牛顿流体传热方程

牛顿流体传热方程

Equation of Energy for Newtonian Fluids with Constant ρ ρ and k k

控制方程表达通式：

ρC^pDTDt=k∇2T+μΦΦv ρ C ^ p D T D t = k ∇ 2 T + μ Φ Φ v

---

1.直角坐标系( x,y,z x , y , z )

直角坐标系Cartesian coordinates (  x,y,z   x,y,z  ):	NO.
ρC^p(∂T∂t+vx∂T∂x+vy∂T∂y+vz∂T∂z)=k[∂2T∂x2+∂2T∂y2+∂2T∂z2]+μΦΦv ρ C ^ p ( ∂ T ∂ t + v x ∂ T ∂ x + v y ∂ T ∂ y + v z ∂ T ∂ z ) = k [ ∂ 2 T ∂ x 2 + ∂ 2 T ∂ y 2 + ∂ 2 T ∂ z 2 ] + μ Φ Φ v	1-1

---

2.圆柱坐标系（ r,θ,z r , θ , z )

圆柱坐标系Cylindrical coordinates coordinates ( r, θ, z  r,  θ , z  ):	NO.
ρC^p(∂T∂t+vr∂T∂r+vθr∂T∂θ+vz∂T∂z)=k[1r∂∂r(r∂T∂r)+1r2∂2T∂θ2+∂2T∂z2]+μΦΦv ρ C ^ p ( ∂ T ∂ t + v r ∂ T ∂ r + v θ r ∂ T ∂ θ + v z ∂ T ∂ z ) = k [ 1 r ∂ ∂ r ( r ∂ T ∂ r ) + 1 r 2 ∂ 2 T ∂ θ 2 + ∂ 2 T ∂ z 2 ] + μ Φ Φ v	2-1

---

3.球坐标系（ r,θ,ϕ r , θ , ϕ )

球坐标系Spherical coordinates（ r, θ, ϕ  r,  θ ,  ϕ   ):	NO.
ρC^p(∂T∂t+vr∂T∂r+vθr∂T∂θ+vϕrsinθ∂T∂ϕ)=k[1r2∂∂r(r2∂T∂r)+1r2sinθ∂∂θ(sinθ∂T∂θ)+1r2sin2θ∂2T∂ϕ2]+μΦΦv ρ C ^ p ( ∂ T ∂ t + v r ∂ T ∂ r + v θ r ∂ T ∂ θ + v ϕ r s i n θ ∂ T ∂ ϕ ) = k [ 1 r 2 ∂ ∂ r ( r 2 ∂ T ∂ r ) + 1 r 2 s i n θ ∂ ∂ θ ( s i n θ ∂ T ∂ θ ) + 1 r 2 s i n 2 θ ∂ 2 T ∂ ϕ 2 ] + μ Φ Φ v	3-1

---

参考文献

1. R. Byron Bird, Warren E. stewart, Edwin N. Lightfoot.* Transport phenomena:Revised second edition* John Wiely &Sons, Inc.