-direction (parallel to the incline), and assuming steady, laminar, and fully developed flow (
Standard ( k)-(ε ) model (high Re): [ \frac\partial k\partial t + \baru j \frac\partial k\partial x_j = \frac\partial\partial x_j \left( \frac\nu_t\sigma_k \frac\partial k\partial x_j \right) + \mathcalP - \varepsilon ] [ \frac\partial \varepsilon\partial t + \baru j \frac\partial \varepsilon\partial x_j = \frac\partial\partial x_j \left( \frac\nu_t\sigma \varepsilon \frac\partial \varepsilon\partial x_j \right) + C \varepsilon1 \frac\varepsilonk \mathcalP - C_\varepsilon2 \frac\varepsilon^2k ] with ( \nu_t = C_\mu \frack^2\varepsilon ), and constants: ( C_\mu=0.09,\ \sigma_k=1.0,\ \sigma_\varepsilon=1.3,\ C_\varepsilon1=1.44,\ C_\varepsilon2=1.92 ).
A viscous, incompressible fluid flows between two infinite parallel plates separated by distance
-direction (parallel to the incline), and assuming steady, laminar, and fully developed flow (
Standard ( k)-(ε ) model (high Re): [ \frac\partial k\partial t + \baru j \frac\partial k\partial x_j = \frac\partial\partial x_j \left( \frac\nu_t\sigma_k \frac\partial k\partial x_j \right) + \mathcalP - \varepsilon ] [ \frac\partial \varepsilon\partial t + \baru j \frac\partial \varepsilon\partial x_j = \frac\partial\partial x_j \left( \frac\nu_t\sigma \varepsilon \frac\partial \varepsilon\partial x_j \right) + C \varepsilon1 \frac\varepsilonk \mathcalP - C_\varepsilon2 \frac\varepsilon^2k ] with ( \nu_t = C_\mu \frack^2\varepsilon ), and constants: ( C_\mu=0.09,\ \sigma_k=1.0,\ \sigma_\varepsilon=1.3,\ C_\varepsilon1=1.44,\ C_\varepsilon2=1.92 ). advanced fluid mechanics problems and solutions
A viscous, incompressible fluid flows between two infinite parallel plates separated by distance -direction (parallel to the incline), and assuming steady,