Boundary Element Methods for Heat Transfer with Phase Change Problems: Theory and Application

Boundary Element Methods for Phase Change Over Domains with Fixed Boundaries

Author(s): S. G. Ahmed

Pp: 154-232 (79)

DOI: 10.2174/9789815040883122010006

* (Excluding Mailing and Handling)

Abstract

In the present chapter, the principles of the boundary element methods for phase change problems over domains with fixed boundaries are developed briefly. The details are developed starting from the 1-D diffusion problems over domains with fixed boundaries subjected to different types of boundary and initial conditions. In these problems, a new criterion has emerged: the existence of a moving boundary, which requires special treatment when solving overall problems. 


Keywords: Boundary elements methods, phase change problems, moving boundary problems, Stefan condition.

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      • 13. app/Models/UserAccess/UserAccess.php:1266
      • 14. app/Http/Controllers/ChapterController.php:1518
      • 15. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
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      • 13. app/Models/UserAccess/UserAccess.php:1266
      • 14. app/Http/Controllers/ChapterController.php:1549
      • 15. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 16. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • select b.banner_link, b.banner_name, b.banner_script, b.banner_remarks, b.banner_file_name, b.banner_placement, bd.content_type, bd.content_id from `tbl_banner` as `b` inner join `tbl_banner_detail` as `bd` on `bd`.`banner_id` = `b`.`banner_id` inner join `users` as `u` on `u`.`id` = `b`.`updated_by` where `b`.`banner_ebook` = 1 and `bd`.`content_type` = 'B' and `bd`.`content_id` = 3362 and `b`.`banner_from_date` <= 1739848230 and `b`.`banner_to_date` >= 1739848230 and `b`.`banner_status` = 'A' order by `b`.`banner_id` desc
      1.29msalphaeurekaselec_live_10_06_2022Banner.php#95
      Bindings
      • 0: 1
      • 1: B
      • 2: 3362
      • 3: 1739848230
      • 4: 1739848230
      • 5: A
      Backtrace
      • 13. app/Models/Banner.php:95
      • 14. app/Http/helpers.php:404
      • 17. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
      • 18. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 19. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:73
    • select count(*) as aggregate from `uc_cart_products` where cart_id='9981f73ff0090d136d8aeab1a3f970eb'
      250μsalphaeurekaselec_live_10_06_2022Cart.php#271
      Backtrace
      • 15. app/Models/Cart.php:271
      • 16. view::layouts._header:260
      • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
      • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:73
    App\Models\Keywords
    4Keywords.php#?
    App\Models\Chapter
    1Chapter.php#?
    App\Models\Ebook
    1Ebook.php#?
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        PHPDEBUGBAR_STACK_DATA
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        path_info
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        status_code
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        status_text
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        format
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        request_query
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        request_request
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        request_headers
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        request_cookies
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        ClearShow all
        Date ↕MethodURLData
        #12025-02-18 03:10:30GET/chapter/17211112186