<transcript><audio_4> espace t2 un flux thermique qui va donc passer ici qui va traverser la paroi constitué du matériau donc on a le flux fit est donc la loi de fourrier nous dit que</transcript><transcript><audio_5> de flux thermique qui est égal à moins lambda fois gradient de T. Le gradient ici étant une dérivée spatiale. Et donc on a T, la température. Si on se place dans</transcript><transcript><audio_6> mettre un axe OX orienté de la gauche vers la droite, on aura J qui est égal à J fois I, I étant un vecteur unitaire, et J en norme qui est égal à phi sur S qui correspond donc au flux par unité de surface.</transcript><transcript><audio_7> gradient de t qui est égal à d2t sur dx fois i et on va donc pouvoir obtenir la loi de Fourier unidimensionnelle qui nous dit que phi sur s fois i est égal à moins lambda d2t sur dx fois i. On a donc une relation vectorielle</transcript><transcript><audio_8> avec nos deux vecteurs unitaires. On va donc pouvoir maintenant travailler uniquement sur les normes. Et donc, phi sur S est égal à moins lambda d2t sur dx. On a donc d2t sur dx, qui est égal à</transcript><transcript><audio_9> avoir cette relation qui va me permettre d'avoir accès à l'évolution de la température dans le matériau. J'ai donc ici d2t sur dx qui est égal à moins phi lambda s, connaissant d2t</transcript> between this space T1 and this space T2 a thermal flow which will not pass to here which will cross the wall made of the material therefore  we have the fit flux made of the material therefore  we have the fit flux and therefore Fourier's law tells us that in the material we have the density vector thermal flux density vector which is equal to minus lambda times gradient of T the gradient here being a spatial derivative and therefore we were the  temperature if we therefore place ourselves in a one-dimensional case we will put an axis Ox oriented from left to right we will have J which is equal to J times i it is time with unit vector and j in norm which is equal to cracks S which therefore corresponds to the flow per unit surface therefore corresponds to the flow per unit surface we also have tea gradient which is equal to D2T on DX times I and we will therefore be able to obtain the one-dimensional Fourier law which tells us that cracks s times I is equal to - lambda of the two t  on DX times i we therefore have a vector relationship with our two health vectors we will now be able to work only on the norms and therefore crack is equal to minus lambda of the two t on DX we therefore have two t on DX which is  equal to minus fi on lambda s I will therefore have this relation which will allow me to have access to the evolution of the temperature in the material I therefore have here two t on DX which is equal to minus fil in DS  knowing 2
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