Receiving Helpdesk

how does transient heat transfer differ from steady state heat transfer

by Finn Robel Published 4 years ago Updated 2 years ago

Key Takeaways

  • In steady-state heat transfer, the temperature is constant throughout time.
  • In transient heat transfer, the temperature changes with time.
  • The heat flux and temperature field images of a circuit board (obtained by conducting steady-state heat transfer analysis) can help designers optimize heat sink geometry and location.

In steady-state heat transfer, the temperature is constant throughout time. In transient heat transfer, the temperature changes with time.

What is transient heat transfer?

Transient heat transfer is the non-steady state transfer of energy through a medium. The transient state refers to a non-constant flow of energy. This changing rate of heat transfer could be due to fluctuating temperature difference over the medium or changing properties throughout the medium.

What is the difference between heat transfer and steady state?

Heat transfer is the transfer of thermal energy from a body, at a high temperature, to another at a lower temperature. Under Steady state conditions the temperature within the system does not change with time. Conversely, under unsteady state conditions the temperature within the system does vary with time. Is heat flux constant at steady state?

What is the difference between a transient and steady state process?

For heat conduction specifically, a steady state process is concerned only with thermal conductivity (usually designated k with units of BTU/ (hr-ft-deg F) or Watt/ (m-deg C)). A transient condition must track the changing amount of heat stored in the material as the temperature changes. As such, the most important parmater becomes t

What is the relationship between heat transfer and temperature gradient?

Heat transfer is the transfer of heat energy from one region to another due to temperature differences between the two. The heat flow is always from a higher temperature to a lower temperature. The temperature gradient is the driving force of any heat transfer and the net heat transfer is equal to zero if there is no temperature gradient.

What is the difference between steady state and transient state?

In general, nearly every process or system has both a steady state and a transient state. Also, a steady state establishes after a specific time in your system. However, a transient state is essentially the time between the beginning of the event and the steady state.

What is a steady state heat transfer?

Steady-state conduction is said to exist when the temperature at all locations in a substance is constant with time, as in the case of heat flow through a uniform wall.

What is steady state and transient thermal analysis?

Transient thermal analysis considers the thermal capacitance of a material (also known as thermal inertia), while Steady State analysis only considers the Thermal Conductivity and ignore the Capacitance.

What does the transient conduction mean?

Transient condition means. a) Conduction when temperature at a point varies with time.

What is meant by steady state?

Definition of steady state : a state or condition of a system or process (such as one of the energy states of an atom) that does not change in time broadly : a condition that changes only negligibly over a specified time.

What is transient analysis in heat transfer?

Transient thermal analysis is the evaluation of how a system responds to fixed and varying boundary conditions over time. For fixed boundary conditions, the time to reach a steady state temperature can be evaluated, as well as how long operating conditions can be sustained before reaching a threshold temperature.

What is steady state heat transfer?

Steady-state heat transfer can be a conduction, convection, or radiation process. Irrespective of the mode of transfer, in a steady-state heat transfer, the heat flow rate remains constant at any point in time.

What influences the heat transfer from the component to the heat sink?

The geometry of the heat sink, aspect ratio of the fins, pressure, and aerodynamics all influence the heat transfer from the component to the heat sink and from the heat sink to the ambient.

What is the transfer of heat energy from one region to another?

Heat transfer is the transfer of heat energy from one region to another due to temperature differences between the two. The heat flow is always from a higher temperature to a lower temperature. The temperature gradient is the driving force of any heat transfer and the net heat transfer is equal to zero if there is no temperature gradient.

How does steady state temperature affect a circuit?

In electronic circuits, the steady-state temperature of a component is harmful to the component’s lifespan when it crosses the limit stated in its datasheet. Failure rates of components exponentially increase as steady-state temperatures increase. However, temperatures can be controlled by attaching heat sinks such as power electronic switches, diodes, or LEDs to components. The geometry of the heat sink, aspect ratio of the fins, pressure, and aerodynamics all influence the heat transfer from the component to the heat sink and from the heat sink to the ambient.

Why does heat flow change?

The heat flow rate keeps changing, and the cause of the varying rates of heat transfer can be either fluctuating temperature differences over the medium or changes in properties of the medium. In the physical world, heat transfer starts as transient and then reaches a steady-state until thermal equilibrium is reached.

A Basic Overview of Steady-State vs. Transient Heat Transfer

  • Heat transferis the transfer of heat energy from one region to another due to temperature differences between the two. The heat flow is always from a higher temperature to a lower temperature. The temperature gradient is the driving force of any heat transfer and the net heat transfer is equal to zero if there is no temperature gradient. The three ...
See more on resources.system-analysis.cadence.com

The Steady-State Temperature’S Impact on Component Failure Rates

  • In electronic circuits, the steady-state temperature of a component is harmful to the component’s lifespan when it crosses the limit stated in its datasheet. Failure rates of components exponentially increase as steady-state temperatures increase. However, temperatures can be controlled by attaching heat sinks such as power electronic switches, diodes, or LEDs to compo…
See more on resources.system-analysis.cadence.com

Steady-State Heat Transfer Analysis

  • The heat flux and temperature field images of a circuit board—obtained by conducting steady-state heat transfer analysis—can help designers optimize heat sink geometry and location. The need for forced convection or cooling fans and slit openings in the casing of a computer processor or an enclosed electronic circuit can be determined from steady-state heat transfer a…
See more on resources.system-analysis.cadence.com

Transient Heat Transfer Analysis

  • If a designer would like to determine the temperature profile versus the time of an electronic circuit board, transient heat transfer analysis should be conducted. In cases where the heat generation of a component stops, designers can determine the rate of cooling using transient heat transfer analysis. The rate of reheating is obtained when heat generation restarts in a comp…
See more on resources.system-analysis.cadence.com

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z 1 2 3 4 5 6 7 8 9
8.3.21PHP Version336msRequest Duration2MBMemory UsageGET {post}Route
  • warninglog[17:48:48] LOG.warning: Creation of dynamic property Barryvdh\Debugbar\DataFormatter\QueryFormatter:...
  • warninglog[17:48:48] LOG.warning: Creation of dynamic property Barryvdh\Debugbar\DataFormatter\QueryFormatter:...
  • warninglog[17:48:48] LOG.warning: Callables of the form ["Swift_SmtpTransport", "Swift_Transport_EsmtpTranspor...
  • warninglog[17:48:48] LOG.warning: Creation of dynamic property Barryvdh\Debugbar\DataFormatter\SimpleFormatter...
  • warninglog[17:48:48] LOG.warning: Creation of dynamic property Barryvdh\Debugbar\DataFormatter\SimpleFormatter...
  • warninglog[17:48:48] LOG.warning: json_decode(): Passing null to parameter #1 ($json) of type string is deprec...
  • warninglog[17:48:48] LOG.warning: json_decode(): Passing null to parameter #1 ($json) of type string is deprec...
  • warninglog[17:48:48] LOG.warning: json_decode(): Passing null to parameter #1 ($json) of type string is deprec...
  • warninglog[17:48:48] LOG.warning: json_decode(): Passing null to parameter #1 ($json) of type string is deprec...
  • warninglog[17:48:48] LOG.warning: json_decode(): Passing null to parameter #1 ($json) of type string is deprec...
  • warninglog[17:48:48] LOG.warning: mt_rand(): Passing null to parameter #2 ($max) of type int is deprecated in ...
  • warninglog[17:48:48] LOG.warning: explode(): Passing null to parameter #2 ($string) of type string is deprecat...
  • Booting (13.03ms)
  • Application (323ms)
  • 1 x Application (96%)
    322.79ms
    1 x Booting (3.87%)
    13.03ms
    7 templates were rendered
    • themes.DevBlog.content.post (resources/views/themes/DevBlog/content/post.blade.php)34blade
      Params
      0
      post
      1
      postContent
      2
      author
      3
      updated_at
      4
      bing_rich_snippet_text
      5
      bing_rich_snippet_link
      6
      bing_related_keywords
      7
      google_related_keywords
      8
      bing_news_title
      9
      bing_news_description
      10
      bing_videos
      11
      bing_images
      12
      bing_search_result_title
      13
      bing_search_result_description
      14
      bing_search_result_url
      15
      bing_paa_questions
      16
      bing_paa_answers
      17
      bing_slider_faq_questions
      18
      bing_slider_faq_answers
      19
      bing_pop_faq_questions
      20
      bing_pop_faq_answers
      21
      bing_tab_faq_questions
      22
      bing_tab_faq_answers
      23
      google_faq_questions
      24
      google_faq_answers
      25
      google_rich_snippet
      26
      google_search_result
      27
      indexedArray
      28
      total_images
      29
      total_videos
      30
      settings
      31
      url_current
      32
      menus
      33
      sidebar
    • themes.DevBlog.layouts.master (resources/views/themes/DevBlog/layouts/master.blade.php)41blade
      Params
      0
      __env
      1
      app
      2
      errors
      3
      post
      4
      postContent
      5
      author
      6
      updated_at
      7
      bing_rich_snippet_text
      8
      bing_rich_snippet_link
      9
      bing_related_keywords
      10
      google_related_keywords
      11
      bing_news_title
      12
      bing_news_description
      13
      bing_videos
      14
      bing_images
      15
      bing_search_result_title
      16
      bing_search_result_description
      17
      bing_search_result_url
      18
      bing_paa_questions
      19
      bing_paa_answers
      20
      bing_slider_faq_questions
      21
      bing_slider_faq_answers
      22
      bing_pop_faq_questions
      23
      bing_pop_faq_answers
      24
      bing_tab_faq_questions
      25
      bing_tab_faq_answers
      26
      google_faq_questions
      27
      google_faq_answers
      28
      google_rich_snippet
      29
      google_search_result
      30
      indexedArray
      31
      total_images
      32
      total_videos
      33
      settings
      34
      url_current
      35
      menus
      36
      sidebar
      37
      i
      38
      __currentLoopData
      39
      loop
      40
      item
    • themes.DevBlog.panels.head (resources/views/themes/DevBlog/panels/head.blade.php)41blade
      Params
      0
      __env
      1
      app
      2
      errors
      3
      post
      4
      postContent
      5
      author
      6
      updated_at
      7
      bing_rich_snippet_text
      8
      bing_rich_snippet_link
      9
      bing_related_keywords
      10
      google_related_keywords
      11
      bing_news_title
      12
      bing_news_description
      13
      bing_videos
      14
      bing_images
      15
      bing_search_result_title
      16
      bing_search_result_description
      17
      bing_search_result_url
      18
      bing_paa_questions
      19
      bing_paa_answers
      20
      bing_slider_faq_questions
      21
      bing_slider_faq_answers
      22
      bing_pop_faq_questions
      23
      bing_pop_faq_answers
      24
      bing_tab_faq_questions
      25
      bing_tab_faq_answers
      26
      google_faq_questions
      27
      google_faq_answers
      28
      google_rich_snippet
      29
      google_search_result
      30
      indexedArray
      31
      total_images
      32
      total_videos
      33
      settings
      34
      url_current
      35
      menus
      36
      sidebar
      37
      i
      38
      __currentLoopData
      39
      loop
      40
      item
    • themes.DevBlog.panels.header (resources/views/themes/DevBlog/panels/header.blade.php)41blade
      Params
      0
      __env
      1
      app
      2
      errors
      3
      post
      4
      postContent
      5
      author
      6
      updated_at
      7
      bing_rich_snippet_text
      8
      bing_rich_snippet_link
      9
      bing_related_keywords
      10
      google_related_keywords
      11
      bing_news_title
      12
      bing_news_description
      13
      bing_videos
      14
      bing_images
      15
      bing_search_result_title
      16
      bing_search_result_description
      17
      bing_search_result_url
      18
      bing_paa_questions
      19
      bing_paa_answers
      20
      bing_slider_faq_questions
      21
      bing_slider_faq_answers
      22
      bing_pop_faq_questions
      23
      bing_pop_faq_answers
      24
      bing_tab_faq_questions
      25
      bing_tab_faq_answers
      26
      google_faq_questions
      27
      google_faq_answers
      28
      google_rich_snippet
      29
      google_search_result
      30
      indexedArray
      31
      total_images
      32
      total_videos
      33
      settings
      34
      url_current
      35
      menus
      36
      sidebar
      37
      i
      38
      __currentLoopData
      39
      loop
      40
      item
    • themes.DevBlog.panels.navbar (resources/views/themes/DevBlog/panels/navbar.blade.php)41blade
      Params
      0
      __env
      1
      app
      2
      errors
      3
      post
      4
      postContent
      5
      author
      6
      updated_at
      7
      bing_rich_snippet_text
      8
      bing_rich_snippet_link
      9
      bing_related_keywords
      10
      google_related_keywords
      11
      bing_news_title
      12
      bing_news_description
      13
      bing_videos
      14
      bing_images
      15
      bing_search_result_title
      16
      bing_search_result_description
      17
      bing_search_result_url
      18
      bing_paa_questions
      19
      bing_paa_answers
      20
      bing_slider_faq_questions
      21
      bing_slider_faq_answers
      22
      bing_pop_faq_questions
      23
      bing_pop_faq_answers
      24
      bing_tab_faq_questions
      25
      bing_tab_faq_answers
      26
      google_faq_questions
      27
      google_faq_answers
      28
      google_rich_snippet
      29
      google_search_result
      30
      indexedArray
      31
      total_images
      32
      total_videos
      33
      settings
      34
      url_current
      35
      menus
      36
      sidebar
      37
      i
      38
      __currentLoopData
      39
      loop
      40
      item
    • themes.DevBlog.panels.footer (resources/views/themes/DevBlog/panels/footer.blade.php)41blade
      Params
      0
      __env
      1
      app
      2
      errors
      3
      post
      4
      postContent
      5
      author
      6
      updated_at
      7
      bing_rich_snippet_text
      8
      bing_rich_snippet_link
      9
      bing_related_keywords
      10
      google_related_keywords
      11
      bing_news_title
      12
      bing_news_description
      13
      bing_videos
      14
      bing_images
      15
      bing_search_result_title
      16
      bing_search_result_description
      17
      bing_search_result_url
      18
      bing_paa_questions
      19
      bing_paa_answers
      20
      bing_slider_faq_questions
      21
      bing_slider_faq_answers
      22
      bing_pop_faq_questions
      23
      bing_pop_faq_answers
      24
      bing_tab_faq_questions
      25
      bing_tab_faq_answers
      26
      google_faq_questions
      27
      google_faq_answers
      28
      google_rich_snippet
      29
      google_search_result
      30
      indexedArray
      31
      total_images
      32
      total_videos
      33
      settings
      34
      url_current
      35
      menus
      36
      sidebar
      37
      i
      38
      __currentLoopData
      39
      loop
      40
      item
    • themes.DevBlog.panels.scripts (resources/views/themes/DevBlog/panels/scripts.blade.php)41blade
      Params
      0
      __env
      1
      app
      2
      errors
      3
      post
      4
      postContent
      5
      author
      6
      updated_at
      7
      bing_rich_snippet_text
      8
      bing_rich_snippet_link
      9
      bing_related_keywords
      10
      google_related_keywords
      11
      bing_news_title
      12
      bing_news_description
      13
      bing_videos
      14
      bing_images
      15
      bing_search_result_title
      16
      bing_search_result_description
      17
      bing_search_result_url
      18
      bing_paa_questions
      19
      bing_paa_answers
      20
      bing_slider_faq_questions
      21
      bing_slider_faq_answers
      22
      bing_pop_faq_questions
      23
      bing_pop_faq_answers
      24
      bing_tab_faq_questions
      25
      bing_tab_faq_answers
      26
      google_faq_questions
      27
      google_faq_answers
      28
      google_rich_snippet
      29
      google_search_result
      30
      indexedArray
      31
      total_images
      32
      total_videos
      33
      settings
      34
      url_current
      35
      menus
      36
      sidebar
      37
      i
      38
      __currentLoopData
      39
      loop
      40
      item
    uri
    GET {post}
    middleware
    web, checkdate
    as
    post.show
    controller
    App\Http\Controllers\Frontend\json_data\PostController@show
    namespace
    where
    file
    app/Http/Controllers/Frontend/json_data/PostController.php:18-166
    7 statements were executed303ms
    • select * from `posts` where `published_at` <= '2025-06-24 17:48:48' and `slug` = 'how-does-transient-heat-transfer-differ-from-steady-state-heat-transfer' and `posts`.`deleted_at` is null limit 1
      3.43ms/app/Providers/RouteServiceProvider.php:54receivinghelpdeskask
      Metadata
      Bindings
      • 0. 2025-06-24 17:48:48
      • 1. how-does-transient-heat-transfer-differ-from-steady-state-heat-transfer
      Backtrace
      • 15. /app/Providers/RouteServiceProvider.php:54
      • 18. /vendor/laravel/framework/src/Illuminate/Routing/Router.php:842
      • 19. Route binding:39
      • 20. /vendor/laravel/framework/src/Illuminate/Pipeline/Pipeline.php:167
      • 21. /vendor/laravel/framework/src/Illuminate/Foundation/Http/Middleware/VerifyCsrfToken.php:78
    • select * from `json_post_contents` where `json_post_contents`.`post_id` = 165130 and `json_post_contents`.`post_id` is not null and `rewrite_id` = 0
      8.9msmiddleware::checkdate:30receivinghelpdeskask
      Metadata
      Bindings
      • 0. 165130
      • 1. 0
      Backtrace
      • 19. middleware::checkdate:30
      • 20. /vendor/laravel/framework/src/Illuminate/Pipeline/Pipeline.php:167
      • 21. /vendor/laravel/jetstream/src/Http/Middleware/ShareInertiaData.php:61
      • 22. /vendor/laravel/framework/src/Illuminate/Pipeline/Pipeline.php:167
      • 23. /vendor/laravel/framework/src/Illuminate/Routing/Middleware/SubstituteBindings.php:50
    • select * from `nova_menu_menus` where `slug` = 'header' limit 1
      610μs/vendor/outl1ne/nova-menu-builder/src/helpers.php:32receivinghelpdeskask
      Metadata
      Bindings
      • 0. header
      Backtrace
      • 15. /vendor/outl1ne/nova-menu-builder/src/helpers.php:32
      • 17. /vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 18. /vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:45
      • 19. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:261
      • 20. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
    • select * from `nova_menu_menu_items` where `nova_menu_menu_items`.`menu_id` = 1 and `nova_menu_menu_items`.`menu_id` is not null and `parent_id` is null order by `parent_id` asc, `order` asc, `name` asc
      680μs/vendor/outl1ne/nova-menu-builder/src/Models/Menu.php:35receivinghelpdeskask
      Metadata
      Bindings
      • 0. 1
      Backtrace
      • 19. /vendor/outl1ne/nova-menu-builder/src/Models/Menu.php:35
      • 20. /vendor/outl1ne/nova-menu-builder/src/helpers.php:33
      • 22. /vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 23. /vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:45
      • 24. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:261
    • select * from `nova_menu_menu_items` where `nova_menu_menu_items`.`parent_id` in (1) order by `order` asc
      280μs/vendor/outl1ne/nova-menu-builder/src/Models/Menu.php:35receivinghelpdeskask
      Metadata
      Backtrace
      • 24. /vendor/outl1ne/nova-menu-builder/src/Models/Menu.php:35
      • 25. /vendor/outl1ne/nova-menu-builder/src/helpers.php:33
      • 27. /vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 28. /vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:45
      • 29. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:261
    • select `id`, `post_title`, `slug` from `posts` where `status` = 'publish' and `posts`.`deleted_at` is null order by RAND() limit 10
      288ms/app/View/Composers/SidebarView.php:22receivinghelpdeskask
      Metadata
      Bindings
      • 0. publish
      Backtrace
      • 14. /app/View/Composers/SidebarView.php:22
      • 15. /app/View/Composers/SidebarView.php:12
      • 16. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:124
      • 17. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:162
      • 20. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:177
    • select * from `fake_users` where `fake_users`.`id` = 30244 limit 1
      810μsview::2dd102cf0462e89a4d4d8bc77355d767652bf9aa:15receivinghelpdeskask
      Metadata
      Bindings
      • 0. 30244
      Backtrace
      • 21. view::2dd102cf0462e89a4d4d8bc77355d767652bf9aa:15
      • 23. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
      • 24. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 25. /vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69
      • 26. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
    App\Models\FakeUser
    1
    Outl1ne\MenuBuilder\Models\MenuItem
    1
    Outl1ne\MenuBuilder\Models\Menu
    1
    App\Models\JsonPostContent
    1
    App\Models\Post
    11
        _token
        djlG2REpf4kx8T2x2oqJ4Fzy5HSeWdC5DbIiYEPE
        _previous
        array:1 [ "url" => "https://receivinghelpdesk.com/ask/how-does-transient-heat-transfer-differ-from...
        _flash
        array:2 [ "old" => [] "new" => [] ]
        PHPDEBUGBAR_STACK_DATA
        []
        path_info
        /how-does-transient-heat-transfer-differ-from-steady-state-heat-transfer
        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:25 [ "cookie" => array:1 [ 0 => "_pk_id.64.7c30=9e931fe8e58cc22e.1750767517.; _pk_ses.64.7c30=1; XSRF-TOKEN=eyJpdiI6IkFOMjRFSUNxazl1czNZUXhSUGtLOXc9PSIsInZhbHVlIjoiL3F0OURiK1loUm5YZCttSUk1aU5oLytlcURQYzhMNHRqZjlBTzBON0laV0tPRzlpcjFSdk4zOW1kQWlzOWs1TFNGSkNFZVNyZnhHNWFIR29UZkFlZ3kxdUhva2wzeGhyc2tKYm41WmN6TExPQjhHK2lGeGFleGxxSXJ1TC84Q1IiLCJtYWMiOiI1Njc0MDA4YjE1NjhlYzhmYmMwMWNjNTY3YTI5Yjc1ODdhMmUyZTMzZjhkYWUzNTAwNjY0NzM0YWU2NmE3MjE3IiwidGFnIjoiIn0%3D; askhelpdesk_session=eyJpdiI6IkE1bXp3Tzc3VHNMdU41WXF4UkF4VVE9PSIsInZhbHVlIjoiNFIyeXJ2Z3RlRXE0TFc2dE5MdWFPUFVYTGZzYVh0WmZtZ1VnK21mZURWWHp4RS9qVGloLzRtd0xZOXh1VGJ5aDZqVGJuMldMMm55YUlpOTlIVWo5Rld1cTZOS21kUkVnUDdPZHVRS3MydE1BRmU2TkdWOXMyT0tSYnl2V3NjdzgiLCJtYWMiOiJlMzZiMGJmZmFiMjZiYzNiMmExNjgyZDA0MjFjYjAxNGZjNjY2ZDU3NDBiYzMxZjIwOWI4Zjc1ZmM4ZDc1YTQ3IiwidGFnIjoiIn0%3D_pk_id.64.7c30=9e931fe8e58cc22e.1750767517.; _pk_ses.64.7c30=1; XSRF-TOKEN=eyJpdiI6IkFOMjRFSUNxazl1czNZUXhSUGtLOXc9PSIsInZhbHVlIjoiL3F0OURiK1loUm5YZCttSUk1aU5oL" ] "cf-ipcountry" => array:1 [ 0 => "US" ] "cf-connecting-ip" => array:1 [ 0 => "216.73.216.102" ] "cdn-loop" => array:1 [ 0 => "cloudflare; loops=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 => ""Chromium";v="130", "HeadlessChrome";v="130", "Not?A_Brand";v="99"" ] "cache-control" => array:1 [ 0 => "no-cache" ] "pragma" => array:1 [ 0 => "no-cache" ] "accept-encoding" => array:1 [ 0 => "gzip, br" ] "cf-ray" => array:1 [ 0 => "954c2b7fa8be72eb-ORD" ] "priority" => array:1 [ 0 => "u=0, i" ] "sec-fetch-dest" => array:1 [ 0 => "document" ] "sec-fetch-user" => array:1 [ 0 => "?1" ] "cf-visitor" => array:1 [ 0 => "{"scheme":"https"}" ] "connection" => array:1 [ 0 => "close" ] "x-forwarded-proto" => array:1 [ 0 => "https" ] "x-forwarded-for" => array:1 [ 0 => "216.73.216.102, 172.70.127.51" ] "x-server-addr" => array:1 [ 0 => "154.12.239.204" ] "host" => array:1 [ 0 => "receivinghelpdesk.com" ] ]
        request_server
        0 of 0
        array:56 [ "USER" => "runcloud" "HOME" => "/home/runcloud" "SCRIPT_NAME" => "/ask/index.php" "REQUEST_URI" => "/ask/how-does-transient-heat-transfer-differ-from-steady-state-heat-transfer" "QUERY_STRING" => "" "REQUEST_METHOD" => "GET" "SERVER_PROTOCOL" => "HTTP/1.0" "GATEWAY_INTERFACE" => "CGI/1.1" "REDIRECT_URL" => "/ask/how-does-transient-heat-transfer-differ-from-steady-state-heat-transfer" "REMOTE_PORT" => "57656" "SCRIPT_FILENAME" => "/home/runcloud/webapps/ReceivingHelpDesk/ask/index.php" "SERVER_ADMIN" => "you@example.com" "CONTEXT_DOCUMENT_ROOT" => "/home/runcloud/webapps/ReceivingHelpDesk/" "CONTEXT_PREFIX" => "" "REQUEST_SCHEME" => "http" "DOCUMENT_ROOT" => "/home/runcloud/webapps/ReceivingHelpDesk/" "REMOTE_ADDR" => "172.70.127.51" "SERVER_PORT" => "80" "SERVER_ADDR" => "127.0.0.1" "SERVER_NAME" => "receivinghelpdesk.com" "SERVER_SOFTWARE" => "Apache/2.4.63 (Unix) OpenSSL/1.1.1f" "SERVER_SIGNATURE" => "" "LD_LIBRARY_PATH" => "/RunCloud/Packages/apache2-rc/lib" "PATH" => "/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin" "HTTP_COOKIE" => "_pk_id.64.7c30=9e931fe8e58cc22e.1750767517.; _pk_ses.64.7c30=1; XSRF-TOKEN=eyJpdiI6IkFOMjRFSUNxazl1czNZUXhSUGtLOXc9PSIsInZhbHVlIjoiL3F0OURiK1loUm5YZCttSUk1aU5oLytlcURQYzhMNHRqZjlBTzBON0laV0tPRzlpcjFSdk4zOW1kQWlzOWs1TFNGSkNFZVNyZnhHNWFIR29UZkFlZ3kxdUhva2wzeGhyc2tKYm41WmN6TExPQjhHK2lGeGFleGxxSXJ1TC84Q1IiLCJtYWMiOiI1Njc0MDA4YjE1NjhlYzhmYmMwMWNjNTY3YTI5Yjc1ODdhMmUyZTMzZjhkYWUzNTAwNjY0NzM0YWU2NmE3MjE3IiwidGFnIjoiIn0%3D; askhelpdesk_session=eyJpdiI6IkE1bXp3Tzc3VHNMdU41WXF4UkF4VVE9PSIsInZhbHVlIjoiNFIyeXJ2Z3RlRXE0TFc2dE5MdWFPUFVYTGZzYVh0WmZtZ1VnK21mZURWWHp4RS9qVGloLzRtd0xZOXh1VGJ5aDZqVGJuMldMMm55YUlpOTlIVWo5Rld1cTZOS21kUkVnUDdPZHVRS3MydE1BRmU2TkdWOXMyT0tSYnl2V3NjdzgiLCJtYWMiOiJlMzZiMGJmZmFiMjZiYzNiMmExNjgyZDA0MjFjYjAxNGZjNjY2ZDU3NDBiYzMxZjIwOWI4Zjc1ZmM4ZDc1YTQ3IiwidGFnIjoiIn0%3D_pk_id.64.7c30=9e931fe8e58cc22e.1750767517.; _pk_ses.64.7c30=1; XSRF-TOKEN=eyJpdiI6IkFOMjRFSUNxazl1czNZUXhSUGtLOXc9PSIsInZhbHVlIjoiL3F0OURiK1loUm5YZCttSUk1aU5oL" "HTTP_CF_IPCOUNTRY" => "US" "HTTP_CF_CONNECTING_IP" => "216.73.216.102" "HTTP_CDN_LOOP" => "cloudflare; loops=1" "HTTP_SEC_FETCH_MODE" => "navigate" "HTTP_SEC_FETCH_SITE" => "none" "HTTP_ACCEPT" => "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" "HTTP_USER_AGENT" => "Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)" "HTTP_UPGRADE_INSECURE_REQUESTS" => "1" "HTTP_SEC_CH_UA_PLATFORM" => ""Windows"" "HTTP_SEC_CH_UA_MOBILE" => "?0" "HTTP_SEC_CH_UA" => ""Chromium";v="130", "HeadlessChrome";v="130", "Not?A_Brand";v="99"" "HTTP_CACHE_CONTROL" => "no-cache" "HTTP_PRAGMA" => "no-cache" "HTTP_ACCEPT_ENCODING" => "gzip, br" "HTTP_CF_RAY" => "954c2b7fa8be72eb-ORD" "HTTP_PRIORITY" => "u=0, i" "HTTP_SEC_FETCH_DEST" => "document" "HTTP_SEC_FETCH_USER" => "?1" "HTTP_CF_VISITOR" => "{"scheme":"https"}" "HTTP_CONNECTION" => "close" "HTTP_X_FORWARDED_PROTO" => "https" "HTTP_X_FORWARDED_FOR" => "216.73.216.102, 172.70.127.51" "HTTP_X_SERVER_ADDR" => "154.12.239.204" "HTTP_HOST" => "receivinghelpdesk.com" "HTTPS" => "on" "REDIRECT_STATUS" => "200" "REDIRECT_HTTPS" => "on" "FCGI_ROLE" => "RESPONDER" "PHP_SELF" => "/ask/index.php" "REQUEST_TIME_FLOAT" => 1750767528.9229 "REQUEST_TIME" => 1750767528 ]
        request_cookies
        0 of 0
        array:4 [ "_pk_id_64_7c30" => null "_pk_ses_64_7c30" => null "XSRF-TOKEN" => "djlG2REpf4kx8T2x2oqJ4Fzy5HSeWdC5DbIiYEPE" "askhelpdesk_session" => "X8ycGcuCMxvztgs7aVLTDWU8X9MtpzYKsjjewv2T" ]
        response_headers
        0 of 0
        array:7 [ "content-type" => array:1 [ 0 => "text/html; charset=UTF-8" ] "cache-control" => array:1 [ 0 => "private, must-revalidate" ] "date" => array:1 [ 0 => "Tue, 24 Jun 2025 12:18:48 GMT" ] "pragma" => array:1 [ 0 => "no-cache" ] "expires" => array:1 [ 0 => -1 ] "set-cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6Ik1HcExnV1VHb3pVUGJrUVBLSjZmNnc9PSIsInZhbHVlIjoibFNRM1RITlhOZVJNWThmVDZ0WXhoZlFHQ3cvenFtWDFtaXgyaG84NzZlb3hWOFc0WkUyZnVQUzJNQWlTeVNWb2dqdTlYaWMraThnbUxyQWM4RjNSYnBFL3FkMTkza3dReXNSeS93WTJOaWZGUHBPS1YzcEoyV2REbjEvQVhBWXoiLCJtYWMiOiIwZDk0ODFhYmI0NmRjYjQ4ODViZmVmY2QyMTFlNGFkMDkxOWYxZWU2ZDc1NmM5MTBjZmUxZGM4OWQ3ZWNhODRlIiwidGFnIjoiIn0%3D; expires=Tue, 24-Jun-2025 14:18:49 GMT; Max-Age=7200; path=/; samesite=laxXSRF-TOKEN=eyJpdiI6Ik1HcExnV1VHb3pVUGJrUVBLSjZmNnc9PSIsInZhbHVlIjoibFNRM1RITlhOZVJNWThmVDZ0WXhoZlFHQ3cvenFtWDFtaXgyaG84NzZlb3hWOFc0WkUyZnVQUzJNQWlTeVNWb2dqdTlYa" 1 => "askhelpdesk_session=eyJpdiI6IkNwYUR3MGZQaEhud254NTVWUWVvQmc9PSIsInZhbHVlIjoiL0FrR3V0T1A3YSt3UVgyUU10V2ZrMDFmRlkvUXdwV2QzL3J2aEFoMTAyblBZZXdGS1kvbzBpS2hlTTJBenIvQlg0WDVrSW85RUFEU3psVEtHRDNPbG5aTlRTaWpqTGR3dVRqQXkzcHkxdENUWDMrRFY2d2pYdm5FY3pIdXp1aXQiLCJtYWMiOiIzOTY2YjNiMWE4ZGQ4MWMyZWRiYmY5NzI0Yjk4ZjZjZWQzODBiNzBkN2NiYWI2N2VhZjIyYmE0MGRlMDQ1MmJkIiwidGFnIjoiIn0%3D; expires=Tue, 24-Jun-2025 14:18:49 GMT; Max-Age=7200; path=/; httponly; samesite=laxaskhelpdesk_session=eyJpdiI6IkNwYUR3MGZQaEhud254NTVWUWVvQmc9PSIsInZhbHVlIjoiL0FrR3V0T1A3YSt3UVgyUU10V2ZrMDFmRlkvUXdwV2QzL3J2aEFoMTAyblBZZXdGS1kvbzBpS2hlTTJBenIv" ] "Set-Cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6Ik1HcExnV1VHb3pVUGJrUVBLSjZmNnc9PSIsInZhbHVlIjoibFNRM1RITlhOZVJNWThmVDZ0WXhoZlFHQ3cvenFtWDFtaXgyaG84NzZlb3hWOFc0WkUyZnVQUzJNQWlTeVNWb2dqdTlYaWMraThnbUxyQWM4RjNSYnBFL3FkMTkza3dReXNSeS93WTJOaWZGUHBPS1YzcEoyV2REbjEvQVhBWXoiLCJtYWMiOiIwZDk0ODFhYmI0NmRjYjQ4ODViZmVmY2QyMTFlNGFkMDkxOWYxZWU2ZDc1NmM5MTBjZmUxZGM4OWQ3ZWNhODRlIiwidGFnIjoiIn0%3D; expires=Tue, 24-Jun-2025 14:18:49 GMT; path=/XSRF-TOKEN=eyJpdiI6Ik1HcExnV1VHb3pVUGJrUVBLSjZmNnc9PSIsInZhbHVlIjoibFNRM1RITlhOZVJNWThmVDZ0WXhoZlFHQ3cvenFtWDFtaXgyaG84NzZlb3hWOFc0WkUyZnVQUzJNQWlTeVNWb2dqdTlYa" 1 => "askhelpdesk_session=eyJpdiI6IkNwYUR3MGZQaEhud254NTVWUWVvQmc9PSIsInZhbHVlIjoiL0FrR3V0T1A3YSt3UVgyUU10V2ZrMDFmRlkvUXdwV2QzL3J2aEFoMTAyblBZZXdGS1kvbzBpS2hlTTJBenIvQlg0WDVrSW85RUFEU3psVEtHRDNPbG5aTlRTaWpqTGR3dVRqQXkzcHkxdENUWDMrRFY2d2pYdm5FY3pIdXp1aXQiLCJtYWMiOiIzOTY2YjNiMWE4ZGQ4MWMyZWRiYmY5NzI0Yjk4ZjZjZWQzODBiNzBkN2NiYWI2N2VhZjIyYmE0MGRlMDQ1MmJkIiwidGFnIjoiIn0%3D; expires=Tue, 24-Jun-2025 14:18:49 GMT; path=/; httponlyaskhelpdesk_session=eyJpdiI6IkNwYUR3MGZQaEhud254NTVWUWVvQmc9PSIsInZhbHVlIjoiL0FrR3V0T1A3YSt3UVgyUU10V2ZrMDFmRlkvUXdwV2QzL3J2aEFoMTAyblBZZXdGS1kvbzBpS2hlTTJBenIv" ] ]
        session_attributes
        0 of 0
        array:4 [ "_token" => "djlG2REpf4kx8T2x2oqJ4Fzy5HSeWdC5DbIiYEPE" "_previous" => array:1 [ "url" => "https://receivinghelpdesk.com/ask/how-does-transient-heat-transfer-differ-from-steady-state-heat-transfer" ] "_flash" => array:2 [ "old" => [] "new" => [] ] "PHPDEBUGBAR_STACK_DATA" => [] ]