Council of Scientific and Industrial Research

Kirti Srivastava

Rohit Sharma

Rishi Narain Singh

R N Singh

Bushra Fatima

An analytical closed form solution to mean and variance in heat flow is obtained by solving the stochastic heat conduction equation incorporating randomness in the thermal conductivity. The method has a wide range of applications in quantifying the thermal state of the crust and in obtaining closed form expressions for subsurface heat flow structure along with its error bounds. The exact formulae employed can be used to better evaluate the thermal state for related oil and natural gas applications and also in tectonic studies and in studies related to the crystallization of minerals.

Stochastic analytical solution to quantify the earth's subsurface heat flow

Analytical solutions to error bounds on the temperature depth distribution have been given in this invention. Solving the one dimensional steady state heat conduction equation for different sets of boundary conditions and radiogenic heat generation and incorporating Gaussian randomness in the thermal conductivity analytical closed form solutions to the mean and variance in the temperature depth distribution have been obtained. These closed form analytical solutions of mean and variance for the temperature field for different conditions have been used to compute and display the plot and results of the temperature depth profiles along with its error bounds. Quantifying the error statistics in the system output due to errors in the system input is very essential for a better evaluation of the system behavior. Earth Scientists involved in understanding the subsurface thermal structure relevant to geodynamical studies will benefit using these findings.

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Andhra Pradesh, India

Kirti Srivastava