Heatsink

Dissipate heat from power semiconductors to ambient temperature

Since R2021b

Libraries:
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:

$Q_{d i s s i p a t e d} = h (v_{f l u i d}, Δ T) \cdot A_{t o t a l} \cdot \frac{E f f (h)}{100} \cdot (T_{h e a t s i n k} - T_{a m b i e n t}),$

where:

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

$Q_{d i s s i p a t e d} = h (v_{f l u i d}, Δ T) \cdot A_{t o t a l} \cdot \frac{E f f (h)}{100} \cdot (T_{h e a t s i n k} - T_{a m b i e n t}),$

where:

$h (v_{f l u i d}, Δ T) = h_{n a t u r a l} (Δ T) + h_{f o r c e d} (v_{f l u i d})$
$h_{n a t u r a l} (Δ T) = \frac{k_{f l u i d}}{H} {(0.825 + \frac{0.387 R a_{H}^{1 / 6}}{{(1 + {(\frac{0.492}{\Pr})}^{9 / 16})}^{8 / 27}})}^{2}$
$h_{f o r c e d} (v_{f l u i d}) = \frac{k_{f l u i d}}{b} {(\frac{1}{{(\frac{Re \Pr}{2})}^{3}} + \frac{1}{{(0.664 \sqrt{Re} \Pr^{0.33} \sqrt{1 + \frac{3.65}{\sqrt{Re}}})}^{3}})}^{- 0.33}$
$R a_{H} = \frac{g β}{ν α} H^{3} a b s (Δ T)$ is the Rayleigh number.
$Re = \frac{b^{2}}{ν d} a b s (v_{f l u i d})$ 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.
k_fluid 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:

$A_{t o t a l} = (2 H (d + t) + d t) N .$

Then this equation computes the efficiency of a rectangular fin:

$E f f (h) = 100 \frac{\tanh (\sqrt{\frac{2 h}{k t}} H)}{\sqrt{\frac{2 h}{k t}} H}$

where k is the fin thermal conductivity.

Examples

Optimize Liquid Cooling System of Inverter

Analyze the performance of a liquid cooling system for a three-phase inverter. To find the steady-state temperatures and losses, you first run detailed and reduced order models (ROM). Then you compute the optimal size of the heatsink that maximizes the inverter efficiency and minimizes the lifetime cost.

Open Live Script

Ports

Input

expand all

v — Flow speed
physical

Physical input port associated with the flow speed.

Dependencies

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

Conserving

expand all

A — Ambient temperature
thermal

Thermal conserving port associated with the ambient temperature.

C — Case
thermal

Thermal conserving port associated with the case.

Parameters

expand all

Steady State

Parameterization — Parameterization type
`Assume rectangular parallel fins` (default) | `Datasheet` | `Tabulated convection and fin efficiency`

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

Convection — Convection type
`Natural` (default) | `Forced - specify flow speed`

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

Fin height — Fin height
`38.1e-3` `m` (default) | positive scalar

Height of the fin.

Dependencies

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

Fin thickness — Fin thickness
`6.5e-4` `m` (default) | positive scalar

Thickness of the fin.

Dependencies

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

Fin depth — Fin depth
`139.7e-3` `m` (default) | positive scalar

Depth of the fin.

Dependencies

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

Gap between fins — Gap between fins
`9.4e-3` `m` (default) | positive scalar

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 — Number of fins
`11` (default) | positive scalar

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.

Fin thermal conductivity — Fin thermal conductivity
`237` `W/(m*K)` (default) | positive scalar

Thermal conductivity of the fins.

Dependencies

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

Vector of temperature rises above ambient, T — Vector of temperature rises above ambient temperature
`[10, 30, 50, 70, 90]` `K` (default) | vector of positive scalars

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, v — Vector of fluid flow speed
`[0, 1, 2, 3]` `m/s` (default) | vector of positive scalars

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.

Corresponding heat dissipated to ambient, Q_TLU1(T) — Corresponding heat dissipated to ambient against temperature
`[6.1, 23.6, 44.5, 67.5, 92.3]` `W` (default) | vector of positive scalars

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.

Corresponding heat dissipated to ambient, Q_TLU2(T, v) — Corresponding heat dissipated to ambient against temperature and flow speed
`[6.1, 18.8, 22.8, 25.7; 23.6, 61.1, 73, 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]` `W` (default) | vector of positive scalars

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.

Corresponding convective heat transfer coefficient, h_TLU1(T) — Corresponding convective heat transfer coefficient against temperature
`[5.4, 7.02, 7.98, 8.68, 9.26]` `W/(m^2*K)` (default) | vector of positive scalars

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.

Corresponding convective heat transfer coefficient, h_TLU2(T, v) — Corresponding convective heat transfer coefficient against temperature and flow speed
`[5.4, 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]` (default) | `W/(m^2*K)` | vector of positive scalars

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.

Vector of convective heat transfer coefficients, h — Vector of convective heat transfer coefficients
`[5, 10, 15, 20, 25, 30]` `W/(m^2*K)` (default) | vector of positive scalars

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.

Corresponding fin efficiency (percent), eff_TLU(h) — Fin efficiency that corresponds to heat transfer coefficients
`[96.97, 94.16, 91.53, 89.08, 86.78, 84.62]` (default) | vector of positive scalars

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 heat exchange surface area — Total heat exchange surface area
`0.1171` `m^2` (default) | positive scalar

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.

Fluid kinematic viscosity — Fluid kinematic viscosity
`1.51e-5` `m^2/s` (default) | positive scalar

Kinematic viscosity of the fluid.

Fluid thermal diffusivity — Fluid thermal diffusivity
`2.07e-5` `m^2/s` (default) | positive scalar

Thermal diffusivity of the fluid.

Fluid thermal conductivity — Fluid thermal conductivity
`25e-3` `W/(m*K)` (default) | positive scalar

Thermal conductivity of the fluid.

Fluid coefficient of volume thermal expansion — Fluid coefficient of volume thermal expansion
`3.3e-3` `1/K` (default) | positive scalar

Fluid coefficient of the volume thermal expansion.

Dynamics

Heatsink mass — Heatsink mass
`0.35` `kg` (default) | positive scalar

Mass of the heatsink.

Heatsink specific heat — Heatsink specific heat
`437` `J/(K*kg)` (default) | positive scalar

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.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2021b

Heatsink

Description

Parameterization: Datasheet

Parameterization: Tabulated Convection and Fin Efficiency

Parameterization: Assume Rectangular Parallel Fins

Examples

Optimize Liquid Cooling System of Inverter

Ports

Input

v — Flow speed physical

Dependencies

Conserving

A — Ambient temperature thermal

C — Case thermal

Parameters

Steady State

Parameterization — Parameterization type Assume rectangular parallel fins (default) | Datasheet | Tabulated convection and fin efficiency

Convection — Convection type Natural (default) | Forced - specify flow speed

Fin height — Fin height 38.1e-3 m (default) | positive scalar

Dependencies

Fin thickness — Fin thickness 6.5e-4 m (default) | positive scalar

Dependencies

Fin depth — Fin depth 139.7e-3 m (default) | positive scalar

Dependencies

Gap between fins — Gap between fins 9.4e-3 m (default) | positive scalar

Dependencies

Number of fins — Number of fins 11 (default) | positive scalar

Dependencies

Fin thermal conductivity — Fin thermal conductivity 237 W/(m*K) (default) | positive scalar

Dependencies

Vector of temperature rises above ambient, T — Vector of temperature rises above ambient temperature [10, 30, 50, 70, 90] K (default) | vector of positive scalars

Dependencies

Vector of fluid flow speed, v — Vector of fluid flow speed [0, 1, 2, 3] m/s (default) | vector of positive scalars

Dependencies

Corresponding heat dissipated to ambient, Q_TLU1(T) — Corresponding heat dissipated to ambient against temperature [6.1, 23.6, 44.5, 67.5, 92.3] W (default) | vector of positive scalars

Dependencies

Dependencies

Corresponding convective heat transfer coefficient, h_TLU1(T) — Corresponding convective heat transfer coefficient against temperature [5.4, 7.02, 7.98, 8.68, 9.26] W/(m^2*K) (default) | vector of positive scalars

Dependencies

Dependencies

Vector of convective heat transfer coefficients, h — Vector of convective heat transfer coefficients [5, 10, 15, 20, 25, 30] W/(m^2*K) (default) | vector of positive scalars

Dependencies

Corresponding fin efficiency (percent), eff_TLU(h) — Fin efficiency that corresponds to heat transfer coefficients [96.97, 94.16, 91.53, 89.08, 86.78, 84.62] (default) | vector of positive scalars

Dependencies

Total heat exchange surface area — Total heat exchange surface area 0.1171 m^2 (default) | positive scalar

Dependencies

Fluid Properties

Fluid kinematic viscosity — Fluid kinematic viscosity 1.51e-5 m^2/s (default) | positive scalar

Fluid thermal diffusivity — Fluid thermal diffusivity 2.07e-5 m^2/s (default) | positive scalar

Fluid thermal conductivity — Fluid thermal conductivity 25e-3 W/(m*K) (default) | positive scalar

Fluid coefficient of volume thermal expansion — Fluid coefficient of volume thermal expansion 3.3e-3 1/K (default) | positive scalar

Dynamics

Heatsink mass — Heatsink mass 0.35 kg (default) | positive scalar

Heatsink specific heat — Heatsink specific heat 437 J/(K*kg) (default) | positive scalar

References

Extended Capabilities

C/C++ Code Generation Generate C and C++ code using Simulink® Coder™.

Version History

See Also

v — Flow speed
physical

A — Ambient temperature
thermal

C — Case
thermal

Parameterization — Parameterization type
`Assume rectangular parallel fins` (default) | `Datasheet` | `Tabulated convection and fin efficiency`

Convection — Convection type
`Natural` (default) | `Forced - specify flow speed`

Fin height — Fin height
`38.1e-3` `m` (default) | positive scalar

Fin thickness — Fin thickness
`6.5e-4` `m` (default) | positive scalar

Fin depth — Fin depth
`139.7e-3` `m` (default) | positive scalar

Gap between fins — Gap between fins
`9.4e-3` `m` (default) | positive scalar

Number of fins — Number of fins
`11` (default) | positive scalar

Fin thermal conductivity — Fin thermal conductivity
`237` `W/(m*K)` (default) | positive scalar

Vector of temperature rises above ambient, T — Vector of temperature rises above ambient temperature
`[10, 30, 50, 70, 90]` `K` (default) | vector of positive scalars

Vector of fluid flow speed, v — Vector of fluid flow speed
`[0, 1, 2, 3]` `m/s` (default) | vector of positive scalars

Corresponding heat dissipated to ambient, Q_TLU1(T) — Corresponding heat dissipated to ambient against temperature
`[6.1, 23.6, 44.5, 67.5, 92.3]` `W` (default) | vector of positive scalars

Corresponding convective heat transfer coefficient, h_TLU1(T) — Corresponding convective heat transfer coefficient against temperature
`[5.4, 7.02, 7.98, 8.68, 9.26]` `W/(m^2*K)` (default) | vector of positive scalars

Vector of convective heat transfer coefficients, h — Vector of convective heat transfer coefficients
`[5, 10, 15, 20, 25, 30]` `W/(m^2*K)` (default) | vector of positive scalars

Corresponding fin efficiency (percent), eff_TLU(h) — Fin efficiency that corresponds to heat transfer coefficients
`[96.97, 94.16, 91.53, 89.08, 86.78, 84.62]` (default) | vector of positive scalars

Total heat exchange surface area — Total heat exchange surface area
`0.1171` `m^2` (default) | positive scalar

Fluid kinematic viscosity — Fluid kinematic viscosity
`1.51e-5` `m^2/s` (default) | positive scalar

Fluid thermal diffusivity — Fluid thermal diffusivity
`2.07e-5` `m^2/s` (default) | positive scalar

Fluid thermal conductivity — Fluid thermal conductivity
`25e-3` `W/(m*K)` (default) | positive scalar

Fluid coefficient of volume thermal expansion — Fluid coefficient of volume thermal expansion
`3.3e-3` `1/K` (default) | positive scalar

Heatsink mass — Heatsink mass
`0.35` `kg` (default) | positive scalar

Heatsink specific heat — Heatsink specific heat
`437` `J/(K*kg)` (default) | positive scalar

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.