Heat dissipation to the environment from power semiconductor devices.
Description
The Heatsink unit simulates a heat sink that dissipates heat from power semiconductors. Heat from the enclosure passes through the fins and is dissipated to ambient temperature by convection. The block description assumes that the environment is a working fluid.
In the block it is possible to set parameters using tabulated heat transfer characteristics or based on the geometry of the heat sink using empirical formulae to describe convection. If the Convection parameter is set to Forced, it is necessary to set the flow rate through the inlet port v.
Parametrization: tabular characteristics
To parameterise the Heatsink unit by means of tabular characteristics, set parameterization to Datasheet and set the values of the parameters Vector of temperature rises above ambient, T and Corresponding heat dissipated to ambient, Q_TLU1(T).
If the forced convection mode is selected for modelling (parameter Convection has the value Forced - specify flow speed), then the values of parameters Vector of temperature rises above ambient, T and Corresponding heat dissipated to ambient, Q_TLU2(T,v) must be set.
parameterization: tabulated values of convective heat transfer coefficients and fin efficiencies
Set the Parameterization parameter to Tabulated convection and fin efficiency to parameterise the Heatsink block based on two parameters:
Convective heat transfer coefficient as a function of fluid velocity (for forced convection) and the difference between the enclosure temperature and ambient temperature;
the fin efficiency factor as a function of the convective heat transfer coefficient.
The equation for calculating the dissipated heat is as follows:
,
where:
- convective heat transfer coefficient given as a function of the fluid flow rate (for forced convection) and the difference between the enclosure temperature and the ambient temperature;
- is the total area of the heat transfer surface;
- fin efficiency factor in per cent, given as a function of the convective heat transfer coefficient. The fin efficiency factor is the ratio of the actual amount of heat dissipated by a fin to the amount of heat it would dissipate if its entire surface were at case temperature. This value depends on the geometry of the fin and its thermal conductivity.
parameterization: rectangular parallel ribs
If parameterization is set to Assume rectangular parallel fins, the block uses the following equations to calculate the heat dissipation:
,
where
;
;
;
- Rayleigh number;
- Reynolds number;
m/s² - free fall acceleration;
- coefficient of thermal expansion of the fluid;
- kinematic viscosity of the liquid;
- thermal diffusivity of liquid;
- thermal conductivity of liquid;
- rib height;
- rib length;
- rib width;
- distance between the ribs.
The total heat exchange area for ribs with height and cross-section at , taking into account that one side of the rib stands on the base of the radiator, can be calculated according to the formula:
.
The efficiency factor of a rectangular fin is determined by the formula:
,
where is the thermal conductivity of the rib.
Ports
Input
v - flow rate scalar
Input signal specifying the value of flow velocity.
Dependencies
To use this port, set Convection to Forced - specify flow speed.
Non-directional
A - ambient temperature heat
Heat port related to ambient temperature.
C is the temperature of the enclosure heat
Heat port associated with the hull temperature.
Parameters
Steady State
parameterization - parameterization method Assume rectangular parallel fins (by default) | Datasheet | Tabulated convection and fin efficiency
Method of block parameterization, options for selection:
Convection - type of convection Natural (by default) | Forced - specify flow speed.
Selection of the type of modelled convection:
Natural - modelling of natural convection.
Forced - specify flow speed - modelling of forced convection, when this parameter value is selected, the v port for specifying the flow speed appears in the block.
Fin height - height of the rib 0.0381 m (by default) | positive scalar.
Rib height.
Dependencies
To use this parameter, set the Parameterization parameter to Assume rectangular parallel fins.
Fin thickness is the width of the fin 0.00065 m (by default) | positive scalar
Rib width.
Dependencies
To use this parameter, set the Parameterization parameter to Assume rectangular parallel fins.
Fin depth is the length of the edge 0.1397 m (by default) | positive scalar.
Rib length.
Dependencies
To use this parameter, set the Parameterization parameter to Assume rectangular parallel fins.
Gap between fins - distance between edges 0.0094 m (by default) | positive scalar.
Distance between fins.
Dependencies
To use this parameter, set the Parameterization parameter to Assume rectangular parallel fins and the Convection parameter to Forced - specify flow speed.
Number of fins - number of edges 11 (By default) | positive scalar
Number of edges. The value of this parameter must be equal to or greater than 1.
Dependencies
To use this parameter, set the Parameterization parameter to Assume rectangular parallel fins.
Fin thermal conductivity - fin thermal conductivity 237.0 W/(m*K) (by default) | positive scalar.
Rib thermal conductivity.
Dependencies
To use this parameter, set the Parameterization parameter to Assume rectangular parallel fins.
Vector of temperature rises above ambient, T - vector of values of difference between enclosure temperature and ambient temperature [10.0, 30.0, 50.0, 70.0, 90.0] K (by default) | `vector of positive scalars'.
A vector of values for the difference between the enclosure temperature and the ambient temperature. The values of this parameter must be positive and strictly increasing.
Dependencies
To use this parameter, set the Parameterization parameter to Datasheet or Tabulated convection and fin efficiency.
Vector of fluid flow velocity, v - vector of fluid flow velocity [0.0, 1.0, 2.0, 3.0] m/s (by default) | `vector of positive scalars'.
The velocity vector of the fluid flow. The values of this parameter must be positive and strictly increasing.
Dependencies
To use this parameter, set parameterization to `Datasheet' or `Tabulated convection and fin efficiency' and Convection to `Forced - specify flow velocity'.
Corresponding heat dissipated to ambient, Q_TLU1(T) - heat dissipated to ambient, corresponding to the difference between the enclosure temperature and the ambient temperature [6.1, 23.6, 44.5, 67.5, 92.3] W (by default) | `vector of positive scalars'.
A vector of values of heat dissipated to the environment corresponding to the values of the difference between the enclosure temperature and the ambient temperature. The values in this parameter correspond to the values of the temperature difference in Vector of temperature rises above ambient, T. The values of this parameter must be positive and strictly increasing.
Dependencies
To use this parameter, set the Parameterization parameter to `Datasheet' and the Convection parameter to `Natural'.
Corresponding heat dissipated to ambient, Q_TLU2(T, v) - heat dissipated to ambient corresponding to the difference between the enclosure temperature and ambient temperature and the flow rate [6.1 18.8 22.8 25.7; 23.6 61.1 73.0 81.5; 44.5 106.4 125.9 140.1; 67.5 153.5 180.7 200.3; 92.3 202.1 236.9 262.0] W (by default) | `positive scalar matrix'.
Matrix of values of heat dissipated to the environment corresponding to the values of the flow rate and the difference between the enclosure temperature and the ambient temperature. The values in this parameter correspond to the values of the temperature difference in Vector of temperature rises above ambient, T.
Dependencies
To use this parameter, set parameterization to `Datasheet' and Convection to `Forced - specify flow velocity'.
Corresponding convective heat transfer coefficient, h_TLU1(T) - convective heat transfer coefficients corresponding to the difference between the enclosure temperature and the ambient temperature [5.4, 7.02, 7.98, 8.68, 9.26] W/(m²*K) (by default) | `vector of positive scalars'.
Values of the convective heat transfer coefficients corresponding to the values of the difference between the enclosure temperature and the ambient temperature.
Dependencies
To use this parameter, set parameterization to `Tabulated convection and fin efficiency' and Convection to `Natural'.
Corresponding convective heat transfer coefficient, h_TLU2(T, v) - convective heat transfer coefficients corresponding to the difference in case temperature and ambient temperature and flow rate [5.4 17.86 17.86 22.17 25.41; 7.02 19.49 23.8 27.03; 7.97 20.44 24.75 27.99; 8.68 21.15 25.46 28.69; 9.26 21.73 26.04 29.27] W/(m²*K) (by default) | matrix of positive scalars
Values of convective heat transfer coefficients corresponding to the values of the enclosure and ambient temperature differences and flow velocities.
Dependencies
To use this parameter, set parameterization to `Tabulated convection and fin efficiency' and Convection to `Forced - specify flow velocity'.
Vector of convective heat transfer coefficients, h - vector of convective heat transfer coefficients [5.0, 10.0, 15.0, 20.0, 25.0, 30.0] W/(m²*K) (by default) | vector of positive scalars.
Convective heat transfer coefficients. This parameter depends on the temperature difference caused by natural convection and the fluid velocity caused by forced convection. The values of this parameter must be positive and strictly increasing.
Dependencies
To use this parameter, set parameterization to `Tabulated convection and fin efficiency'.
Corresponding fin efficiency (percent), eff_TLU(h) - fin efficiencies corresponding to heat transfer coefficients [96.97, 94.16, 91.53, 89.08, 86.78, 84.62] (by default) | `vector of positive scalars'.
Rib efficiency factors in per cent, corresponding to convective heat transfer coefficients. The fin efficiency factor is the ratio of the actual amount of heat dissipated by a fin to the amount of heat it would dissipate if its entire surface were at body temperature. This value depends on the geometry of the fin and its thermal conductivity.
Dependencies
To use this parameter, set the Parameterization parameter to `Tabulated convection and fin efficiency'.
Total heat exchange surface area - total heat exchange surface area 0.1171 m² (by default) | positive scalar.
Total heat exchange surface area.
Dependencies
To use this parameter, set the Parameterization parameter to Tabulated convection and fin efficiency.
Fluid Properties
To use this parameter group, set parameterization to Assume rectangular parallel fins.
To use this parameter, set the Parameterization parameter to `Assume rectangular parallel fins'.
The Fluid coefficient of volume thermal expansion is the coefficient of thermal expansion of the fluid 0.0033 1/K (by default) | `positive scalar'.
Fluid coefficient of thermal expansion.
Dependencies
To use this parameter, set parameterization to `Assume rectangular parallel fins'.
Dynamics
Heatsink mass - heatsink mass 0.35 kg (by default) | positive scalar
Heatsink mass.
Heatsink specific heat - specific heat capacity of heatsink 437.0 J/(K*kg) (by default) | `positive scalar `
Specific heat capacity of the heat sink.
References
Churchill, Stuart W.; Chu, Humbert H.S. Correlating equations for laminar and turbulent free convection from a vertical plate. International Journal of Heat and Mass Transfer (November 1975): 1323-1329.
Teertstra, P., Yovanovich, M.M., and Culham, J.R.. Analytical Forced Convection Modeling of Plate Fin Heat Sinks. Proceedings of the 15th IEEE Semi-Therm Symposium (1999): pp. 34-41.