I'm trying to solve for the heat transfer in 2D within a fluid. The geometry I'm using is a rectangle of water heated from the bottom. The code I'm using is as follows:
Needs["NDSolve`FEM`"]
\[Rho]water = 1000;
kwater = 0.598012`;
\[Mu]water = 0.0010015961431205716`;
Cwater = 4184;
\[Alpha]water = 0.00018`;
g = 9.81;
Theat = 375;
HeatModel= {Cwater \[Rho]water D[T[x,y,t],t]+Cwater \[Rho]water u[x,y,t],Cwater \[Rho]water v[x,y,t]}. Grad[T[x, y, t],{x, y}]+Div[(-kwater Grad[T[x, y, t],{x, y}]),{x, y}];
CFDModel={\[Rho]water {u[x, y, t], v[x, y, t]} . Grad[u[x, y, t],{x, y}]+Div[(-\[Mu]water Grad[u[x, y, t],{x, y}]),{x, y}] +D[p[x,y,t],x]+D[u[x,y,t],t],\[Rho]water {u[x, y, t], v[x, y, t]} . Grad[v[x, y, t],{x, y}] + Div[(-\[Mu]water Grad[v[x, y, t],{x, y}]),{x,y}]+D[p[x,y,t],y]+D[v[x,y,t],t],D[u[x,y,t],x]+D[v[x,y,t],y]}
{Subscript[F, x], Subscript[F, y]} = {0, \[Alpha]water g \[Rho]water (T[x, y, t] - 300)};
r0 = 0.03;
h = 0.2;
\[CapitalOmega] = Rectangle[{0, 0}, {r0, h}];
mesh = ToElementMesh[\[CapitalOmega], {{0, r0}, {0, h}}, "MaxCellMeasure" -> {"Length" -> 20*10^-4}];
bcbase = {DirichletCondition[T[x, y, t] == Theat, y == 0]};
bcnoslip1 =DirichletCondition[{u[x, y, t] == 0, v[x, y, t] == 0}, y == 0 || y == h];
bcpressure = DirichletCondition[p[x, y, t] == 0, y == h];
bcnoslip2 =DirichletCondition[{u[x, y, t] == 0, v[x, y, t] == 0}, x == 0 || x == r0];
ics1 = {T[x, y, 0] == 300, (D[T[x, y, t] == 0, t]) /. t -> 0};
ic2 = {u[x, y, 0] == 0, v[x, y, 0] == 0, p[x, y, 0] == 0};
bcs = {bcbase, bcnoslip1, bcpressure, bcnoslip2, ics1, ic2};
pde = {CFDModel == {Subscript[F, x], Subscript[F, y], 0}, HeatModel == 0, bcs};
solveNS =NDSolveValue[pde, {u, v, p, T}, {x, y} \[Element] mesh, {t, 0, 10}, Method -> {"PDEDiscretization" -> {"MethodOfLines", "SpatialDiscretization" -> {"FiniteElement","InterpolationOrder" -> {u -> 2, v -> 2, p -> 1, T -> 2}}}}]
When the code is ran, the only error message thrown is that -- Message Text not fonud --. Interesintgly NDSolve outputs a result but the time range in the output goes from t=0s to t=0s, while the time domain provided in NDSolve is from t=0s to t=10s. Does anyone know what's wrong? Thanks!!