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Assume that the heat flux is linear in the temperature gradient (represented by g), (p, 0, g) = k(p,0)g, where k(p, 0) 0 is

Assume that the heat flux is linear in the temperature gradient (represented by g), (p, 0, g) =  k(p,0)g,

Assume that the heat flux is linear in the temperature gradient (represented by g), (p, 0, g) = k(p,0)g, where k(p, 0) 0 is the thermal conductivity of the material. Show that balances of mass, linear momentum and energy yield the partial differential equations: Dp Dt +pV v=0. Dv Dt De Dt pc- -Peq + ((Vv + (Vv))) + V(AV v) + bo, ) 2|dev(D)| + k(Tr(D)) - Peq (0, p) Tr(D) + V (kV0) + q. 20 = 0

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