#### 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) 646-2335

**Email:** jfrankel@nmsu.edu

**Office:** Jett Hall, Room 104

### Research Interests:

Heat Transfer in Hypersonics, Slug Calorimentry and Thin-Film 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 (2018-2021)
- AIAA Special Awards, AIAA TN (May 2018): For â€śrecognizing your work in engineering analysis and the development of CIEMâ€ť
- AIAA Technical Chair Thermophysics Conference, AIAA Aerospace Science Meeting (ASM)- Nashville, TN January 2012.
- AIAA Thermophysics Technical Committee (2009-2012)
- AIAA TC-Thermophysics Liaison to TC-Ground Testing (2009-2012)
- Guest Professor, Ocean University of China, Qingdao, China (2009-2012)
- 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 07â€“Jan 08)
- AIAA Associate Fellow, American Institute of Aeronautics and Astronautics (2005)
- AIAA Thermophysics Technical Committee (2003-2006)
- AIAA Thermophysics Technical Committee (2000-2003)
- 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 Books-Institute 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 â€śRate-based sensors for advance real-time analysis and diagnosticsâ€ť, U.S. Patent No. 7539587, May 26, 2009.

### Research Projects (Partial Listing):

- â€śNew Paradigms for Inverse Heat Conduction Problems: Creative analytics and experiments utilizing advanced technologiesâ€ś, PI/PD: J.I. Frankel, National Science Foundation, CBET-1703442, Amount Received: $302,314, Duration: 1 Aug. 2017- 31 July 2021.
- â€śA High Temperature, High Heat Flux Electrical Heater Test Facility for Rapid Evaluation of Surface Thermal Conditions, Alternative Sensing and Cross Calibrationâ€ť, PI: J.I. Frankel, subcontracted from University of Dayton Research Institute, Amount Received: $208,784, Duration: 1 January 2018- 31 December 2020.
- â€śTotal Heat Transfer Calibration in Multilayer Platesâ€ť, PI/PD: J.I. Frankel, Co-Pi: M. Keyhani, MBDA-France, Amount Received: $208,259 (186,780 Euro), Award Period: Sept. 1, 2015- March 1, 2019.
- â€śA Novel Calibration Method for Estimating Transient Surface Heat Flux under Hypersonic Heating Conditions for Global Reach Vehiclesâ€ť, PI/PD J.I. Frankel, and Co-Pi: M. Keyhani, Air Force Research Laboratory (WP), Contract Number: FA8650-13C-2326, Amount Received: $374,181, Award Period: Dec. 1, 2012-Dec 10, 2017. Plus supplement of 14K for UG support.
- â€śTransformative Calibration Method for Prediction of Surface Heat Fluxâ€ť, PI/PD J.I. Frankel, Co-Pi: M. Keyhani, National Science Foundation (CBET-1234419), Amount Received: $249,915, Award Period: Aug. 15, 2012-August 14, 2016.
- â€śEAGER: Experimental Verification to a Transformative Calibration Methodâ€ť, PI/PD J.I. Frankel, Co-Pi: M. Keyhani, National Science Foundation (CBET-1137625 Combustion, Fire and Plasma Systems), Amount Received: $57,503: Breakdown: $48,500 (CBET), with supplement $9,003 (OISE-1148763); Award Period: Aug. 1, 2011-July 31, 2012.
- â€śEAGER: Application of Calibration Convolution Integrals to Diffusion Transportâ€ť, PI/PD J.I. Frankel, Co-Pi: M. Keyhani, National Science Foundation (CBET-1153476), Amount Requested: $28,954, Award Period: September 1, 2011-August 31, 2012.
- â€śHeating rate sensor and analytic tools for the prediction of surface heat flux and temperature of TPS via in-depth sensor dataâ€ť, PI/PD J.I. Frankel, Co-Pi: 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, 2010-July 31, 2014.
- â€śTime Derivative of Temperature Sensor Development for Advanced Thermal Science Applicationsâ€ť Aerospace Testing Alliance, Contract Number: 09-16-FRANKEL, Amount Awarded: $45,000, Award Period: 2/1/09-12/31/09.
- â€śRate-Based Sensor Development for Advancing Heat Transfer Measurementsâ€ť (PI/PD J.I. Frankel, Co-PIâ€™s: M. Keyhani, R. Arimilli, and J. Wu), National Science Foundation, CBET-0601236, Amount: $114,855, Award Period: April 15, 2006-September 15, 2007.
- â€śInverse Process Analysis for the Acquisition of Thermophysical Property Dataâ€ť (PI/PD J.I. Frankel (UTK), Co-PIâ€™s: A. Sabau (ORNL), W. Porter (ORNL), Department of Energy (DE-FC07-01ID14249), Amount Awarded: $750,000 (UTK: $345,000, ORNL, $405,000), Award Period: October 1, 2001-September 30, 2004.
- â€śA New Unified Space/Time Treatment for Solving Direct and Thermal Design Problems in Radiative and Conductive Transportâ€ť, National Science Foundation (CTS-96-19192) and Sandia National Laboratories, Amount Awarded: $170,150 (NSF-CTS: $95,150 SNL: $75,000), Award Period: Nov. 1, 1997-October 31, 2001 (includes NSF-REU supplement of $5,000).

### Research (Archival) Papers

**Frankel, J.I.**, Geraets, R.T.P. (Oxford), McGilvray, M. (Oxford) and H.C. Chen (Rheem), â€śAlternative Data Reduction Equation for Shock Tunnel Experiments Using Diamond Slug Calorimetryâ€ť, AIAA J. Thermophysics and Heat Transfer (under “minor” revision).**Frankel, J.I.**, and K. Ekici, â€śRevisiting Slug Calorimeters for Hypersonicsâ€ť, Aerospace Science and Technology Journal, (accepted, 3/2020).- Ekici, K., Djeddi, R., Li, H., Hang, and
**J.I. Frankel**, â€śModeling Periodic and Non-periodic Response of Dynamical Systems Using an Efficient Chebyshev-Based Time-Spectral Approachâ€ť J. Computational Physics, (accepted 5/2020). **Frankel, J.I.**and H.C. Chen, â€śAnalytical Developments and Experimental Validation of a Thermocouple Model through an Experimentally Acquired Impulse Response Functionâ€ť, Int. J. Heat and Mass Transfer, Vol. 141 (2019), pp. 1301-1314. doi: 10.1016/j.ijheatmasstransfer.2019.05.098**Frankel, J.I.**, and H.C. Chen, â€śHeat Flux Data Reduction using a Pre-conditioner Test Function for Thin Film Analysisâ€ť, 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**, â€śEstimating the Thermal Effusivity for Coaxial Thermocouple Using a Quantified Aluminum Nitride Heaterâ€ť, AIAA J. Thermophysics and Heat Transfer (in press) https://doi.org/10.2514/1.T5743 - Chen, H.C.,
**Frankel, J.I.**and M. Keyhani, â€śTwo-Probe Calibration Integral Equation Method for Nonlinear Inverse Heat Conduction Problem of Surface Temperature Estimationâ€ť, Numerical Heat Transfer, Part B, (minor revision due Jan 2020). **Frankel, J.I.**, Chen, H.C., and K. Mathew, â€śDesign-to-Validation of a New Heat Flux Source with Uncertainty Analysisâ€ť, AIAA J. Thermophysics and Heat Transfer, Vol. 33, No. 2 (2019), pp. 517-535.http://arc.aiaa.org/doi/abs/10.2514/1.T5519.- Myrick, J.A., Keyhani, M, and
**J.I. Franke**l, â€śCalibration of a Plate Sensor for Determination of Total Heat Transfer into a Surface with a Spatially Varying Heat Fluxâ€ť, Experimental Thermal and Fluid Science Vol. 97 (2018), pp 145-159. doi: 10.1016/j.expthermflusci.2018.04.005 - Chen, H.C.,
**Frankel, J.I**. and M. Keyhani, â€śTwo-Probe Calibration Integral Equation Method for Nonlinear Inverse Heat Conduction Problem of Surface Heat Flux Estimationâ€ť, Int. J. Heat Mass Transfer, Vol. 121 (2018), pp. 246-26, doi: 10.1016/j.ijheatmasstransfer.2017.12.072 - Chen, H.C.,
**Frankel, J.I**. and M. Keyhani, â€śNonlinear Inverse Heat Conduction Problem of Surface Temperature Estimation by the Calibration Integral Equation Methodâ€ť, Numerical Heat Transfer, Part B Vol. 73, Issue 5 (2018) pp. 263-291 doi.org/10.1080/10407790.2018.1464316 - Chen, H.C.,
**Frankel, J.I.**and M. Keyhani, â€śNonlinear Inverse Heat Conduction: Digitally Filtered Space Marching with Phase-Plane and Cross-Correlation Analysisâ€ť, Numerical Heat Transfer, Part B, Vol. 72, Issue 2, (2017), pp. 109-129. doi: 10.1080/10407790.2017.1347004. - Chen, Y-Y,
**Frankel, J.I.**and M. Keyhani, â€śA New Front Surface Heat Flux Calibration Method for 1-D Nonlinear Thermal System with a Time-Varying Back Boundary Conditionâ€ť, J. Engineering Mathematics, Vol. 105, Issue 1 (2017) pp. 157-187. doi: 10.1007/s10665-016-9888-0. - Myrick, J.A., Keyhani, M, and
**J.I. Frankel**, â€śDetermination of Surface Heat Flux and Temperature Using In-Depth Temperature Data – Experimental Verificationâ€ť, Int. J. Heat and Mass Transfer, Vol. 111, (2017), pp. 982-998, doi.org/10.1016/j.ijheatmasstransfer.2017.04.029. **Frankel, J.I.**and M. Keyhani, â€śResponse Function Formulation for Calibration Integral Equation Method: Conceptâ€ť, Journal of Engineering Mathematics, Vol. 110, Issue 1 (2018), pp. 75-95. DOI: 10.1007/s10665-017-9932-8.**Frankel, J.I.**, Chen, H.C., and M. Keyhani, â€śNew Step Response Formulation for Inverse Heat Conductionâ€ť, AIAA J.Thermophysics and Heat Transfer, Vol. 31, No. 4 (2017), pp. 989-996 http://arc.aiaa.org/doi/abs/10.2514/1.T5067.**Frankel, J.I.**, and M. Keyhani, â€śCross Correlation and Inverse Heat Conduction by a Calibration Methodâ€ť, AIAA J.Thermophysics and Heat Transfer, Vol. 31, No. 3 (2017), pp. 746-756 http://arc.aiaa.org/doi/abs/10.2514/1.T5059.- Myrick, J.A., Keyhani, M, and
**J.I. Frankel**, â€śInverse Prediction of Temperature through Time Rescaling of High Temperature Experimental Dataâ€ť, Journal of Thermal Science and Engineering Applications, Vol.8, No. 4 (2016) 041005 (12 pages) doi: 10.1115/1.4034093. - Chen, Y-Y., Keyhani, M. and
**J.I. Frankel**, â€śA New Thermophysical Property Estimation Approach based on Calibration Equations and Rescaling Principleâ€ť, Journal of Thermal Science and Engineering Applications, Vol. 8, No. 2 (2015) pp. 021013-021023, doi: 10.1115/1.4032179. **Frankel, J.I.**and M. Keyhani, â€śInverse Ablation Analysis and the Calibration Integral Equation Methodâ€ť, AIAA J.Thermophysics and Heat Transfer, Vol. 31, No. 1 (2017), pp. 10-19. doi: 10.2514/1.T4625.- Chen, Y-Y.,
**Frankel, J.I.**, and M. Keyhani, â€śA Nonlinear, Rescaling Based Inverse Heat Conduction Calibration Method and Optimal Regularization Parameter Strategyâ€ť, AIAA J. Thermophysics and Heat Transfer, Vol. 30, No. 1 (2016), pp.67-88 (doi: 10.2514/1.T4572). - Chen, H.C.,
**J.I. Franke**l, and M. Keyhani, â€śTwo-Dimensional Formulation for Inverse Heat Conduction Problems by the Calibration Integral Equation Methodâ€ť, Applied Mathematical Modeling, Volume 40, Issues 13â€“14, (2016), pp. 6588â€“6603 (doi:10.1016/j.apm.2016.02.003). **Frankel, J.I.**and D. BottlĂ¤nder, â€śAcoustic Interferometry and the Calibration Integral Equation Method for Inverse Heat Conductionâ€ť, AIAA J. Thermophysics and Heat Transfer, Vol. 29, No. 4 (2015), pp. 862-869- LĂ¶hle, S. (Univ. Stuttgart) and
**J.I. Frankel**, â€śPhysical Insight into System Identification Parameters Applied to Inverse Heat Conduction Problemsâ€ť, AIAA J. Thermophysics and Heat Transfer, Vol. 29, No. 3 (2015), pp 467-472, doi: 10.2514/1.T4431. **Frankel, J.I.**and M. Keyhani, â€śCalibration Integral Equation Method for Two-Probe Inverse Heat Conductionâ€ť AIAA J. Thermophysics and Heat Transfer, Vol. 28, No. 3 (2014) pp. 548-553. doi: 10.2514/1.T4374.**Frankel, J.I.**, M. Keyhani, â€śPhase-Plane Analysis and Cross-Correlation for Estimating Optimal Regularization Parameters in Inverse Heat Conduction Problemsâ€ť, AIAA J. Thermophysics and Heat Transfer, Vol. 28, No. 3 (2014) pp. 542-548. (doi: 10.2514/1.T4357).- Chen, Y.Y.,
**Frankel, J.I.**, and M. Keyhani, â€śA New Nonlinear Surface Heat Flux Calibration Method based on Kirchhoff Transformation and Rescaling Principlesâ€ť, Inverse Problems in Sciences and Engineering, Vol. 22, #8 (2014), pp. 1394-1421. (http://dx.doi.org/10.1080/17415977.2014.880906). **Frankel, J.I.**, and M. Keyhani, â€śTheoretical Development of a New Surface Heat Flux Calibration Method for Thin-Film Resistive Temperature Gauges and Co-Axial Thermocouplesâ€ť, Shock Waves, Vol. 23, Issue 2, pp 177-188 (2013). doi: 10.1007/s00193-012-0418-3**Frankel, J.I.**and M. Keyhani, â€śNonlinear Inverse Calibration Heat Conduction through Property Physicsâ€ť, AIAA J. Thermophysics and Heat Transfer, Vol. 28, No. 2, pp. 203-217 (2014)- Elkins, B., M. Keyhani, and
**J.I. Frankel**, â€śSurface Heat Flux Prediction Through Physics-Based Calibration- Part 2: Experimental Verification, AIAA Journal of Thermophysics and Heat Transfer, Vol. 27, No. 2 , pp. 206-216 (2013).doi: 10.2514/1.T3918 **Frankel, J.I.**, M. Keyhani, and B. Elkins, â€śSurface Heat Flux Prediction through Physics-Based Calibration- Part 1: Theory, AIAA Journal of Thermophysics and Heat Transfer, Vol. 27, No. 2, pp. 189-205 (2013). doi: 10.2514/1.T3917**Frankel, J.I.**, Keyhani, M, â€śMoving Low-Pass Gauss Filter with Automatically Defined Influence Region for Diffusive Studiesâ€ť, AIAA J. Thermophysics and Heat Transfer, Vol. 26, #1, pp. 176-181 (2012).- Elkins, B.S., Keyhani, M., and
**J.I. Frankel**,â€ťGlobal Time Method for the Inverse Heat Conduction Problemâ€ť, Inverse Problems in Science and Engineering, Vol. 20, Issue 5, pp. 651-664 (2012). **Frankel, J.I.**, M. Keyhani, R.V. Arimilli, and B. Elkins, â€śA New Rate-Based Sensor Approach for Measuring Thermal Diffusivityâ€ť, AIAA J. Thermophysics and Heat Transfer, Vol. 24, #4, pp. 811-817 (2010).**Frankel, J.I.**, M. Keyhani, R.V. Arimilli, and B. Elkins, â€śA New, Anisotropic, Two-Dimensional, Transient Heat Flux-Temperature Integral Relationship for Half-Space Diffusionâ€ť, Zeitschrift fĂĽr angewandte Mathematik und Mechanik (ZAMM) , Vol.90, No. 2, pp. 161-170 (2010).- Elkins, B.E., M. G. Huang, and
**J.I. Frankel**, â€śIn-Situ Higher-Time Derivative of Temperature Sensors for Aerospace Heat Transferâ€ť, Int. Journal of Thermal Sciences, Vol. 52, pp. 31-39 (2012). **Frankel, J.I.**, M. Keyhani, and R.V. Arimilli, â€śA New, Orthotropic, Two-Dimensional, Transient Heat Flux-Temperature Integral Relationship for Half-Space Diffusionâ€ť, AIAA J. Thermophysics and Heat Transfer , Vol. 24, #1, pp. 212-215 (2010).**Frankel, J.I.**, M. Keyhani, and M.G. Huang, â€śLocal Sensitivity Analysis for the Heat Flux Temperature Integral Relationship in the Half Spaceâ€ť, Applied Mathematics and Computations, Vol. 217, pp. 363-375 (2010).**Frankel, J.I.**, M. Keyhani, and R. Arimilli, â€śNew Three-Dimensional Heat Flux-Temperature Integral Relation for Half-Space Transient Diffusionâ€ť, Journal of the Franklin Institute, Vol. 347, pp. 1681-1688 (2010).- Kruttiventi, J, J. Wu and
**J.I. Frankel**, â€śReal-Time Low-Noise Differentiation of Low Frequency Signals in Heat-Transfer Applicationsâ€ť, IEEE Transactions on Instrumentation and Measurements, Vol. 59, #3, pp. 596-603 (2010). **Frankel, J.I.**, â€śA New Asymptotic Temperature-Heat Flux Integral Relationship in Cylindric Coordinatesâ€ť, AIAA J. Thermophysics and Heat Transfer, Vol. 23, #1, pp. 191-196 (2009).**Frankel, J.I.**, â€śTemperature-Heat Flux Integral Relationship in the Half-Space by Fourier Transformsâ€ť, AIAA J. Thermophysics and Heat Transfer, Vol. 22, #4, pp. 786-791 (2008).**Frankel, J.I.**, M. Keyhani, R.V. Arimilli, and J. Wu, â€śLocating Sudden Changes in Heat Flux using Higher-Temporal Derivative of Temperatureâ€ť, AIAA. J. Spacecraft and Rockets, Vol. 45, #3, pp. 631-635 (2008).**Frankel, J.I.**, and C. Chisholm, â€śIntegral Equation and Sensitivity Analyses of Creep Behavior for PVDF Thin Filmsâ€ť, Mechanics of Materials, Vol. 40, #7, pp 594-601 (2008).**Frankel, J.I**and V.V. Kulish, â€śA New Flux Integral Relationship for Half-Space Transient Heat Conduction with Arbitrary Initial Conditionâ€ť, Engineering Analysis with Boundary Elements, Vol. 32, pp. 162-167 (2008).**Frankel, J.I.**, R.V.Arimilli, M.Keyhani, and J. Wu, â€śHeating Rate dT/dt Measurements Developed from In-Situ Thermocouples using a Voltage-Rate Interfaceâ€ť, Int. Comm. of Heat and Mass Transfer , Vol. 35, pp. 885-891 (2008)**Frankel, J.I.**, M. Keyhani, R.V. Arimilli, and J. Wu, â€śA New Multidimensional Integral Relationship between Heat Flux and Temperature for Direct Internal Assessment of Heat Fluxâ€ť, Zeitschrift fĂĽr angewandte Mathematik und Physik (ZAMP), Vol. 59, #5, pp. 869-888 (2008).**Frankel, J.I.**, â€śGeneralizing the Method of Kulish to One-Dimensional Unsteady Heat Conducting Slabsâ€ť, AIAA J. Thermophysics and Heat Transfer, vol. 20, #4, pp. 945-950 (2006).**Frankel, J.I.**, â€śRegularization of Inverse Heat Conduction by Combination of Rate Sensors Analysis and Analytic Continuationâ€ť, J. Engineering Mathematics, vol. 57, pp. 181-198 (2007).**Frankel, J.I.**, and R.V. Arimilli, â€śInferring Convective and Radiative Heating Loads from Transient Surface Temperature Measurements in the Half-Spaceâ€ť, Inverse Problems in Sciences and Engineering vol. 15, No. 5, pp. 463-488 (2007).**Frankel, J.I.**, W.D. Porter, and A.S. Sabau, â€śAnalysis of a Modified Push-Rod Dilatometerâ€ť, J. Thermal Analysis and Calorimetry, vol. 82, pp. 171-177, (2005).**Frankel, J.I.**, â€śMotivation for the Development of New Thermal Rate Sensors for Material Science Applicationsâ€ť, International Journal of Materials and Product Technology (Special Issue: Quenching and Distortion), Invited Paper, vol. 24, No. 1-4, pp. 199-206, (2005).**Frankel, J.I.**, and J.J. Lawless, â€śNumerically Stabilizing Ill-Posed Moving Surface Problems through Heat Rate Sensorsâ€ť, AIAA J. Thermophysics and Heat Transfer, vol. 19, #4, pp. 587-592, (2005).**Frankel, J.I.**, G.E. Osborne, and K. Taira, Stabilization of Ill-Posed Problems through Thermal Rate Sensorsâ€ť, AIAA J. Thermophysics and Heat Transfer, vol. 20, #2, pp. 238-246, (2006).**Frankel, J.I.**, and K. Taira, â€śIntegral Equation Formulation and Error Estimation for Radial Flow Between Two Flat Disksâ€ť, Journal of Computational and Applied Mathematics, vol. 181, pp. 103-124, (2005).**Frankel, J.I.**, M. Keyhani, and K. Taira, â€śIn-Phase Error Estimation of Experimental Data and Optimal First Derivativesâ€ť, AIAA Journal, vol. 42, #5, pp. 1017-1024, (2004).**Frankel, J.I.**, â€śInverse Heat Conduction and Data-Type Issuesâ€ť, Boundary Element Communications, vol. 11, #4, pp. 37-42, (2000).- Hale, S.W., M. Keyhani, and
**J.I. Frankel**, â€śDesign and Control of Interfacial Temperature Gradients in Solidificationâ€ť, International Journal of Heat and Mass Transfer, vol. 43, #20, pp. 3795-3810, (2000). **Frankel, J.I.**, and M. Keyhani, â€śA Global Time Treatment for Inverse Heat Conduction Problemsâ€ť, Journal of Heat Transfer, vol. 119, pp. 673-683 (1997).**Frankel, J.I.**, and G.E. Osborne, â€śA New Time Treatment for Solving Partial Integro-Differential Equations of Radiative Transportâ€ť, IMA Journal of Numerical Analysis, vol. 19, pp. 91-103 (1999).**Frankel, J.I.**and M. Keyhani, â€śA New Approach for Solving Inverse Solidification Design Problemsâ€ť, Numerical Heat Transfer, Part B, vol. 30, #2, pp. 161-178 (1996).**Frankel, J.I.**, â€śA Weighted-Residual Solution to an Inverse Stefan Design Problem with Imposed Physical Constraintsâ€ť, Zeitschrift fĂĽr angewandte Mathematik und Physik (ZAMP), vol. 47, pp. 456-466 (1996).**Frankel, J.I.**, â€śDirect Least-Squares Solutions to Integral Equations Containing Discrete Dataâ€ť, AIAA Journal of Thermophysics and Heat Transfer, vol. 10, #1, pp. 182-186 (1996).**Frankel, J.I.**, â€śImplicit Solution Method for a Cumulative Variable Formulation to Radiative/Conductive Transportâ€ť, AIAA Journal of Thermophysics and Heat Transfer, vol. 9, #3, pp. 558-560 (1996).**Frankel, J.I.**, â€śA Residual-Minimization Least-Squares Method for Inverse Heat Conductionâ€ť, Computers and Mathematics with Applications, vol. 32, #4, pp. 117-130 (1996).**Frankel, J.I**., â€śCumulative Variable Formulation to Transient Conductive and Radiative Transport in Participating Mediaâ€ť, AIAA Journal of Thermophysics and Heat Transfer, vol. 9, #2, pp. 210-218 (1995).- LaClair, T., and
**J.I. Frankel**, â€śChebyshev Series Solution for Radiative Transport in a Medium with a Linearly Anisotropic Scattering Phase Functionâ€ť, International Journal for Numerical Methods in Heat and Fluid Flow, vol. 5, #8, pp. 685-704 (1995). **Frankel, J.I.**, â€śA Note on the Integral Formulation of Kumar and Sloanâ€ť, Journal of Computational and Applied Mathematics, vol. 61, pp. 263-274 (1995).**Frankel, J.I.**, â€śSeveral Symbolic Augmented Chebyshev Expansions for Solving the Equation of Radiative Transferâ€ť, Journal of Computational Physics, vol. 117, pp. 350-363 (1995).**Frankel, J.I.**, â€śA Galerkin Solution to a Regularized Cauchy Singular Integro-Differential Equationâ€ť, Quarterly of Applied Mathematics, vol. 53, #2, pp. 245-258 (1995).**Frankel, J.I.**, and S.R. Choudhury, â€śSome New Observations on the Classical Logistic Equation with Heredityâ€ť, Applied Mathematics and Computation, vol. 58, pp. 275-308 (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. 329-342 (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. 105-126, (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. 293-304 (1990).**Frankel, J.I.**, and J.J. Silvestri, “Radiative Exchange between Longitudinal Gray Fins”, J. Thermophysics and Heat Transfer, vol. 5, #1, pp. 120-122 (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. 231-243 (1989).**Frankel, J.I,**“Nonlinear Heat Transfer: Solution of Singular, Nonlinear Integral Equations”, Engineering Analysis, vol. 8, #5, pp. 231-238 (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. 296-302 (1988).- Vick,B., J.H. Beale, and
**J.I. Franke**l, “Integral Equation Solution for Internal Flow Subjected to a Variable Heat Transfer Coefficient”, J. Heat Transfer. vol. 109, pp.856-860 (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.467-477 (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.1293-1305 (1987).**Frankel J.I.**, B.Vick,and M.N. Ozisik, “Flux Formulation in Hyperbolic Heat Conduction”, J. Applied Physics, vol. 58, #9, pp.3340-3345 (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 Semi-Transparent Material”, J. Thermal Stresses, vol.6, #1, pp.129-137 (1983). - Singh, J.,
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