# Heatsink

Dissipate heat from power semiconductors to ambient temperature

• Library:
• Simscape / Electrical / Passive / Thermal

## Description

The Heatsink block models a heatsink that dissipates heat from power semiconductors. The heat from the case conducts through the fins and dissipates to the ambient temperature through convection. The environment and the working fluid are the same

You can parameterize this block from a datasheet, from tabulated heat transfer properties, or from geometry that assumes an empirical convection correlation. If you set the Convection parameter to ```Forced - specify flow speed```, the v input port specifies the flow speed.

### Parameterization: Datasheet

To parameterize the Heatsink block from a datasheet, set the Parameterization parameter to `Datasheet` and specify both the Vector of temperature rises above ambient, T and Corresponding heat dissipated to ambient, Q_TLU1(T) parameters.

If you enable forced convection in the system by setting Convection to `Forced - specify flow speed`, specify both the Vector of temperature rises above ambient, T and Corresponding heat dissipated to ambient, Q_TLU2(T,v) parameters.

### Parameterization: Tabulated Convection and Fin Efficiency

To parameterize the Heatsink block based on the convection coefficient as a function of the coolant flow speed and temperature difference with the ambient temperature and the fin efficiency as a function of the convective coefficient, set the Parameterization parameter to `Tabulated convection and fin efficiency`.

The block uses this equation to calculate the dissipated heat:

`${Q}_{dissipated}=h\left({v}_{fluid},\Delta T\right)\cdot {A}_{total}\cdot \frac{Eff\left(h\right)}{100}\cdot \left({T}_{heatsink}-{T}_{ambient}\right),$`

where:

• `h(vfluid,ΔT)` is the convective heat transfer coefficient tabulated against the fluid flow speed (for forced convection) and the temperature rise above the ambient temperature.

• `Atotal` is the total heat exchange surface area.

• `Eff(h)` is the fin efficiency, in percent values, tabulated against different convective heat transfer coefficients. The fin efficiency is the actual heat dissipated by the fin divided by the heat it would dissipate if all its volume was at the case temperature. This value depends on fin geometry and fin thermal conductivity.

### Parameterization: Assume Rectangular Parallel Fins

If you set the Parameterization parameter to `Assume rectangular parallel fins`, the block uses this equation to calculate the dissipated heat:

`${Q}_{dissipated}=h\left({v}_{fluid},\Delta T\right)\cdot {A}_{total}\cdot \frac{Eff\left(h\right)}{100}\cdot \left({T}_{heatsink}-{T}_{ambient}\right),$`

where:

• $h\left({v}_{fluid},\Delta T\right)={h}_{natural}\left(\Delta T\right)+{h}_{forced}\left({v}_{fluid}\right)$

• ${h}_{natural}\left(\Delta T\right)=\frac{{k}_{fluid}}{H}{\left(0.825+\frac{0.387R{a}_{H}^{1/6}}{{\left(1+{\left(\frac{0.492}{\mathrm{Pr}}\right)}^{9/16}\right)}^{8/27}}\right)}^{2}$

• ${h}_{forced}\left({v}_{fluid}\right)=\frac{{k}_{fluid}}{b}{\left(\frac{1}{{\left(\frac{\mathrm{Re}\mathrm{Pr}}{2}\right)}^{3}}+\frac{1}{{\left(0.664\sqrt{\mathrm{Re}}{\mathrm{Pr}}^{0.33}\sqrt{1+\frac{3.65}{\sqrt{\mathrm{Re}}}}\right)}^{3}}\right)}^{-0.33}$

• $R{a}_{H}=\frac{g\beta }{\nu \alpha }{H}^{3}abs\left(\Delta T\right)$ is the Rayleigh number.

• $\mathrm{Re}=\frac{{b}^{2}}{\nu d}abs\left({v}_{fluid}\right)$ is the Reynolds number.

• `g = 9.81 m/s2` is the acceleration of gravity.

• `β` is the coefficient of volume thermal expansion of the fluid.

• `ν` is the fluid kinematic viscosity.

• `α` is the fluid thermal diffusivity.

• `kfluid` is the fluid thermal conductivity.

• `H` is the fin height.

• `d` is the fin depth.

• `t` is the fin thickness.

• `b` is the gap between fins.

If one side of size `t x d` is welded in the base, this equation calculates the total heat exchange area:

`${A}_{total}=\left(2H\left(d+t\right)+dt\right)N.$`

Then this equation computes the efficiency of a rectangular fin:

`$Eff\left(h\right)=100\frac{\mathrm{tanh}\left(\sqrt{\frac{2h}{kt}}H\right)}{\sqrt{\frac{2h}{kt}}H}$`

where `k` is the fin thermal conductivity.

## Ports

### Input

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Physical input port associated with the flow speed.

#### Dependencies

To enable this port, set Convection to `Forced - specify flow speed`.

### Conserving

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Thermal conserving port associated with the ambient temperature.

Thermal conserving port associated with the case.

## Parameters

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Whether to parameterize the block as a function of rectangular parallel fins, datasheet, or tabulated convection and fin efficiency.

Whether the block models natural convection or uses convection values provided by an input port.

Height of the fin.

#### Dependencies

To enable this parameter, set Parameterization to ```Assume rectangular parallel fins```.

Thickness of the fin.

#### Dependencies

To enable this parameter, set Parameterization to ```Assume rectangular parallel fins```.

Depth of the fin.

#### Dependencies

To enable this parameter, set Parameterization to ```Assume rectangular parallel fins```.

Gap between fins.

#### Dependencies

To enable this parameter, set Parameterization to ```Assume rectangular parallel fins``` and Convection to ```Forced - specify flow speed```.

Number of fins. The value of this parameter must be equal to or greater than `1`.

#### Dependencies

To enable this parameter, set Parameterization to ```Assume rectangular parallel fins```.

Thermal conductivity of the fins.

#### Dependencies

To enable this parameter, set Parameterization to ```Assume rectangular parallel fins```.

Vector of temperature rises above the ambient temperature. The values in this parameter must be positive and strictly ascending.

#### Dependencies

To enable this parameter, set Parameterization to `Datasheet` or ```Tabulated convection and fin efficiency```.

Vector of fluid flow speed. The values in this parameter must be positive and strictly ascending.

#### Dependencies

To enable this parameter, set Parameterization to `Datasheet` or ```Tabulated convection and fin efficiency```, and Convection to ```Forced - specify flow speed```.

Vector of heat values dissipated to the ambient temperature tabulated against the temperature rise above the ambient temperature. The values in this parameter correspond to the values in the Vector of temperature rises above ambient, T parameter. The values in this parameter must be positive and ascending.

#### Dependencies

To enable this parameter, set Parameterization to `Datasheet` and Convection to `Natural`.

Vector of heat values dissipated to the ambient temperature tabulated against the flow speed and temperature rise above the ambient temperature. The values in this parameter correspond to the values in the Vector of temperature rises above ambient, T parameter.

#### Dependencies

To enable this parameter, set Parameterization to `Datasheet` and Convection to ```Forced - specify flow speed```.

Convective heat transfer coefficient tabulated against the temperature rise above the ambient temperature.

#### Dependencies

To enable this parameter, set Parameterization to ```Tabulated convection and fin efficiency``` and Convection to `Natural`.

Convective heat transfer coefficient tabulated against fluid flow speed caused by forced convection, and temperature rise above the ambient temperature caused by natural convection.

#### Dependencies

To enable this parameter, set Parameterization to ```Tabulated convection and fin efficiency``` and Convection to ```Forced - specify flow speed```.

Convective heat transfer coefficients. This parameter depends on the temperature difference caused by natural convection, and the fluid flow speed caused by forced convection . The values of this parameter must be positive and strictly ascending.

#### Dependencies

To enable this parameter, set Parameterization to ```Tabulated convection and fin efficiency```.

Fin efficiency tabulated against different convective heat transfer coefficients. Fin efficiency is the actual heat dissipated by the fin divided by the heat it would dissipate if all its volume was at case temperature. This parameter depends on fin geometry and fin thermal conductivity.

#### Dependencies

To enable this parameter, set Parameterization to ```Tabulated convection and fin efficiency```.

Total area of the surface of the heat exchange.

#### Dependencies

To enable this parameter, set Parameterization to ```Tabulated convection and fin efficiency```.

### Fluid Properties

To enable these settings, set Parameterization to ```Assume rectangular parallel fins```.

Kinematic viscosity of the fluid.

Thermal diffusivity of the fluid.

Thermal conductivity of the fluid.

Fluid coefficient of the volume thermal expansion.

### Dynamics

Mass of the heatsink.

Specific heat of the heatsink.

## References

[1] 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.

[2] Teertstra, P., Yovanovich, M.M., and Culham, J.R.. Analytical Forced Convection Modeling of Plate Fin Heat Sinks. Proceedings of 15th IEEE Semi-Therm Symposium (1999): pp. 34-41.