Validation Case: Heat Transfer in a Perforated Plate

This project belongs to the heat transfer analysis type. The aim of this test case is to validate the following parameter using a transient thermal solver, with a surface and a convective heat flux boundary condition on a perforated plate:

• Temperature \([K]\) on a single node for 12 consecutive timesteps.

The simulation results of SimScale were compared to the results presented in case B of [TTLP301]\(^1\).

Geometry

The geometry used for the analysis with the highlighted node N1 can be seen below. It is a random thick plate with straight and curved edges.

The coordinates for each vertex of the plate are displayed in the following table:

	A	B	C	D	E	F	G	H	I	J
x \([m]\)	0.635	0.9395	0.9395	0.5427	0.3175	0.635	0.9395	0.9395	0.5428	0.3175
y \([m]\)	0	0	0.8338	0.9401	0.5499	0	0	0.8338	0.9401	0.5499
z \([m]\)	0	0	0	0	0	0.2	0.2	0.2	0.2	0.2

Analysis Type and Domain

Tool type : Code_Aster

Analysis type : Heat transfer, linear

Time dependency: Transient

Mesh and element types: Four mesh cases were considered for the analysis of the perforated plate; with 1st order and 2nd order tetrahedral, as well as 1st order and 2nd order hexahedral elements. The hexahedral mesh was locally computed and uploaded to the SimScale Workbench.

Case	Mesh type	Number of nodes	Number of 3D elements	Element type
(A)	1st order tetrahedral	5340	25676	Standard
(B)	2nd order tetrahedral	16807	10976	Standard
(C)	1st order hexahedral	1210	840	Standard
(D)	2nd order hexahedral	4433	840	Standard

Below, the 1st order tetrahedral mesh for case A is visualized:

And the mesh that was uploaded for case C is presented below:

Simulation Setup

Material/Solid

• Isotropic:
  • Density \(ρ\) = 1 \( kg \over \ m³ \),
  • Thermal conductivity \(\kappa\) = 0.1 \( W \over \ m \ K\),
  • Specific heat = 1 \( J \over \ kg \ K\)  

Initial conditions

• Initial Temperature = 273.15 \(K\)  

Boundary conditions

• Surface heat flux on face AFJE:
  • Heat flux value = 1 \(W \over \ m²\)  
• Convective heat flux on face CHID
  • Reference temperature \(T_{0}\) = 273.15 \(K\)
  • Heat transfer coefficient = 1 \(W \over \ m² \ K\)  

Results Comparison

The temperature values at node N1 for 12 time steps obtained with SimScale are compared against the results presented in case B of [TTLP301]\(^1\).

Timesteps \([s]\)	[TTLP301] \([K]\)	Case A \([K]\)	Error [%]	Case B \([K]\)	Error [%]	Case C \([K]\)	Error [%]	Case D \([K]\)	Error [%]
0.1	274.195	274.201	2.19E-03	274.203	2.92E-03	274.198	1.09E-03	274.204	3.28E-03
0.2	274.597	274.601	1.46E-03	274.604	2.55E-03	274.6	1.09E-03	274.604	2.55E-03
0.3	274.892	274.895	1.09E-03	274.898	2.18E-03	274.894	7.28E-04	274.898	2.18E-03
0.4	275.132	275.135	1.09E-03	275.138	2.18E-03	275.134	7.27E-04	275.138	2.18E-03
0.5	275.339	275.342	1.09E-03	275.345	2.18E-03	275.341	7.26E-04	275.345	2.18E-03
0.6	275.523	275.526	1.09E-03	275.529	2.18E-03	275.525	7.26E-04	275.529	2.18E-03
0.7	275.691	275.695	1.45E-03	275.697	2.18E-03	275.694	1.09E-03	275.697	2.18E-03
0.8	275.848	275.852	1.45E-03	275.854	2.18E-03	275.851	1.09E-03	275.854	2.18E-03
0.9	276.996	275.999	1.09E-03	276.001	1.81E-03	275.998	7.25E-04	276.001	1.81E-03
1.0	276.136	276.14	1.45E-03	276.142	2.17E-03	276.139	1.09E-03	276.142	2.17E-03
1.1	276.27	276.274	1.45E-03	276.276	2.17E-03	276.273	1.09E-03	276.276	2.17E-03
1.2	276.398	276.403	1.81E-03	276.404	2.17E-03	276.402	1.45E-03	276.404	2.17E-03

All of the cases are in a good agreement with the reference results.

You can see the temperature distribution on the plate for the last time step of Case A below:

Last updated: January 26th, 2021