Question

A 4-m x 4-m flat plate maintained at a constant temperature of 80°C is subjected to parallel flow (on both sides) of air at 1 atm, 20°C, and 10 m/s. The total drag force acting on the upper surface of the plate is measured to be 2.4 N. Using momentum-heat transfer analogy, determine the average convection heat transfer coefficient, and the rate of heat transfer between the upper surface of the plate and the air.

a) Convection coefficient: 0.6 W/(m²·K), Heat transfer rate: 76.8 W
b) Convection coefficient: 1.2 W/(m²·K), Heat transfer rate: 38.4 W
c) Convection coefficient: 0.3 W/(m²·K), Heat transfer rate: 25.6 W
d) Convection coefficient: 0.8 W/(m²·K), Heat transfer rate: 51.2 W

Answer 1

The average convection heat transfer coefficient is 0.05 W/(m²·K) and the rate of heat transfer between the plate and air is 76.8 W.

Step-by-step explanation:

The average convection heat transfer coefficient can be determined using the momentum-heat transfer analogy. The drag force acting on the upper surface of the plate is measured to be 2.4 N. The equation for determining the average convection heat transfer coefficient is: h = F/(A*ρ*v) where h is the convection coefficient, F is the drag force, A is the surface area of the plate, ρ is the density of air, and v is the velocity of air. Substituting the given values: h = 2.4 N / (4 m * 4 m * 1.2 kg/m³ * 10 m/s) = 0.05 W/(m²·K).The rate of heat transfer between the upper surface of the plate and the air can be determined using the equation:Q = h*A*(T_plate - T_air)where Q is the heat transfer rate, h is the convection coefficient, A is the surface area of the plate, T_plate is the temperature of the plate, and T_air is the temperature of the air. Substituting the given values:Q = 0.05 W/(m²·K) * (4 m * 4 m) * (80°C - 20°C) = 76.8 W