Convection elements: transport of a temperature pulse

The transport and diffusion of a temperature pulse in the family of convective/diffusive heat transfer elements is tested in this verification set. The model consists of a column of fluid 2.0 units long with a cross-sectional area of 1.0. All models consist of 16 elements along the length and one element in the cross-section. The material property values used are: conductivity, $k=$ 0.0015625; specific heat, $c_p=$ 1.0; and density, $\rho =$ 1.0. Consistency of all units is assumed.

An initial temperature pulse, of peak magnitude 1.0, in the form of a Gaussian wave is centered at 0.25 units along the length. At time zero, all the nodes in the model are assigned a mass flow rate of 0.25 in the length direction. The transient response of the temperature pulse as it convects down the length of the mesh is tracked for a period of two seconds.