Mathematical Problems in Engineering / 2011 / Article / Tab 4

Research Article

On the Critical Behaviour of Exothermic Explosions in Class A Geometries

Table 4

Comparison of critical values obtained by different methods.

Exact methodVariational methodHermite-PadΓ© approachPresent work

Slab 𝛿 c r = 0 . 8 7 8 4 6
πœƒ c r = 1 . 1 8 6
𝛿 c r = 0 . 8 7 8 3 5 5
πœƒ c r = 1 . 1 6 7 1 6
𝛿 c r = 0 . 8 7 8 4 5
πœƒ c r = 1 . 1 8 6 8 4
𝛿 c r = 0 . 8 7 8 4 6
πœƒ c r = 1 . 1 8 6 8 4

Cylinder β€”
β€”
𝛿 c r = 1 . 9 9 9 9 8
πœƒ c r = 1 . 3 8 0 1 1 9 7
𝛿 c r = 2
πœƒ c r = 1 . 3 8 6 2 9
𝛿 c r = 2
πœƒ c r = 1 . 3 8 6 2 8

Sphereβ€”
β€”
𝛿 c r = 3 . 3 2 1 9 9
πœƒ c r = 1 . 6 0 7 4 6
β€”
β€”
𝛿 c r = 3 . 3 2 3 2 4
πœƒ c r = 1 . 6 1 7 8 2