The mathematics of heat conduction are well known and are based on Fourier's Law, which says that the heat flow is proportional to the gradient in temperature. For a tabular intrusion (a dike or a sill) intruded "instantenously" into a country rock at a uniform temperature, the temperature gradient is one-dimensional and the temperatures over time can be calculated by an equation given by J.C. Jaeger (1964, model ii.). The diagram above, graphs in red the temperatures for both the dike and the host rock as calculated by the Jaeger equation for various choices of boundary condiditions and time.
Move the Time Slider to show changes of temperature with time after an instantaneous intrusion. The horizontal scale gives the distance relative to the center of the vertical dike. The solution is symmetrical relative to the dike center, so the graph focuses on one side of the dike center. Click the "Show Max T Values" button to show the highest temperatures reached. Use the small sliders to change the starting temperatures of the dike (650-1200°C) and of the country rock (0-800°C), the width of the dike (10-2000m), and the thermal diffusivity (0.5e-6 to 2.0e-6 m2/s). The same thermal diffusivity is used for both the dike and the host rock.
