τ xy +
∂ (τ yx ) dy
∂y
σ x +
∂ (σ x ) dx
σ x
∂x
P x
P x +
∂ (P x ) dx
∂x
τ yx
ρv dx dz.u +
∂ (ρv dx dz.u) dy
∂x
ρu.u dy dz +
∂ (ρu.u dy dz) dx
∂x
ρu.udydz
ρv dx dz.u
U ∞
y
U ∞
x
133
Heat Convection Equations
FIGURE 6.6
Conservation of momentum.
For a steady-state, constant-property flow, the left-hand side can be expressed as
∂ (τ yx ) dy
∂y
σ x +
∂ (σ x ) dx
σ x
∂x
P x
P x +
∂ (P x ) dx
∂x
τ yx
ρv dx dz.u +
∂ (ρv dx dz.u) dy
∂x
ρu.u dy dz +
∂ (ρu.u dy dz) dx
∂x
ρu.udydz
ρv dx dz.u
U ∞
y
U ∞
x
133
Heat Convection Equations
FIGURE 6.6
Conservation of momentum.
For a steady-state, constant-property flow, the left-hand side can be expressed as