A heat sink really shouldn't be hot (although it is a relative term, of course) at all. At higher temperature than ambient air certainly but not hot.
When a heat sink is in intimate contact with a source of heat, like a CPU, heat is transferred in accordance with Newton's Cooling Law:
$$\frac{dQ}{dt}=uA(T_{CPU}-T_{Sink})$$
Where $u$ is a heat transfer coefficient (CPU to sink) and $A$ is the area of contact between the CPU and the heat sink.
Note that $\frac{dQ}{dt}$ is the heat carried off from the CPU per unit of time.
Higher values of $T_{Sink}$, as the basic formula shows, actually decrease $\frac{dQ}{dt}$, which becomes effectively zero when $T_{CPU}-T_{Sink}=0$.
To prevent this from happening, the heat sink itself has to transfer accumulated heat, usually to the surrounding air, in which case another heat transfer equation comes into play:
$$\frac{dQ}{dt}=hA_{Sink}(T_{Sink}-T_{air})$$
Where $h$ is the convection heat transfer coefficient (sink to air) and $A_{Sink}$ the sink's surface area exposed to the air. $h$ is very dependent on speed or airflow which explains why forced air circulation (fan assisted ventilation) is often used.
In steady state ($T_{CPU}\approx \text{Constant}$), we have:
$$\dot, with $\dot{Q}_{CPU}=uA(T_{CPU}-T_{Sink})=hA_{Sink}(T_{Sink}-T_{air})$$
From here we can determine$ power generated by the CPU:
$$\dot{Q}_{CPU}=(T_{CPU}-T_{air})\Big[\frac{1}{uA}+\frac{1}{hA_{sink}}\Big]=(T_{CPU}-T_{air})\frac{1}{K}$$
Or:
$$T_{CPU}=T_{air}+K\dot{Q}_{CPU}$$
With:
$$K=\frac{uhAA_{Sink}}{hA_{Sink}+uA}$$
The influence of the various factors on $T_{CPU}$ can be readily appreciated.
Ingenious ways of increasing both $h$ (apart from forced circulation) and $A_{sink}$ to lower $T_{CPU}$ have been used like cooling fins or this design (ST-HT4 CPU Cooler Riser):
The highly heat conductive copper bands mostly release the heat from the U-bends.
A heat sink really shouldn't be hot (although it is a relative term, of course) at all. At higher temperature than ambient air certainly but not hot.
When a heat sink is in intimate contact with a source of heat, like a CPU, heat is transferred in accordance with Newton's Cooling Law:
$$\frac{dQ}{dt}=uA(T_{CPU}-T_{Sink})$$
Where $u$ is a heat transfer coefficient (CPU to sink) and $A$ is the area of contact between the CPU and the heat sink.
Note that $\frac{dQ}{dt}$ is the heat carried off from the CPU per unit of time.
Higher values of $T_{Sink}$, as the basic formula shows, actually decrease $\frac{dQ}{dt}$, which becomes effectively zero when $T_{CPU}-T_{Sink}=0$.
To prevent this from happening, the heat sink itself has to transfer accumulated heat, usually to the surrounding air, in which case another heat transfer equation comes into play:
$$\frac{dQ}{dt}=hA_{Sink}(T_{Sink}-T_{air})$$
Where $h$ is the convection heat transfer coefficient (sink to air) and $A_{Sink}$ the sink's surface area exposed to the air. $h$ is very dependent on speed or airflow which explains why forced air circulation (fan assisted ventilation) is often used.
In steady state ($T_{CPU}\approx \text{Constant}$), we have:
$$\dot{Q}_{CPU}=uA(T_{CPU}-T_{Sink})=hA_{Sink}(T_{Sink}-T_{air})$$
From here we can determine:
$$\dot{Q}_{CPU}=(T_{CPU}-T_{air})\Big[\frac{1}{uA}+\frac{1}{hA_{sink}}\Big]=(T_{CPU}-T_{air})\frac{1}{K}$$
Or:
$$T_{CPU}=T_{air}+K\dot{Q}_{CPU}$$
The influence of the various factors on $T_{CPU}$ can be readily appreciated.
Ingenious ways of increasing both $h$ (apart from forced circulation) and $A_{sink}$ to lower $T_{CPU}$ have been used like cooling fins or this design (ST-HT4 CPU Cooler Riser):
The highly heat conductive copper bands mostly release the heat from the U-bends.
A heat sink really shouldn't be hot (although it is a relative term, of course) at all. At higher temperature than ambient air certainly but not hot.
When a heat sink is in intimate contact with a source of heat, like a CPU, heat is transferred in accordance with Newton's Cooling Law:
$$\frac{dQ}{dt}=uA(T_{CPU}-T_{Sink})$$
Where $u$ is a heat transfer coefficient (CPU to sink) and $A$ is the area of contact between the CPU and the heat sink.
Note that $\frac{dQ}{dt}$ is the heat carried off from the CPU per unit of time.
Higher values of $T_{Sink}$, as the basic formula shows, actually decrease $\frac{dQ}{dt}$, which becomes effectively zero when $T_{CPU}-T_{Sink}=0$.
To prevent this from happening, the heat sink itself has to transfer accumulated heat, usually to the surrounding air, in which case another heat transfer equation comes into play:
$$\frac{dQ}{dt}=hA_{Sink}(T_{Sink}-T_{air})$$
Where $h$ is the convection heat transfer coefficient (sink to air) and $A_{Sink}$ the sink's surface area exposed to the air. $h$ is very dependent on speed or airflow which explains why forced air circulation (fan assisted ventilation) is often used.
In steady state ($T_{CPU}\approx \text{Constant}$), we have, with $\dot{Q}_{CPU}$ power generated by the CPU:
$$\dot{Q}_{CPU}=(T_{CPU}-T_{air})\Big[\frac{1}{uA}+\frac{1}{hA_{sink}}\Big]=(T_{CPU}-T_{air})\frac{1}{K}$$
Or:
$$T_{CPU}=T_{air}+K\dot{Q}_{CPU}$$
With:
$$K=\frac{uhAA_{Sink}}{hA_{Sink}+uA}$$
The influence of the various factors on $T_{CPU}$ can be readily appreciated.
Ingenious ways of increasing both $h$ (apart from forced circulation) and $A_{sink}$ to lower $T_{CPU}$ have been used like cooling fins or this design (ST-HT4 CPU Cooler Riser):
The highly heat conductive copper bands mostly release the heat from the U-bends.
