Benchmark C6

VMC6
2D Heat Transfer With Convection

Overview

Reference:J. Barlow, G. A. O. Davis, "Selected FE Benchmarks in Structural and Thermal Analysis", NAFEMS Rept. FEBSTA, Rev. 1, October 1986, Test No. T4 (modified).
Analysis Type(s):Thermal Analysis (ANTYPE = 0)
Element Type(s):
2D 6-Node Triangular Thermal Solid Elements (PLANE35)
2D Thermal Solid Elements (PLANE55)
2D 8-Node Thermal Solid Elements (PLANE77)
Input Listing:vmc6.dat

Test Case

A two-dimensional rectangular body is insulated at the left edge and has the bottom edge held at a prescribed temperature T1. Two other edges are subjected to a convection environment with a convection coefficient h and an ambient temperature T0. Determine the steady-state temperature on the right edge, at a location 0.2 m above the bottom (Target Point-1) for a series of test cases with increasing mesh refinements for each element type.

Figure 598: 2D Rectangular Body Problem Sketch

2D Rectangular Body Problem Sketch

Material PropertiesGeometric PropertiesLoading
k = 52 W/m°C
Parameter Definition
N1 = Element edge length
a = 0.6 m
b = 1.0 m
c = 0.2 m
h = 750 W/m2°C
T0 = 0°C
T1 = 100°C

Figure 599: Representative Mesh Options

Representative Mesh Options

Results Comparison - Triangle Mesh

ETYPN1DOFTemp(°C)Temperature Ratio
Quadrilateral Mesh
55[1].22419.31.06
55.17718.91.03
77[1].26216.40.90
77.121318.71.02
Triangle Mesh
35.29317.90.98
35.131718.31.00
55.22820.91.14
55.18819.01.04
77.29317.90.98
77.131718.31.00
Uniform Triangle Mesh
35[1]27716.50.90
35.127318.31.00
55.22422.41.22
55.17718.91.04
77[1]27716.50.90
77.127318.31.00

  1. Test case corresponds to NAFEMS test specification

Assumptions, Modeling Notes, and Solution Comments

  1. The lower order PLANE55 element converges toward the solution from above the target temperature while, in general, the higher order PLANE35 and PLANE77 elements converge from below the target temperature.

  2. For the coarse meshes, the lower order PLANE55 element, in triangular form, does not predict accurate results. However, further mesh refinement produces more accurate results.

  3. The higher order PLANE35 triangular element and the higher order PLANE77 element in triangular form, produce identical results.