## Is Air or Water Cooling Better?

You have experienced convection cooling if you’ve ever extended your hand out the window of a moving vehicle or into a flowing water stream. With the surface of your hand at a temperature of 30°C, determine the convection heat flux for (a) in air at -5°C with a convection coefficient of 40 W/m^2∙K and (b) in a water stream at 10°C with a convection coefficient of 90 W/m^2∙K. (c) Based on the answers, at which condition (air vs. water) would you feel colder?

Hint
Newton's law of cooling:
$$q"=h(T_s-T_\infty )$$$where $$q"$$ is the heat flux, $$h$$ is the fluid’s convection heat-transfer coefficient, $$T_s$$ is the surface temperature, and $$T_{\infty}$$ is the bulk fluid temperature. Hint 2 The hand will feel colder for the condition which results in the larger heat loss. ASSUMPTIONS : (1) Temperature is uniform over the hand’s surface. (2) Convection coefficient is uniform over the hand. (3) Negligible radiation exchange between hand and surroundings in the case of air flow. The hand will feel colder for the condition which results in the larger heat loss. The heat loss can be determined from Newton’s law of cooling, which is: $$q"=h(T_s-T_\infty )$$$
where $$q"$$ is the heat flux, $$h$$ is the fluid’s convection heat-transfer coefficient, $$T_s$$ is the surface temperature, and $$T_{\infty}$$ is the bulk fluid temperature. For the air stream:
$$q_{air}"=40\frac{W}{m^2\cdot K}[(30+273)-(-5+273)]K=1,400\:W/m^2$$$For the water stream: $$q_{water}"=90\frac{W}{m^2\cdot K}[(30+273)-(10+273)]K=1,800\:W/m^2$$$
You’d feel colder in the water due to the higher heat transfer rate.
(a) $$1,400\:W/m^2$$
(b) $$1,800\:W/m^2$$
(c) You’d feel colder in the water due to the higher heat transfer rate.