Temperature distribution about a cooling volcanic intrusion

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Abstract
Temperature distributions are derived for the conductive transfer of heat from a vertical volcanic feeding dyke or pipe of radius α, injected into a rock mass of thermal diffusivity χ which has an initial steady-state temperature distribution due to an underlying magmatic layer of constant temperature at depth h. The temperature at a distance χ from the centre of the intrusion and a depth z below the surface is found when the dyke or pipe has cooled for time t after injection. Results are expressed in terms of the parameters ξ = x/h α = a/h ζ = s/h, and and numerical results, including graphs of the surface thermal gradient and of the temperature at the centre of the dyke or pipe, are given for α = 0·01, 0≤ξ≤0·30, 0.01≤ ζ ≤ ζ ≤ 0.80, and 0.001 ≤ τ ≤0·050.

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