.. _sec_H_resist:

Heat resist
-----------

.. _fig_heat_resist:
.. figure:: ../media/heat/image1266.svg
   :width: 200in
   :align: center

   Schematic of a heat resist.

**Fall type**

=========== ============================================ ======
type label  description                                  active
=========== ============================================ ======
Heat resist Resistance according user-defined polynomial No
=========== ============================================ ======

.. _mathematical-model-57:

Mathematical model
^^^^^^^^^^^^^^^^^^

The head loss is given by:

.. math:: 
   :label: eq_heat_resist

   \Delta H = a + bQ + cQ|Q|

with:

============================= =========================================================================================== ============================
variable                      Description                                                                                 Units
============================= =========================================================================================== ============================
:math:`\Delta H`              Head loss over resist                                                                       m
:math:`a`                     Constant loss                                                                               m
:math:`b`                     Linear loss                                                                                 m\ :sup:`2`/s
:math:`c`                     Quadratic loss                                                                              m\ :sup:`5`/s\ :sup:`2`
:math:`Q`                     Flow rate                                                                                   m\ :sup:`3`/s
============================= =========================================================================================== ============================

The head loss equation :eq:`eq_heat_resist` can be rewritten in terms of pressure and mass flow rate:

.. math:: 

   \Delta P = a\rho g + gb\dot{m} + gc\frac{{\dot{m}}^{2}}{\rho} - \Delta z \rho g

============================= =========================================================================================== ============================
variable                      Description                                                                                 Units
============================= =========================================================================================== ============================
:math:`\Delta P`              Pressure loss over resist                                                                   Pa
:math:`\rho`                  Fluid density at upstream connection point                                                  kg/m\ :sup:`3`
:math:`g`                     Gravitational acceleration                                                                  m/s\ :sup:`2`
:math:`\dot{m}`               Mass flow rate                                                                              kg/s
:math:`\Delta z`              Height difference over the resist                                                           m
============================= =========================================================================================== ============================

The temperature is calculated from an energy balance as:

.. math:: 
   
   c_{p1}\dot{m}T_{1} - c_{p2}\dot{m}T_{2} + fr \cdot Q_{\text{gen}} = 0

with:

============================= ========================================================= =======================
variable                      Description                                               Units
============================= ========================================================= =======================
:math:`c_{p1}/c_{p2}`         specific head of the fluid                                J/kg/K
:math:`T_{1}/T_{2}`           upstream/ downstream temperature                          K
:math:`Q_{gen}`               generated heat                                            W
:math:`fr`                    Fraction of generated heat transferred to the fluid       \-
============================= ========================================================= =======================

The heat generated by friction (:math:`Q_{gen}`) is defined by:

.. math:: 

   Q_{gen} = ag\dot{m} + bg\frac{{\dot{m}}^{2}}{\rho} + cg\frac{{\dot{m}}^{3}}{\rho^{2}}

Note that the coefficient “a” is a constant loss coefficient, that is only valid for positive flow. If the flow is negative, the head loss contribution “a” (defined as H1-H2) is equal to that of a positive flow. This is useful when modeling osmotic membranes.

.. _heat-resist-1:

Heat Resist
^^^^^^^^^^^

.. _hydraulic-specifications-66:

Hydraulic specifications
""""""""""""""""""""""""

+--------------------------+-------+---------------------------+-------+---------+---------+
| description              | Input | unit                      | range | default | remarks |
+==========================+=======+===========================+=======+=========+=========+
| a in a+bQ+CQ|Q\|         | Real  | [m]                       |       |         |         |
+--------------------------+-------+---------------------------+-------+---------+---------+
| b in a+bQ+CQ|Q\|         | Real  | [s\ :sup:`2`/m\ :sup:`2`] |       |         |         |
+--------------------------+-------+---------------------------+-------+---------+---------+
| c in a+bQ+CQ|Q\|         | Real  | [s\ :sup:`4`/m\ :sup:`5`] |       |         |         |
+--------------------------+-------+---------------------------+-------+---------+---------+
| Frac. Gen. heat to fluid | Real  | [-]                       | 0-1   | 0       |         |
+--------------------------+-------+---------------------------+-------+---------+---------+

See also the loss equation :eq:`eq_heat_resist` in the :ref:`mathematical-model-57` section.

.. _component-specific-output-60:

Component specific output
"""""""""""""""""""""""""

Generated heat flux [W]

.. _h-actions-50:

H-actions
"""""""""

None

.. _component-messages-58:

Component messages
""""""""""""""""""

======= ==== ===========
Message Type Explanation
\            
======= ==== ===========

References

.. _pipe-1: