Part 1: Theory, AIAA Journal of Thermophysics and Heat Transfer, Vol. 27, No. 2, pp. 189205 (2013). doi: 10.2514/1.T3917
 Frankel, J.I., Keyhani, M, “Moving LowPass Gauss Filter with Automatically Defined Influence Region for Diffusive Studies”, AIAA J. Thermophysics and Heat Transfer, Vol. 26, #1, pp. 176181 (2012).
 Elkins, B.S., Keyhani, M., and J.I. Frankel ,”Global Time Method for the Inverse Heat Conduction Problem”, Inverse Problems in Science and Engineering, Vol. 20, Issue 5, pp. 651664 (2012).
 Frankel, J.I., M. Keyhani, R.V. Arimilli, and B. Elkins, “A New RateBased Sensor Approach for Measuring Thermal Diffusivity”, AIAA J. Thermophysics and Heat Transfer, Vol. 24, #4, pp. 811817 (2010).
 Frankel, J.I., M. Keyhani, R.V. Arimilli, and B. Elkins, “A New, Anisotropic, TwoDimensional, Transient Heat FluxTemperature Integral Relationship for HalfSpace Diffusion”, Zeitschrift für angewandte Mathematik und Mechanik (ZAMM) , Vol.90, No. 2, pp. 161170 (2010).
 Elkins, B.E., M. G. Huang, and J.I. Frankel, “InSitu HigherTime Derivative of Temperature Sensors for Aerospace Heat Transfer”, Int. Journal of Thermal Sciences, Vol. 52, pp. 3139 (2012).
 Frankel, J.I., M. Keyhani, and R.V. Arimilli, “A New, Orthotropic, TwoDimensional, Transient Heat FluxTemperature Integral Relationship for HalfSpace Diffusion”, AIAA J. Thermophysics and Heat Transfer , Vol. 24, #1, pp. 212215 (2010).
 Frankel, J.I., M. Keyhani, and M.G. Huang, “Local Sensitivity Analysis for the Heat Flux Temperature Integral Relationship in the Half Space”, Applied Mathematics and Computations, Vol. 217, pp. 363375 (2010).
 Frankel, J.I., M. Keyhani, and R. Arimilli, “New ThreeDimensional Heat FluxTemperature Integral Relation for HalfSpace Transient Diffusion”, Journal of the Franklin Institute, Vol. 347, pp. 16811688 (2010).
 Kruttiventi, J, J. Wu and J.I. Frankel, “RealTime LowNoise Differentiation of Low Frequency Signals in HeatTransfer Applications”, IEEE Transactions on Instrumentation and Measurements, Vol. 59, #3, pp. 596603 (2010).
 Frankel, J.I., “A New Asymptotic TemperatureHeat Flux Integral Relationship in Cylindric Coordinates”, AIAA J. Thermophysics and Heat Transfer, Vol. 23, #1, pp. 191196 (2009).
 Frankel, J.I., “TemperatureHeat Flux Integral Relationship in the HalfSpace by Fourier Transforms”, AIAA J. Thermophysics and Heat Transfer, Vol. 22, #4, pp. 786791 (2008).
 Frankel, J.I., M. Keyhani, R.V. Arimilli, and J. Wu, “Locating Sudden Changes in Heat Flux using HigherTemporal Derivative of Temperature”, AIAA. J. Spacecraft and Rockets, Vol. 45, #3, pp. 631635 (2008).
 Frankel, J.I., and C. Chisholm, “Integral Equation and Sensitivity Analyses of Creep Behavior for PVDF Thin Films”, Mechanics of Materials, Vol. 40, #7, pp 594601 (2008).
 Frankel, J.I and V.V. Kulish, “A New Flux Integral Relationship for HalfSpace Transient Heat Conduction with Arbitrary Initial Condition”, Engineering Analysis with Boundary Elements, Vol. 32, pp. 162167 (2008).
 Frankel, J.I., R.V.Arimilli, M.Keyhani, and J. Wu, “Heating Rate dT/dt Measurements Developed from InSitu Thermocouples using a VoltageRate Interface”, Int. Comm. of Heat and Mass Transfer , Vol. 35, pp. 885891 (2008)
 Frankel, J.I., M. Keyhani, R.V. Arimilli, and J. Wu, “A New Multidimensional Integral Relationship between Heat Flux and Temperature for Direct Internal Assessment of Heat Flux”, Zeitschrift für angewandte Mathematik und Physik (ZAMP), Vol. 59, #5, pp. 869888 (2008).
 Frankel, J.I., “Generalizing the Method of Kulish to OneDimensional Unsteady Heat Conducting Slabs”, AIAA J. Thermophysics and Heat Transfer, vol. 20, #4, pp. 945950 (2006).
 Frankel, J.I., “Regularization of Inverse Heat Conduction by Combination of Rate Sensors Analysis and Analytic Continuation”, J. Engineering Mathematics, vol. 57, pp. 181198 (2007).
 Frankel, J.I., and R.V. Arimilli, “Inferring Convective and Radiative Heating Loads from Transient Surface Temperature Measurements in the HalfSpace”, Inverse Problems in Sciences and Engineering vol. 15, No. 5, pp. 463488 (2007).
 Frankel, J.I., W.D. Porter, and A.S. Sabau, “Analysis of a Modified PushRod Dilatometer”, J. Thermal Analysis and Calorimetry, vol. 82, pp. 171177, (2005).
 Frankel, J.I., “Motivation for the Development of New Thermal Rate Sensors for Material Science Applications”, International Journal of Materials and Product Technology (Special Issue: Quenching and Distortion), Invited Paper, vol. 24, No. 14, pp. 199206, (2005).
 Frankel, J.I., and J.J. Lawless, “Numerically Stabilizing IllPosed Moving Surface Problems through Heat Rate Sensors”, AIAA J. Thermophysics and Heat Transfer, vol. 19, #4, pp. 587592, (2005).
 Frankel, J.I., G.E. Osborne, and K. Taira, Stabilization of IllPosed Problems through Thermal Rate Sensors”, AIAA J. Thermophysics and Heat Transfer, vol. 20, #2, pp. 238246, (2006).
 Frankel, J.I., and K. Taira, “Integral Equation Formulation and Error Estimation for Radial Flow Between Two Flat Disks”, Journal of Computational and Applied Mathematics, vol. 181, pp. 103124, (2005).
 Frankel, J.I., M. Keyhani, and K. Taira, “InPhase Error Estimation of Experimental Data and Optimal First Derivatives”, AIAA Journal, vol. 42, #5, pp. 10171024, (2004).
 Frankel, J.I., “Inverse Heat Conduction and DataType Issues”, Boundary Element Communications, vol. 11, #4, pp. 3742, (2000).
 Hale, S.W., M. Keyhani, and J.I. Frankel, “Design and Control of Interfacial Temperature Gradients in Solidification”, International Journal of Heat and Mass Transfer, vol. 43, #20, pp. 37953810, (2000).
 Frankel, J.I., and M. Keyhani, “A Global Time Treatment for Inverse Heat Conduction Problems”, Journal of Heat Transfer, vol. 119, pp. 673683 (1997).
 Frankel, J.I., and G.E. Osborne, “A New Time Treatment for Solving Partial IntegroDifferential Equations of Radiative Transport”, IMA Journal of Numerical Analysis, vol. 19, pp. 91103 (1999).
 Frankel, J.I. and M. Keyhani, “A New Approach for Solving Inverse Solidification Design Problems”, Numerical Heat Transfer, Part B, vol. 30, #2, pp. 161178 (1996).
 Frankel, J.I., “A WeightedResidual Solution to an Inverse Stefan Design Problem with Imposed Physical Constraints”, Zeitschrift für angewandte Mathematik und Physik (ZAMP), vol. 47, pp. 456466 (1996).
 Frankel, J.I., “Direct LeastSquares Solutions to Integral Equations Containing Discrete Data”, AIAA Journal of Thermophysics and Heat Transfer, vol. 10, #1, pp. 182186 (1996).
 Frankel, J.I., “Implicit Solution Method for a Cumulative Variable Formulation to Radiative/Conductive Transport”, AIAA Journal of Thermophysics and Heat Transfer, vol. 9, #3, pp. 558560 (1996).
 Frankel, J.I., “A ResidualMinimization LeastSquares Method for Inverse Heat Conduction”, Computers and Mathematics with Applications, vol. 32, #4, pp. 117130 (1996).
 Frankel, J.I., “Cumulative Variable Formulation to Transient Conductive and Radiative Transport in Participating Media”, AIAA Journal of Thermophysics and Heat Transfer, vol. 9, #2, pp. 210218 (1995).
 LaClair, T., and J.I. Frankel, “Chebyshev Series Solution for Radiative Transport in a Medium with a Linearly Anisotropic Scattering Phase Function”, International Journal for Numerical Methods in Heat and Fluid Flow, vol. 5, #8, pp. 685704 (1995).
 Frankel, J.I., “A Note on the Integral Formulation of Kumar and Sloan”, Journal of Computational and Applied Mathematics, vol. 61, pp. 263274 (1995).
 Frankel, J.I., “Several Symbolic Augmented Chebyshev Expansions for Solving the Equation of Radiative Transfer”, Journal of Computational Physics, vol. 117, pp. 350363 (1995).
 Frankel, J.I., “A Galerkin Solution to a Regularized Cauchy Singular IntegroDifferential Equation”, Quarterly of Applied Mathematics, vol. 53, #2, pp. 245258 (1995).
 Frankel, J.I., and S.R. Choudhury, “Some New Observations on the Classical Logistic Equation with Heredity”, Applied Mathematics and Computation, vol. 58, pp. 275308 (1993).
 Frankel, J.I., “Computational Attributes of the Integral Form of the Equation of Transfer”, Journal of Quantitative Spectroscopy and Radiative Transfer, vol. 46, #4, pp. 329342 (1991).
 Frankel, J.I., “A Regularized and Preconditioned Boundary Integral Solution to Heat Transfer in a Participating Gas Flow between Parallel Plates”, Numerical Heat Transfer, Part B, vol. 19, #1, pp. 105126, (1991).
 Frankel, J.I. and S.R. Sonikar, “Combined Radiative and Convective Heat Transfer of a Compressible, Transparent Gas through a Tube”, Comm. Int. J. Heat and Mass Transfer, vol. 17, #3, pp. 293304 (1990).
 Frankel, J.I., and J.J. Silvestri, “Radiative Exchange between Longitudinal Gray Fins”, J. Thermophysics and Heat Transfer, vol. 5, #1, pp. 120122 (1991).
 Frankel J.I., “Green’s Function Solution to Heat Transfer of a Transparent Gas through a Tube”,Numerical Heat Transfer, Part B, vol. 16, #2, pp. 231243 (1989).
 Frankel, J.I, “Nonlinear Heat Transfer: Solution of Singular, Nonlinear Integral Equations”, Engineering Analysis, vol. 8, #5, pp. 231238 (1991).
 Frankel J.I., and and T.P. Wang, “Radiative Exchange from an Array of Gray Fins using a Couple Integral Equation Formulation”, J. Thermophysics and Heat Transfer, vol. 2, #4, pp. 296302 (1988).
 Vick,B., J.H. Beale, and J.I. Frankel, “Integral Equation Solution for Internal Flow Subjected to a Variable Heat Transfer Coefficient”, J. Heat Transfer. vol. 109, pp.856860 (1987).
 Frankel J.I. and B.Vick, “An Exact Methodology for Solving Nonlinear Diffusion Equations Based on Integral Transforms”, Applied Numerical Mathematics, vol. 3, pp.467477 (1987).
 Frankel,J.I., B.Vick, and M.N. Ozisik,”General Formulation and Analysis of Hyperbolic Heat Conduction in Composite Media”, Int. J. Heat and Mass Transfer, vol. 30, #7, pp.12931305 (1987).
 Frankel J.I., B.Vick,and M.N. Ozisik, “Flux Formulation in Hyperbolic Heat Conduction”, J. Applied Physics, vol. 58, #9, pp.33403345 (1985).
 Thomas, J.R., J.I Frankel, and D.P.H. Hasselman, “Effect of Interface Reflections and Angle of Incidence of Radiation on Thermal Stresses in SemiTransparent Material”, J. Thermal Stresses, vol.6, #1, pp.129137 (1983).
 Singh, J., J.I. Frankel J.R.Thomas,and D.P.H. Hasselman, “Thermal Stresses in Partially Absorbing Flat Plate Due to Sudden Interruption of the Steady State Asymmetric Radiation,II; Convective Cooling at Front Surface”, J. Thermal Stresses, vol. 6, #1, pp.2534 (1983).
 Frankel J.I., J.Singh, J.R.Thomas, and D.P.H. Hasselman, “Thermal Stresses in Partially Absorbing Flat Plate Due to Sudden Interruption of the Steady State Asymmetric Radiation, I; Convective Cooling at Rear Surface”, J. Thermal Stresses, vol. 6, #1, pp.1524 (1983).