# 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(v`

is the convective heat transfer coefficient tabulated against the fluid flow speed (for forced convection) and the temperature rise above the ambient temperature._{fluid},ΔT)`A`

is the total heat exchange surface area._{total}`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/s`

is the acceleration of gravity.^{2}`β`

is the coefficient of volume thermal expansion of the fluid.`ν`

is the fluid kinematic viscosity.`α`

is the fluid thermal diffusivity.`k`

is the fluid thermal conductivity._{fluid}`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:

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

where `k`

is the fin thermal
conductivity.

## Ports

### Input

### Conserving

## Parameters

## Model Examples

## 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.

## Extended Capabilities

## Version History

**Introduced in R2021b**