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Consider the one-dimensional, transient (ie. time-dependent) heat conduction equation without heat generating sources OT , 81 where ? is density, Cp heat capacity, k thermal conductivity, T temperature. x distance, and t time If the thermal conductivity, density and heat capacity are constant over the model domain, the equation can be simplified to aT T Ot where is the thermal diffusivity (a common value for rocks is K = 10-6 m2/s). We are interested in the temperature evolution versus time, T(r, t), given an initial temperature distribution Figure.1. An example would be the intrusion of a basaltic dike in cooler country rocks. The country rock has a temperature of 300C' and the dike a total width W -5m, with a magma temperature of 1200C. In addition we assume that the temperature far away from the dike center (at /21 where L 100m) remains at a constant temperature, 300 Let the Ta(t) be maximum temperature of dike when time is t Plot Td(t) graph by using natural cubic spline interpolation Find the time t such Ta(ti) 600C by using bisection, Newton's method or secant method country rock Figure 1: Setup of the thermal cooling model considered here Consider the one-dimensional, transient (ie. time-dependent) heat conduction equation without heat generating sources OT , 81 where ? is density, Cp heat capacity, k thermal conductivity, T temperature. x distance, and t time If the thermal conductivity, density and heat capacity are constant over the model domain, the equation can be simplified to aT T Ot where is the thermal diffusivity (a common value for rocks is K = 10-6 m2/s). We are interested in the temperature evolution versus time, T(r, t), given an initial temperature distribution Figure.1. An example would be the intrusion of a basaltic dike in cooler country rocks. The country rock has a temperature of 300C' and the dike a total width W -5m, with a magma temperature of 1200C. In addition we assume that the temperature far away from the dike center (at /21 where L 100m) remains at a constant temperature, 300 Let the Ta(t) be maximum temperature of dike when time is t Plot Td(t) graph by using natural cubic spline interpolation Find the time t such Ta(ti) 600C by using bisection, Newton's method or secant method country rock Figure 1: Setup of the thermal cooling model considered here