6.10. Heat resist

Fig. 6.10.1 Schematic of a heat resist.

Fall type

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

6.10.1. Mathematical model

The head loss is given by:

(6.10.1)\[\Delta H = a + bQ + cQ|Q|\]

with:

variable	Description	Units
\(\Delta H\)	Head loss over resist	m
\(a\)	Constant loss	m
\(b\)	Linear loss	m2/s
\(c\)	Quadratic loss	m5/s2
\(Q\)	Flow rate	m3/s

The head loss equation (6.10.1) can be rewritten in terms of pressure and mass flow rate:

(6.10.2)\[\Delta P = a\rho g + gb\dot{m} + gc\frac{{\dot{m}}^{2}}{\rho} - \Delta z \rho g\]

variable	Description	Units
\(\Delta P\)	Pressure loss over resist	Pa
\(\rho\)	Fluid density at upstream connection point	kg/m3
\(g\)	Gravitational acceleration	m/s2
\(\dot{m}\)	Mass flow rate	kg/s
\(\Delta z\)	Height difference over the resist	m

The temperature is calculated from an energy balance as:

(6.10.3)\[c_{p1}\dot{m}T_{1} - c_{p2}\dot{m}T_{2} + fr \cdot Q_{\text{gen}} = 0\]

with:

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

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

(6.10.4)\[Q_{gen} = ag\dot{m} + bg\frac{{\dot{m}}^{2}}{\rho} + cg\frac{{\dot{m}}^{3}}{\rho^{2}}\]

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.

6.10.2. Heat Resist

6.10.2.1. Hydraulic specifications

description	Input	unit	range	default	remarks
a in a+bQ+CQ|Q|	Real	[m]
b in a+bQ+CQ|Q|	Real	[s2/m2]
c in a+bQ+CQ|Q|	Real	[s4/m5]
Frac. Gen. heat to fluid	Real	[-]	0-1	0

See also the loss equation (6.10.1) in the Mathematical model section.

6.10.2.2. Component specific output

Generated heat flux [W]

6.10.2.3. H-actions

None

6.10.2.4. Component messages

Message	Type	Explanation

References