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 give 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.
The following questions about the dike thermal model may help you understand some features of contact metamorphism. Click the "Show Coordinates" button to read more easily the temperature and distance at the mouse position. Press "Enter" after you type in or choose an answer.
Yes. 500°C is the maximum temperature achieved in the host rock, at its contact with the intrusion.
No. Be sure to set the intrusion and host rock temperatures, and the dike width to match the question. And click on the "Show Max T Values" button before you move the Temperature Slider. Try again.
Yes. 500°C is the maximum temperature achieved in the host rock, at its contact with the intrusion.
No. 500°C is the maximum temperature achieved in the host rock, at its contact with the intrusion.
Yes. 300°C is the maximum temperature achieved in the host rock at a distance of 300m from the intrusion. Contact metamorphic effects will not extend very far from an intrusion.
No. Be sure to give the distance from the contact, not the center of the intrusion. Try again.
Yes. 300°C is the maximum temperature achieved in the host rock at a distance of 300m from the intrusion. Contact metamorphic effects will not extend very far from an intrusion.
No. 300°C is the maximum temperature achieved in the host rock at a distance of 300m from the intrusion. Contact metamorphic effects will not extend very far from an intrusion.
Yes. 500°C is the maximum temperature achieved in the host rock, at its contact with the intrusion. This is the same maximum temperature we found for a 1 km wide dike. The width of the dike does not change the maximum temperature.
No. Be sure to set the intrusion and host rock temperatures, and the dike width to match the question. And click on the "Show Max T Values" button before you move the Temperature Slider. Try again.
Yes. 500°C is the maximum temperature achieved in the host rock, at its contact with the intrusion. This is the same maximum temperature we found for a 1 km wide dike. The width of the dike does not change the maximum temperature.
No. 500°C is the maximum temperature achieved in the host rock, at its contact with the intrusion. This is the same maximum temperature we found for a 1 km wide dike. The width of the dike does not change the maximum temperature.
Yes. 750°C is the maximum temperature achieved in the host rock, at its contact with the intrusion. The maximum temperature is the average of the initial dike temperature and the intital host rock temperature. And that temperature is reached at the contact.
No. Be sure to set the intrusion and host rock temperatures, and the dike width to match the question. And click on the "Show Max T Values" button before you move the Temperature Slider. Try again.
Yes. 750°C is the maximum temperature achieved in the host rock, at its contact with the intrusion. The maximum temperature is the average of the initial dike temperature and the intital host rock temperature. And that temperature is reached at the contact.
No. 750°C is the maximum temperature achieved in the host rock, at its contact with the intrusion. The maximum temperature is the average of the initial dike temperature and the intital host rock temperature. And that temperature is reached at the contact.
Yes. A higher diffusivity increased the rate of heat flow and cooling.
No.A higher diffusivity increased the rate of heat flow and cooling.
Good work overall with the questions. Based on the dike model, contact metamorphism should be restricted to distances around an intrusive body that are less than the distance across of the intrusion. However, there are complications to contact metamorphism that are not revealed by this conduction model.
