• D V Ramana

      Articles written in Journal of Earth System Science

    • Application of the Fourier method to the numerical solution of moving boundary problem in heat conduction

      A Manglik D V Ramana A O Gliko R N Singh

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      An algorithm for the solution of a nonlinear problem of phase boundary movement and evolution of temperature distribution due to the perturbation in the basal heat flux has been discussed. The reduction of the problem to a system of nonlinear ordinary differential equations with the help of a Fourier series method leads to a stiff system. This stiffness is taken care of by the use of a modified Euler’s method. Various cases of basal heat flow variation have been considered to show the performance and stability of the technique for such a nonlinear system. The first case of step-wise function is taken to analyse the performance of the technique, and the study has been extended to other general cases of linear increase, periodic variation, and box and triangular function type variations in the heat flux. In the step-wise case the phase boundary attains a constant position rapidly if the supplied heat flux is sufficiently large. The effect of periodicity in the heat flow is clearly depicted in the phase boundary movement, where the phase boundary oscillates about the mean position at large times. The absence of any constant level in the case of linear increase in heat flux is due to a very large value of heat flux. In the cases of box car and triangular heat flux the boundary starts moving downward after the cessation of excess heat flux but does not immediately return to its original preperturbation state, instead approaches it at large times. This technique may be applied to more general cases of heat flow variation.

    • Seismically constrained two-dimensional crustal thermal structure of the cambay basin

      S Thiagarajan D V Ramana S N Rai

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      The temperature field within the crust is closely related to tectonic history as well as many other geological processes inside the earth. Therefore, knowledge of the crustal thermal structure of a region is of great importance for its tectonophysical studies. This work deals with the two-dimensional thermal modelling to delineate the crustal thermal structure along a 230 km long Deep Seismic Sounding (DSS) profile in the north Cambay basin. In this work P-wave velocities obtained from the DSS studies have been converted into heat generation values for the computation of temperature distribution. The model result reveals the Curie isotherm at a depth of ≈22 km and Moho temperature at around 900‡C.

    • Modelling near subsurface temperature with mixed type boundary condition for transient air temperature and vertical groundwater flow

      Rajeev Ranjan Kumar D V Ramana R N Singh

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      Near-subsurface temperatures have signatures of climate change. Thermal models of subsurface have been constructed by prescribing time dependent Dirichlet type boundary condition wherein the temperature at the soil surface is prescribed and depth distribution of temperature is obtained. In this formulation it is not possible to include the relationship between air temperatures and the temperature of soil surface. However, if one uses a Robin type boundary condition, a transfer coefficient relates the air and soil surface temperatures which helps to determine both the temperature at the surface and at depth given near surface air temperatures. This coefficient is a function of meteorological conditions and is readily available. We have developed such a thermal model of near subsurface region which includes both heat conduction and advection due to groundwater flows and have presented numerical results for changes in the temperature–depth profiles for different values of transfer coefficient and groundwater flux. There are significant changes in temperature and depth profiles due to changes in the transfer coefficient and groundwater flux. The analytical model will find applications in the interpretation of the borehole geothermal data to extract both climate and groundwater flow signals.

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