# Application of the symbolic and numerical computing programme Mathematica for simulating compartmental fires

 Author: Mok, Kwok-fai Title: Application of the symbolic and numerical computing programme Mathematica for simulating compartmental fires Degree: M.Sc. Year: 1998 Subject: Fires -- Mathematical modelsMathematica (Computer file)Hong Kong Polytechnic University -- Dissertations Department: Multi-disciplinary Studies Pages: x, 90, [88] leaves : ill. ; 30 cm Language: English InnoPac Record: http://library.polyu.edu.hk/record=b1421251 URI: http://theses.lib.polyu.edu.hk/handle/200/1989 Abstract: A thorough study on the application of the symbolic computing techniques to solve mathematical problems involved in simulating compartmental fires was reported. Literature survey on selected symbolic programmes and their application in engineering were also accomplished. A general review on compartmental fires was carried out. MATHEMATICA, one of the general-purpose symbolic computing software packages, was used as an example to perform the study. Comparisons of numerical solutions by MATHEMATICA with exact solutions for eleven ordinary differential equations including one 'stiff' type were performed. Results of which show that MATHEMATICA solutions were only deviated by less than 0.05% from the exact solutions. These findings clearly demonstrate that MATHEMATICA can give very good solutions to various types of differential equations. CHOWMOK-1, a zone fire model developed from MATHEMATICA based on the model ASET, was applied for predicting the smoke layer interface height and the average smoke temperature within a single compartment. Results predicted by CHOWMOK-1 were compared with those by ASET-BX (a simplified version of ASET) for five sets of steady burning fires of heat release rate of 200kw, 300kw, 500kw, 1,000kw and 1,320kW; and two sets of unsteady fires of heat release rate increased by 1 kWs-1 and 2 kWs-1. It is observed that results by CHOWMOK-1 were consistent with those from ASET-BX. Therefore, CHOWMOK-1 is considered to be acceptable as a reference for fire engineering design. Limitations and deficiencies of CHOWMOK-1 have also been explored and discussed in details. Recommendations of how to overcome the limitations and deficiencies have been discussed. Suggestions for future development of CHOWMOK-1 have also been highlighted.

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