High temperature High temperature thermal diffusivity of thermal diffusivity of combustion synthesized combustion synthesized samples samples Dominique Vrel Dominique Vrel CNRS-LIMHP, UPR 1311, CNRS-LIMHP, UPR 1311, 99 avenue Jean-Baptiste Clément, 93430 Villetaneuse, France 99 avenue Jean-Baptiste Clément, 93430 Villetaneuse, France Nikhil Karnatak, Ellen M. Heian, Sylvain Dubois, Nikhil Karnatak, Ellen M. Heian, Sylvain Dubois, Marie-France Beaufort, Benoît Cochepin Marie-France Beaufort, Benoît Cochepin CNRS-LMP, UMR 6630, Bât. SP2MI, Bd M. & P. Curie, BP 30179 CNRS-LMP, UMR 6630, Bât. SP2MI, Bd M. & P. Curie, BP 30179 86962 Futuroscope-Chasseneuil du Poitou Cedex, France 86962 Futuroscope-Chasseneuil du Poitou Cedex, France
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High temperature thermal diffusivity of combustion synthesized samples Dominique Vrel CNRS-LIMHP, UPR 1311, 99 avenue Jean-Baptiste Clément, 93430 Villetaneuse,
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High temperature thermal High temperature thermal diffusivity of combustion diffusivity of combustion
Nikhil Karnatak, Ellen M. Heian, Sylvain Dubois, Nikhil Karnatak, Ellen M. Heian, Sylvain Dubois, Marie-France Beaufort, Benoît CochepinMarie-France Beaufort, Benoît Cochepin
CNRS-LMP, UMR 6630, Bât. SP2MI, Bd M. & P. Curie, BP 30179CNRS-LMP, UMR 6630, Bât. SP2MI, Bd M. & P. Curie, BP 3017986962 Futuroscope-Chasseneuil du Poitou Cedex, France86962 Futuroscope-Chasseneuil du Poitou Cedex, France
Impossible at high temperature on reactantsImpossible at high temperature on reactants
Easy at low temperature on reactants and Easy at low temperature on reactants and productsproducts
Not possible during reaction Not possible during reaction (coupled equations with kinetics)(coupled equations with kinetics)
… … Not practically possible on products at high Not practically possible on products at high temperature: retemperature: re--crystallization, sintering, stress crystallization, sintering, stress relaxation, homogenization of structure and relaxation, homogenization of structure and composition (long time at high temperature)composition (long time at high temperature)
We need to find a way to determine thermalWe need to find a way to determine thermal diffusivity as fast as possible, just after reactiondiffusivity as fast as possible, just after reaction
ii for the space step; for the space step; nn for the time step for the time step 77 space steps (77 pixels on the IR image)77 space steps (77 pixels on the IR image) 25 time steps per second25 time steps per second 2 unknowns: 2 unknowns: and and
To determine the unknowns, starting from an To determine the unknowns, starting from an experimental temperature profile, we model the experimental temperature profile, we model the evolution of temperature with arbitrary values of evolution of temperature with arbitrary values of and and , and then minimize the sum of differences , and then minimize the sum of differences between the final calculated profile and the final between the final calculated profile and the final experimental profileexperimental profile
Noisy dataNoisy data Calculated value of thermal diffusivity sets the Calculated value of thermal diffusivity sets the
lower limit for the real value : method measures lower limit for the real value : method measures only the part of the heat flowing through the only the part of the heat flowing through the sample that contributes to the temperature sample that contributes to the temperature increase and neglects the part that contributes to increase and neglects the part that contributes to the heat losses.the heat losses.
System might reach equilibrium, where the heat System might reach equilibrium, where the heat flowing through the sample only compensate the flowing through the sample only compensate the heat lossesheat losses
measurement of high-temperature thermal diffusivity in a combustion-synthesized measurement of high-temperature thermal diffusivity in a combustion-synthesized ceramic, ceramic, European Physical Journal BEuropean Physical Journal B 3333 (2003), 31-39. (2003), 31-39.
Dominique Vrel, Nikhil Karnatak, Ellen M. Heian, Sylvain Dubois and Marie-France Dominique Vrel, Nikhil Karnatak, Ellen M. Heian, Sylvain Dubois and Marie-France Beaufort, Measurement of thermal diffusivities during self-propagating high Beaufort, Measurement of thermal diffusivities during self-propagating high temperature synthesis, submitted, temperature synthesis, submitted, International Journal of Self-Propagating High-International Journal of Self-Propagating High-Temperature Synthesis. Temperature Synthesis.
Should be applied with careShould be applied with care Cannot be used on any sample; needs instabilityCannot be used on any sample; needs instability Could be improved by a « controlled hot spot ».Could be improved by a « controlled hot spot ».