Write down the continuity,momentum and the energy equation?
Continuity Equation : ∂ρ/∂t + v·∇ ρ = −ρ ∇·v Momentum Equation : ρ(∂v/∂t + v·∇ v) = −∇p + ρg − 2/3 ∇(μ∇ ·v) + 2∇ ·(μS) Energy Equation : ρcp(∂T/∂t + v·∇ T) = ∇ ·(k∇T ) − 2/3 μ(∇ ·v)^2 + 2μS:S + βT(Dp/Dt)
What is the difference in natural convective heat transfer mode from a horizontal plate, when hot surface faces upwards and when hot surface faces downwards?
The rate of heat transfer to or from a horizontal surface depends on whether the surface is facing upward or downward. For a hot surface in a cooler environment, the net force acts upward, forcing the heated fluid to rise. If the hot surface is facing upward, the heated fluid rises freely, inducing strong natural convection currents and thus effective heat transfer increases. But if the hot surface is facing downward, the plate will block the heated fluid that tends to rise (except near the edges), impeding heat transfer. The opposite is true for a cold plate in a warmer environment since the net force (weight minus buoyancy force) in this case acts downward, and the cooled fluid near the plate tends to descend.
Classify physical behaviours by Partial Differential Equations?
Elliptic PDE : div grad φ = 0 (eq. 2D heat conduction equation) Parabolic PDE : ∂φ/∂t = α div grad φ (eq. unsteady Diffusion equation) Hyperbolic PDE : ∂ 2φ/∂t2 = c2 div grad φ (eq. higher order wave equation)