Question

You've 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 degree C. determine the convection heat flux for a vehicle speed of 35 km/h in air at -5 degree C with a convection coefficient of 40 W/m2 . K and a velocity of 0.2 m/s in a water stream at 10 degree C with a convection coefficient of 900 W/m2 K. Which condition would feel colder?

Answer 1

a) The convection heat flux for the air stream is 1400 W/m²

b) The convection heat flux for the water stream is 18000 W/m²

Step-by-step explanation:

a) The convection heat flux for the air stream is:

`Q_(air) =h(T_(s) -T\alpha )`

Where

h = 40 W/m²K

Ts = 30°C = 303.15 K

T∞ = -5°C = 268.15 K

Qair = 40(303.15 - 268.15) = 1400 W/m²

b) The convection heat flux for the water stream is:

`Q_(water) =h(T_(s) -T\alpha )`

Where

h = 900 W/m²K

Ts = 30°C = 303.15 K

T∞ = 10°C = 283.15 K

Qwater = 900(303.15 - 283.15) = 18000 W/m²

Answer 2

Concept and Reasons

“Heat is a form of energy which transfers between bodies that are kept under thermal interactions. When there is a temperature difference between two bodies or a body with its surroundings then the heat transfer occurs.”

Heat transfer occurs in three ways and they are Conduction, Convection and Radiation.

Convection:

“Convective heat transfer occurs within a fluid itself and it is carried out by transfer of one fraction of the fluid to the remaining portion. Therefore there will be transfer of molecules during convection”. Convection can be classified into two types forced convection and natural convection.

Fundamentals

Heat transfer coefficient is the ratio of the heat flux to the temperature difference.

h=q/ΔT

Here, heat flux is q, and temperature difference is ΔT .

Newton’s law of cooling

“Newton's law of cooling states that the rate of change of the temperature of an object is proportional to the difference between its own temperature and the ambient temperature”.

The Newton’s law of cooling is given by

Q = hA(Ts-T.) …… (1)

Here, heat transfer rate is Q, heat transfer coefficient is h, cross-sectional area is A, surface temperature is , and ambient (surrounding) temperature is .

Assumptions that are made:

1.Temperature is uniform over the surface of the skin.

2.Convection coefficient is uniform for both the stream over the hand.

3.In the case of air transfer between the hand and the surroundings, the transmission of radiation is negligible.

It is presumed that the coefficient of temperature and convection over the hand is uniform to decide the heat loss and state which condition feels colder.

a)

The convection heat flux for the air stream can be determined from newton’s law of cooling, equation (1) can be written as,

(a)

The convection heat flux for the air stream can be determined from newton’s law of cooling, equation (1) can be written as,

Qair = h(Ts -T∞.)

Here, heat transfer rate for air is Q(air) .

Substitute, 40 W/m²K for h, 30 degrees for Ts , and 5 degress for T∞

Qair = (40 W/m².K)(30-(-5))K

=1400 W/m²

Part a

The convection heat flux for the air stream is 1400 W/m².

(b)

The convection heat flux for the water stream can be determined from Newton’s law of cooling, equation (1) can be written as,

Qwater = h(Ts -T∞)

Here, heat transfer rate for Qwater is .

Substitute, 900 W/m².K for h, 30 degrees for Ts , and 10 degress for T∞

Osweater = (900 W/m²-K)(30–10)K

=18000 W/m²

Part b

The convection heat flux for the water stream Qwater

is 18000 W/m²

Explanation

Substitute the surrounding temperature, convection coefficient, and surface temperature in the equation of newton’s law of cooling to calculate the convection heat flux for the water stream.

The hand feels colder in water stream when compared to air stream and uncomfortable in both the water and air stream when compared to the hand in normal room condition.