This is a nice day to talk about wind chill. It was about -40F wind chill this morning here.
Most of the members here know what the wind chill is but there is sometimes confusion on what exactly wind chill is telling us. Some people will have the mistaken belief that a wind chill of say -25F means that your automobile needs to have antifreeze protection to less than -25F.
Wind chill is actually a heat transfer effect. The simplest way to look at this is to use a simplified heat equation.
$$\dot{Q} = \dot{m} C_p (T_{hot} – T_{cold})$$
$$\dot{Q}$$ = heat flow
$$\dot{m}$$ = mass flow rate (air)
$$C_p$$ = heat capacity (air)
$$T_{hot} $$= Person, automobile, etc.
$$T_{cold}$$ = air temp.
So if you increase $$(T_{hot} – T_{cold})$$ you increase heat flow
If you increase the $$\dot{m}$$ you increase the heat flow
If you were to have a fluid with a higher $$C_p$$ you would increase the heat flow.
One of the limitation of this simplified equation is if the $$\dot{m}$$ is zero then $$\dot{Q}$$ is zero (in practice this is never actually true because there will always be some movement of the air at the skin surface due to convection, unless the skin temp is equal to the air temp).
Anyway if there air temp is less than the skin temp you will have heat flow out of the skin. If the air temp is held constant and the mass flow is increased then the heat flow out of your skin will increase just as if you decreased $$T_{cold}$$. What is actually happening is that the air molecules that have a low Translational Kinetic Energy (TKE) will come in contact with the skin or warm boundary layer of air near the skin and the high TKE of the skin will transfer its energy to the air molecule increasing the TKE of the air and decreasing the TKE of the skin. With a higher mass flow the more air molecules with low TKE will come in contact with the skin removing more energy from the skin.
So what affect does wind chill have on an automobile? If the car engine is warmed up and then turned off on a cold day the engine will cool following the above equation. The higher the wind speed the faster the engine will cool – so a higher wind chill will actually have an effect on an automobile. But the engine will only cool to the point that $$T_{hot} $$ = $$T_{cold}$$ . No heat transfer can possible occur if there is no delta T, so it does not matter if the wind is blowing at 60 mph and the wind chill is – 48F the car will never be colder than the air temperature of -5F.
Most of the members here know what the wind chill is but there is sometimes confusion on what exactly wind chill is telling us. Some people will have the mistaken belief that a wind chill of say -25F means that your automobile needs to have antifreeze protection to less than -25F.
Wind chill is actually a heat transfer effect. The simplest way to look at this is to use a simplified heat equation.
$$\dot{Q} = \dot{m} C_p (T_{hot} – T_{cold})$$
$$\dot{Q}$$ = heat flow
$$\dot{m}$$ = mass flow rate (air)
$$C_p$$ = heat capacity (air)
$$T_{hot} $$= Person, automobile, etc.
$$T_{cold}$$ = air temp.
So if you increase $$(T_{hot} – T_{cold})$$ you increase heat flow
If you increase the $$\dot{m}$$ you increase the heat flow
If you were to have a fluid with a higher $$C_p$$ you would increase the heat flow.
One of the limitation of this simplified equation is if the $$\dot{m}$$ is zero then $$\dot{Q}$$ is zero (in practice this is never actually true because there will always be some movement of the air at the skin surface due to convection, unless the skin temp is equal to the air temp).
Anyway if there air temp is less than the skin temp you will have heat flow out of the skin. If the air temp is held constant and the mass flow is increased then the heat flow out of your skin will increase just as if you decreased $$T_{cold}$$. What is actually happening is that the air molecules that have a low Translational Kinetic Energy (TKE) will come in contact with the skin or warm boundary layer of air near the skin and the high TKE of the skin will transfer its energy to the air molecule increasing the TKE of the air and decreasing the TKE of the skin. With a higher mass flow the more air molecules with low TKE will come in contact with the skin removing more energy from the skin.
So what affect does wind chill have on an automobile? If the car engine is warmed up and then turned off on a cold day the engine will cool following the above equation. The higher the wind speed the faster the engine will cool – so a higher wind chill will actually have an effect on an automobile. But the engine will only cool to the point that $$T_{hot} $$ = $$T_{cold}$$ . No heat transfer can possible occur if there is no delta T, so it does not matter if the wind is blowing at 60 mph and the wind chill is – 48F the car will never be colder than the air temperature of -5F.
Cool....
