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Modifications necessary in my numerical solution of the heat conduction equation |
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November 23, 2021, 02:24 |
Modifications necessary in my numerical solution of the heat conduction equation
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Hello Foamers,
Here is my explanation about the numerical solution followed by the query. Consider a region of interest to be divided into n elements of width . The midpoints of these elements are . The temperature at these points are at time t. At increment of time t +, the temperature are notified as . The 1D equation, unit The approximation in time for above equation, For i=1 to n-1, where , and are the density (kg/m3), specific heat (J/kg K) and heat release rate (W/m3) of the element at time t, and , are the average conductivities (W/m K) from to and to respectively at time t. After rearranging, the final form of the equation (for T>=500deg) is, where, , and are diffusivities defined by, The above EQU.(1) initializes the temperature distribution for dry coal pyrolysis phenomenon. In case of wet coal pyrolysis, moisture content should be included with the coal. And thereby, I need to modify the above linear equation (when T=100) slightly as, The modification implies the approximation that the moisture evaporation occurs at T = 100deg, where there is no effect of diffusion ( = = 0). In OpenFOAM, I have made my customized solver for dry coal pyrolysis based on EQU.(1) with default settings. For wet coal pyrolysis, I don't know where and how to make changes for implementing EQU.(2). Can someone share ideas here. Thank you |
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