Question

The passenger compartment of a minivan traveling at 60 mph can be modeled as a 3.2-ft-high, 6-ft-wide, and 11-ft- long rectangular box whose walls have an insulating value of R-3 (i.e., a wall thickness–to–thermal conductivity ratio of 3 h · ft2 · °F/Btu). The interior of a minivan is maintained at an average temperature of 70°F during a trip at night while the outside air temperature is 90°F. The average heat transfer coefficient on the interior surfaces of the van is 1.2 Btu/h · ft2 · °F. The air flow over the exterior surfaces can be assumed to be turbulent because of the intense vibrations involved, and the heat transfer coefficient on the front and back surfaces can be taken to be equal to that on the top surface. Disregarding any heat gain or loss by radiation, determine the rate of heat transfer from the ambient air to the van

Answer 1

In order to calculate the rate of heat transfer from the ambient air to the van, we need to use the equation for heat transfer through a surface:

Q = U * A * ΔT

Where:

Q is the heat transfer rate (in Btu/h)

U is the overall heat transfer coefficient (in Btu/h · ft2 · °F)

A is the surface area (in ft2)

ΔT is the temperature difference (in °F)

For this problem, we need to calculate the heat transfer rate through the walls and the front and back surfaces of the van.

First, let's calculate the heat transfer rate through the walls of the van:

U = 1/(1/h + 3/k) = 1/(1/1.2 + 3/3) = 0.8

A = 3.2 * 6 + 6 * 11 = 92.8 ft2

ΔT = 90 - 70 = 20 °F

Qwall = U * A * ΔT = 0.8 * 92.8 * 20 = 1484.8 Btu/h

Now, let's calculate the heat transfer rate through the front and back surfaces of the van:

U = 1/(1/h + 3/k) = 1/(1/1.2 + 3/3) = 0.8

A = 6 * 11 = 66 ft2

ΔT = 90 - 70 = 20 °F

Qfrontback = U * A * ΔT = 0.8 * 66 * 20 = 1056 Btu/h

The total rate of heat transfer from the ambient air to the van is the sum of the heat transfer rate through the walls and the front and back surfaces:

Qtotal = Qwall + Qfrontback = 1484.8 + 1056 = 2540.8 Btu/h

Therefore, the rate of heat transfer from the ambient air to the van is 2540.8 Btu/h.