2. Benchmark solution#

2.1. Calculation method used for the reference solution#

An analytical solution is available in the case of a cylinder of infinite length:

\(T(r)=\frac{{T}_{e}-{T}_{i}}{\mathrm{log}(\frac{{R}_{e}}{{R}_{i}})}\mathrm{log}(r)+\frac{{T}_{i}\mathrm{log}({R}_{e})-{T}_{e}\mathrm{log}({R}_{i})}{\mathrm{log}({R}_{e})-\mathrm{log}({R}_{i})}\)

2.2. Benchmark results#

\(r(m)\)

\(T(°C)\)

.30000

105.55

.32275

99.21

.34550

93.30

.36825

87.76

.39100

82.56

Temperature value as a function of \(r\)

\(r(m)\)

\(\phi (W/{m}^{2})\)

.300

11577.49

.391

8822.98

Value of the flow as a function of \(r\)

2.3. Uncertainty about the solution#

Exact solution.

2.4. Bibliographical references#

  • Guide for the validation of structural calculation software packages. French Society of Mechanics AFNOR 1990 ISBN 2-12-486611-7