Questions
GEOL0012_25-26 **********GEOL0012 Moodle Test (unassessed) 2025/26**********
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Question text1. The one-dimensional heat flow equation is: [math: ρCP∂T∂t=κ∂2T∂z2+A] where ρ, Cp, and κ are the density, specific heat and thermal conductivity, and A represents heat sinks and sources. The boundary conditions in a given system are: (i) T=320 K at z=0 (ii) T=1200 K at z=40 km and we also have [math: κ=3Wm−1K−1]. Assuming no internal heat sources, calculate a) The thermal gradient of the equilibrium geotherm in [math: K/km] to two significant figures.Thermal gradient = Answer 1 Question 3[input] [math: K/km] [6] b) The temperature at a depth of 100km as predicted by this geotherm model. Give answer in K to two significant figures. T(z=100 km) = Answer 2 Question 3[input] K [4]
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The problem gives the one-dimensional heat flow with no internal sources and asks for the thermal gradient of the equilibrium geotherm and the temperature at 100 km depth. Since there are no internal heat sources (A = 0) and we’re likely dealing with a steady state (no explicit time dependence in the equilibrium geotherm), the......Login to view full explanationLog in for full answers
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Question text1. The one-dimensional heat conduction equation for a cooling dyke with no internal heating can be written: [math: ∂T∂t=κ∂2T∂x2]Where [math: T] is temperature, [math: t] is time, [math: x] is horizontal distance, and [math: κ] is the thermal diffusivity, and has a solution of the form: [math: T(x,t)=T02[erf(w−x2(κt))+erf(w+x2(κt))]] At t=0, T=T0 for –[math: w] < x < [math: w], and at t=0, T=0 for |x| > [math: w]. If the half-width of the dyke is [math: w=2.7m], centred on x = 0, and if T0 = 1500 oC and [math: κ] = 10-6 m2s-1 a) calculate the temperature at the centre of the dyke after one week and after one year (365 days) in degrees Celsius to three significant figures. HINT: Use a calculator, an online tool or MATLAB to calculate the error function (in MATLAB simply use erf(your value) ). After one week: [math: T=] Answer 1 Question 1[input] degrees Celsius [3]After one year: [math: T=] Answer 2 Question 1[input] degrees Celsius [3]b) Calculate the temperature of the dyke at the edges after 1 year in degrees Celsius to three significant figures.[math: T=] Answer 3 Question 1[input] degrees Celsius [4]
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