Summary
The transformation group theoretic approach is applied to present an analysis for the problem of time dependent vertical temperature distribution in a stagnant lake during the yearly cycle of solar heating and cooling. The application of a one-parameter group reduces the number of independent variables by one, and consequently the governing partial differential equation with the boundary and initial conditions to an ordinary differential equation with the appropriate corresponding conditions. The obtained differential equation is solved, for some special forms of the water parameters, analytically, whenever possible, and in some other cases numerically using the shooting technique. The temperature distribution across the lake is plotted against the lake depth.
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Boutros, Y.Z., Abd-el-Malek, M.B., El-Awadi, I.A. et al. Group method for temperature analysis of thermally stagnant lakes. Acta Mechanica 133, 131–144 (1999). https://doi.org/10.1007/BF01179014
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DOI: https://doi.org/10.1007/BF01179014