.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/heat_transfer/plot_heat_transfer_benchmark.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_api_gallery_heat_transfer_plot_heat_transfer_benchmark.py>`
        to download the full example code or to run this example in your browser via JupyterLite.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_api_gallery_heat_transfer_plot_heat_transfer_benchmark.py:


Cooling and the lumped time constant
====================================

A small copper sphere has a small Biot number in the chosen convection field.
Its excess temperature should decrease to 1/e of its initial value at one
lumped time constant. All temperatures are absolute.

.. GENERATED FROM PYTHON SOURCE LINES 9-27



.. image-sg:: /api/gallery/heat_transfer/images/sphx_glr_plot_heat_transfer_benchmark_001.png
   :alt: plot heat transfer benchmark
   :srcset: /api/gallery/heat_transfer/images/sphx_glr_plot_heat_transfer_benchmark_001.png
   :class: sphx-glr-single-img





.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from engineeringkit.heat_transfer import biot_number, lumped_temperature

    radius, h, k, rho, cp = 0.005, 10, 400, 8960, 385
    A, V = 4 * np.pi * radius**2, 4 * np.pi * radius**3 / 3
    assert biot_number(h, V / A, k) < 0.1
    tau = rho * cp * V / (h * A)
    t = np.linspace(0, 5 * tau, 101)
    T = lumped_temperature(373, 293, h, A, rho, cp, V, t)
    assert np.isclose(lumped_temperature(373, 293, h, A, rho, cp, V, tau), 293 + 80 / np.e)
    fig, ax = plt.subplots()
    ax.plot(t / tau, (T - 293) / 80)
    ax.set(xlabel="time / time constant", ylabel="normalized excess temperature")

    plt.show()


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.060 seconds)


.. _sphx_glr_download_api_gallery_heat_transfer_plot_heat_transfer_benchmark.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: lite-badge

      .. image:: images/jupyterlite_badge_logo.svg
        :target: ../../../lite/lab/index.html?path=api/gallery/heat_transfer/plot_heat_transfer_benchmark.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_heat_transfer_benchmark.ipynb <plot_heat_transfer_benchmark.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_heat_transfer_benchmark.py <plot_heat_transfer_benchmark.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_heat_transfer_benchmark.zip <plot_heat_transfer_benchmark.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_