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

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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 the thermal conductivity of the material. Show that balances of mass, linear momentum and energy yield the partial differential equations: Dp Dt Р +pV v=0. Dv Dt De Dt pc- -▼Peq + ▼ · (µ(Vv + (Vv)²)) + V(AV · v) + bo, дреа р) 2µ|dev(D)|² + k(Tr(D))² - Peq (0, p) Tr(D) + V (kV0) + q. 20 = 0² 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 Р +pV v=0. Dv Dt De Dt pc- -▼Peq + ▼ · (µ(Vv + (Vv)²)) + V(AV · v) + bo, дреа р) 2µ|dev(D)|² + k(Tr(D))² - Peq (0, p) Tr(D) + V (kV0) + q. 20 = 0² 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 Р +pV v=0. Dv Dt De Dt pc- -▼Peq + ▼ · (µ(Vv + (Vv)²)) + V(AV · v) + bo, дреа р) 2µ|dev(D)|² + k(Tr(D))² - Peq (0, p) Tr(D) + V (kV0) + q. 20 = 0²

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Starting from the balance equations Mass balance t v 0 Momentum balance vt vv ... View the full answer