11 "The scalar models\n",
12 "=================\n",
14 "The transport equation\t\n",
15 "----------------------\n",
18 " \\partial_t H + \\vec{u}\\cdot\\vec{\\nabla} H = \\Phi+\\lambda_{sf}(T_s-T)\n",
23 "- $ H $ the main unknown is the fluid enthalpy field\n",
24 "- $ \\vec{u} $ is the constant transport velocity\n",
25 "- $ \\Phi $ is the heat source term if explicitely known\n",
26 "- $ T_s $ is the rod temperature field provided by the user\n",
27 "- $ T=T_0+\\frac{H-H_0}{c_p}$ is the fluid temperature field\n",
28 "- $ \\lambda_{sf}$ is the fluid-rod heat transfer coefficient provided by the user\n",
29 "- $ c_p $ is the fluid specific heat, provided by the user and assumed constant\n",
31 "See the [Transport equation page](TransportEq.ipynb)\n",
33 "The diffusion equation\t\n",
34 "----------------------\n",
36 " \\partial_t T =d\\triangle T +\\frac{ \\Phi+\\lambda_{sf}(T_f-T)}{\\rho c_p}\n",
39 "- $T$ the main unknown is the rod temperature field\n",
40 "- $d=\\frac{\\lambda}{\\rho c_p}$ is the rod diffusivity\n",
41 "- $\\lambda_{sf}$ is the fluid-rod heat transfer coefficient provided by the user\n",
42 "- $\\rho$ is the rod density assumed constant\n",
43 "- $c_p$ is the rod specific heat, provided by the user and assumed constant\n",
44 "- $\\Phi$ is the heat source term if explicitely known\n",
45 "- $T_f$ is the fluid temperature field provided by the user\n",
47 "See the [Diffusion equation page](DiffusionEq.ipynb)\n",
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