Computational Simulation and Experimental Techniques for Nanofluid Flow

Dual Solutions of Magneto-Radiative Ag-Water Nanofluid Slip Flow Across the Porous Medium Due to a Permeable Contracting Surface with Heat Generation: Stability Analysis

Author(s): Gopinath Mandal * .

Pp: 94-115 (22)

DOI: 10.2174/9789815223705124010008

* (Excluding Mailing and Handling)

Abstract

The current study looks at the heat transfer of a magneto-radiative nanofluid over an exponentially contracting permeable sheet in the existence of heat generation with numerous slip boundary constraints. It also looks at the stability and duality of solutions. Here, a waterbased fluid with silver (Ag) nanoparticles is employed. Before being computed by bvp4c in the Matlab program, the governing nonlinear partial differential equations are converted into dimensionless nonlinear ODEs via a similarity transformation. Due to the contracting surface scenario, a dual-nature solution can only be found if a sufficient suction value is used. We may infer from stability investigation that the first one is stable while the second one is unstable. A stable solution makes sense with the least positive eigenvalues, but a lower unstable solution indicates negative eigenvalues. The Nusselt number and the skin-friction factor may be improved by increases in the silver nanoparticle’s solid volume percentage. The least eigenvalue converges to zero as the suction and contracting surface parameters reach their critical values. Nanofluids that are magnetic and radiative can be used to create beautiful and effective electromagnetic devices, including in the areas of clothing, paper, plastics, food colorants, cars, cancer therapy, medicines, ceramics, soaps, and paints.

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      • 13. app/Models/UserAccess/UserAccess.php:1266
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      • 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 j.user_access_id,j.volume_id,j.user_id,j.from_ip,j.to_ip,j.type,j.track,"Trial Access" as access_base_text, CASE j.type WHEN 111 THEN true ELSE false END as terms_popup, "S" as content_download_type, null as restricted_user_access_key, null as restricted_user_access_type, CASE j.track WHEN 0 THEN false ELSE true END as tracksAccessByVolume,"chapter" as access_level, j.chapter_id from `user_access_chapter_trail` as `j` inner join `user_access_info` as `info` on `j`.`user_access_id` = `info`.`user_access_id` where ((j.from_ip <= 59143663 and j.to_ip >=59143663 )) and ((j.from_date <= 1740473579 and j.to_date >= 1740473579 and j.perpetual= 0) or (j.from_date is null and j.to_date is null and j.perpetual= 1)) and j.chapter_id = 22328) union (select j.user_access_id,j.volume_id,j.user_id,j.from_ip,j.to_ip,j.type,j.track,"Subscribed" as access_base_text, false as terms_popup, "S" as content_download_type, null as restricted_user_access_key, null as restricted_user_access_type, CASE j.track WHEN 0 THEN false ELSE true END as tracksAccessByVolume,"chapter" as access_level, j.chapter_id from `user_access_chapter_corporate` as `j` inner join `user_access_info` as `info` on `j`.`user_access_id` = `info`.`user_access_id` where ((j.from_ip <= 59143663 and j.to_ip >=59143663 )) and ((j.from_date <= 1740473579 and j.to_date >= 1740473579 and j.perpetual= 0) or (j.from_date is null and j.to_date is null and j.perpetual= 1)) and j.chapter_id = 22328) union (select j.user_access_id,j.volume_id,j.user_id,j.from_ip,j.to_ip,j.type,j.track,"Token Based Access" as access_base_text, false as terms_popup, "R" as content_download_type, j.uc_id as restricted_user_access_key, "v" as restricted_user_access_type, CASE j.track WHEN 0 THEN false ELSE true END as tracksAccessByVolume,"chapter" as access_level, j.chapter_id from `user_access_chapter_token` as `j` inner join `user_access_info` as `info` on `j`.`user_access_id` = `info`.`user_access_id` where ((j.from_ip <= 59143663 and j.to_ip >=59143663 )) and ((j.from_date <= 1740473579 and j.to_date >= 1740473579 and j.perpetual= 0) or (j.from_date is null and j.to_date is null and j.perpetual= 1)) and j.chapter_id = 22328)
      990μsalphaeurekaselec_live_10_06_2022UserAccess.php#1266
      Backtrace
      • 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` = 3714 and `b`.`banner_from_date` <= 1740473579 and `b`.`banner_to_date` >= 1740473579 and `b`.`banner_status` = 'A' order by `b`.`banner_id` desc
      1.61msalphaeurekaselec_live_10_06_2022Banner.php#95
      Bindings
      • 0: 1
      • 1: B
      • 2: 3714
      • 3: 1740473579
      • 4: 1740473579
      • 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='159c580082664a27cbe0b5776e5630e1'
      370μsalphaeurekaselec_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\Chapter
    1Chapter.php#?
    App\Models\Ebook
    1Ebook.php#?
        _token
        zZzmVPOKqY7xOSUNrAVT0HFnXitxVAGFGRSuITAc
        uc_cart_id
        159c580082664a27cbe0b5776e5630e1
        _previous
        array:1 [ "url" => "https://alpha.eurekaselect.com/chapter/22328" ]
        _flash
        array:2 [ "old" => [] "new" => [] ]
        PHPDEBUGBAR_STACK_DATA
        []
        path_info
        /chapter/22328
        status_code
        200
        
        status_text
        OK
        format
        html
        content_type
        text/html; charset=UTF-8
        request_query
        []
        
        request_request
        []
        
        request_headers
        0 of 0
        array:17 [ "x-https" => array:1 [ 0 => "1" ] "host" => array:1 [ 0 => "alpha.eurekaselect.com" ] "priority" => array:1 [ 0 => "u=0, i" ] "cookie" => array:1 [ 0 => "wayfindertarget=eyJpdiI6IkltaGt5dWhwbUVJSUkzUm90TFVMb3c9PSIsInZhbHVlIjoiMTR1M2xSeFNpVE9nN2ZDU3N6Vy90VGw2NmlTYjM1dkxhYlVnWnJKUDFCUT0iLCJtYWMiOiIyMTNmYjQ3YzVmZWU2OGQ2OTQ3Mzc1ZWVlZGRiNmZjZjliMmE2NDg1MTc3MjJjZDI4NjUyY2JiZDQwMzRjNGQ5IiwidGFnIjoiIn0%3Dwayfindertarget=eyJpdiI6IkltaGt5dWhwbUVJSUkzUm90TFVMb3c9PSIsInZhbHVlIjoiMTR1M2xSeFNpVE9nN2ZDU3N6Vy90VGw2NmlTYjM1dkxhYlVnWnJKUDFCUT0iLCJtYWMiOiIyMTNmYjQ3YzVmZWU2" ] "accept-encoding" => array:1 [ 0 => "gzip, deflate, br, zstd" ] "sec-fetch-dest" => array:1 [ 0 => "document" ] "sec-fetch-user" => array:1 [ 0 => "?1" ] "sec-fetch-mode" => array:1 [ 0 => "navigate" ] "sec-fetch-site" => array:1 [ 0 => "none" ] "accept" => array:1 [ 0 => "text/html,application/xhtml+xml,application/xml;q=0.9,image/avif,image/webp,image/apng,*/*;q=0.8,application/signed-exchange;v=b3;q=0.7" ] "user-agent" => array:1 [ 0 => "Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)" ] "upgrade-insecure-requests" => array:1 [ 0 => "1" ] "sec-ch-ua-platform" => array:1 [ 0 => ""Windows"" ] "sec-ch-ua-mobile" => array:1 [ 0 => "?0" ] "sec-ch-ua" => array:1 [ 0 => ""HeadlessChrome";v="129", "Not=A?Brand";v="8", "Chromium";v="129"" ] "cache-control" => array:1 [ 0 => "no-cache" ] "pragma" => array:1 [ 0 => "no-cache" ] ]
        request_cookies
        0 of 0
        array:1 [ "wayfindertarget" => null ]
        response_headers
        0 of 0
        array:5 [ "content-type" => array:1 [ 0 => "text/html; charset=UTF-8" ] "cache-control" => array:1 [ 0 => "no-cache, private" ] "date" => array:1 [ 0 => "Tue, 25 Feb 2025 08:52:59 GMT" ] "set-cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6IldlQzJVNlhRR0R1clc5MERvMHJHUVE9PSIsInZhbHVlIjoiNUx5cUE5R2xvaW8rc3ZWR3l5YUUwMFZUSXlUY1pCSFllL0I0MnFPWkJCWnB0UzlzQ1pqNXRGRkplUDZMZHE5RnB5TkFYOVVEc0JzcGNtYkIvVXptVEFSUjlRamRlLzhYbDBkTXlESnhIcGkvYzZIdkx5d1ZGTUFuYWlrTlRkajEiLCJtYWMiOiJmM2E0YmZjMjhiYmNmNzM4OTlmMTJjMzViZTk3OTM0ZTZkNTU1ZTcyNDdiN2JiZmJkZmZmNzA4ZGQyYzBhZTRlIiwidGFnIjoiIn0%3D; expires=Thu, 27 Feb 2025 20:52:59 GMT; Max-Age=216000; path=/; secure; samesite=laxXSRF-TOKEN=eyJpdiI6IldlQzJVNlhRR0R1clc5MERvMHJHUVE9PSIsInZhbHVlIjoiNUx5cUE5R2xvaW8rc3ZWR3l5YUUwMFZUSXlUY1pCSFllL0I0MnFPWkJCWnB0UzlzQ1pqNXRGRkplUDZMZHE5RnB5TkFYO" 1 => "alphaeurekaselectnet_session=eyJpdiI6IlVWSVBRakN0MitQQ1U2c1Q5dVJVcUE9PSIsInZhbHVlIjoiTnZTMU0xQys1SVNFSFNoQVdOc0kyLzJZTXNlVFNkT09UYkh3eWowUzVmSjhSMUtEYjJGUzZKdEtML1NLTnMvN1N4UURIbXYwbWU5cndJajNFMnJwNXNGeWVWS0JTWm9mTWdqWGk5MUtPVkV0Q1lJR0tCWmJqV0JwUHFkVndwUzMiLCJtYWMiOiJjODUyYjZlYWY0MWE5OTk5ZWU0ZDc0MTFjN2UzZTg2ZTIxMzM2ZTgwNjIzOWM5MjQ4M2Y3N2ZlYzY4MGQwZTliIiwidGFnIjoiIn0%3D; path=/; secure; httponly; samesite=laxalphaeurekaselectnet_session=eyJpdiI6IlVWSVBRakN0MitQQ1U2c1Q5dVJVcUE9PSIsInZhbHVlIjoiTnZTMU0xQys1SVNFSFNoQVdOc0kyLzJZTXNlVFNkT09UYkh3eWowUzVmSjhSMUtEYjJGUzZKdEt" ] "Set-Cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6IldlQzJVNlhRR0R1clc5MERvMHJHUVE9PSIsInZhbHVlIjoiNUx5cUE5R2xvaW8rc3ZWR3l5YUUwMFZUSXlUY1pCSFllL0I0MnFPWkJCWnB0UzlzQ1pqNXRGRkplUDZMZHE5RnB5TkFYOVVEc0JzcGNtYkIvVXptVEFSUjlRamRlLzhYbDBkTXlESnhIcGkvYzZIdkx5d1ZGTUFuYWlrTlRkajEiLCJtYWMiOiJmM2E0YmZjMjhiYmNmNzM4OTlmMTJjMzViZTk3OTM0ZTZkNTU1ZTcyNDdiN2JiZmJkZmZmNzA4ZGQyYzBhZTRlIiwidGFnIjoiIn0%3D; expires=Thu, 27-Feb-2025 20:52:59 GMT; path=/; secureXSRF-TOKEN=eyJpdiI6IldlQzJVNlhRR0R1clc5MERvMHJHUVE9PSIsInZhbHVlIjoiNUx5cUE5R2xvaW8rc3ZWR3l5YUUwMFZUSXlUY1pCSFllL0I0MnFPWkJCWnB0UzlzQ1pqNXRGRkplUDZMZHE5RnB5TkFYO" 1 => "alphaeurekaselectnet_session=eyJpdiI6IlVWSVBRakN0MitQQ1U2c1Q5dVJVcUE9PSIsInZhbHVlIjoiTnZTMU0xQys1SVNFSFNoQVdOc0kyLzJZTXNlVFNkT09UYkh3eWowUzVmSjhSMUtEYjJGUzZKdEtML1NLTnMvN1N4UURIbXYwbWU5cndJajNFMnJwNXNGeWVWS0JTWm9mTWdqWGk5MUtPVkV0Q1lJR0tCWmJqV0JwUHFkVndwUzMiLCJtYWMiOiJjODUyYjZlYWY0MWE5OTk5ZWU0ZDc0MTFjN2UzZTg2ZTIxMzM2ZTgwNjIzOWM5MjQ4M2Y3N2ZlYzY4MGQwZTliIiwidGFnIjoiIn0%3D; path=/; secure; httponlyalphaeurekaselectnet_session=eyJpdiI6IlVWSVBRakN0MitQQ1U2c1Q5dVJVcUE9PSIsInZhbHVlIjoiTnZTMU0xQys1SVNFSFNoQVdOc0kyLzJZTXNlVFNkT09UYkh3eWowUzVmSjhSMUtEYjJGUzZKdEt" ] ]
        session_attributes
        0 of 0
        array:5 [ "_token" => "zZzmVPOKqY7xOSUNrAVT0HFnXitxVAGFGRSuITAc" "uc_cart_id" => "159c580082664a27cbe0b5776e5630e1" "_previous" => array:1 [ "url" => "https://alpha.eurekaselect.com/chapter/22328" ] "_flash" => array:2 [ "old" => [] "new" => [] ] "PHPDEBUGBAR_STACK_DATA" => [] ]
        ClearShow all
        Date ↕MethodURLData
        #12025-02-25 08:52:59GET/chapter/22328112192