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C11_Nonisothermal_Equations_of_change_1

C11_Nonisothermal_Equations_of_change_1 - Non-isothermal...

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Non-isothermal Equations of change Energy conservation for homogeneous media Heat source Energy influx Energy outflux Energy influx Energy outflux Sources/ Sinks Energy accumulation z x y Total energy flux () 3 1 ˆ iK i ii i j j j eE U u q p u u ρτ = =+ + + + 3 1 or ˆ i i i j j j H u q u = + + 3 1 g i Wu g ρ = = Energy sources/sinks per unit volume Work done by gravity per unit volume Work by body force Energy balance over a rectangular volume element Total net energy flux ( ) ( ) ( ) xx y y zz x x xx x zz z yy yy y yze e xze e xye e = = +Δ = == + Δ ΔΔ +ΔΔ 3 1 g i Wx y zu g = Δ Δ Work done by gravity ˆ K xy zE U t ΔΔΔ + Energy accumulation Energy sources/sinks xyz S ρΔ

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Non-isothermal Equations of change Energy conservation for homogeneous media Converting the balance into a partial differential form () ˆ . . K EU S t ρ ρρ += + + eu g rate of energy addition rate of energy addition rate of increase per unit volume by per unit volume by of energy per convective transport heat conduct unit volume ˆˆ . (). KK t + uq ±²²³²²´ ±²²³ ² ²´ [] rate of work done on fluid per unit volume ion by pressure forces rate rate of work done on fluid per unit volume by viscous forces . . . . p −∇ + u τ uu g ±³´ ±²³ ²´ ±²³²´ N rate of heat of work done generated/lost on fluid per unit volume per unit volume by gravity force S +
Non-isothermal Equations of change Energy conservation for homogeneous media () ( ) ( ) ( ) total rate of work

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C11_Nonisothermal_Equations_of_change_1 - Non-isothermal...

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