The heat transfer rate due to free convection from a vertical surface, 1 m high and 0.6 m wide, to quiescent air that is 20 K colder than the surface is known. What is the ratio of the heat transfer rate for that situation to the rate corresponding to a vertical surface, 0.6 m high and 1 m wide, when the quiescent air is 20 K warmer than the surface

The ratio of heat transfer rate is 0.88

Explanation:

Given;

Case1 :

height of vertical surface, L = 1 m

width of vertical surface, w = 0.6 m

Case 2:

height of vertical surface, L = 0.6 m

width of vertical surface, w = 1 m

At an assumed film temperature of air = 300 K

then, read off from heat transfer table, temperature inverse β, surface area flow rate v, and Pr, to determine Rayleigh number for the two cases.

β = 1/300 = 0.00333 K⁻¹

v = 15.89 x 10⁻⁶ m²/s

Pr = 0.69

Case 1, L = 1 m

Case 2, L = 0.6 m

From the values of Rayleigh numbers above, case 1 is Turbulent flow while case 2 is laminar flow

Thus: C₁ = 0.1, n₁ = ¹/₃

          C₂ = 0.59, n₂ = 1/4

Ratio of heat transfer rate is given as:

Therefore, the ratio of heat transfer rate is 0.88

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explanation: