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Difficulty: HardHeat Transfer: Convection

A high-power electrical transformer is submerged in a sealed tank of mineral oil to prevent overheating. The exterior of the tank features a series of hollow, vertical cooling tubes connected to the main tank at both the top and the bottom. If the system relies entirely on natural convection (without mechanical pumps) to circulate the fluid and dissipate heat, which of the following accurately describes the required flow path and its driving physical mechanism?

  1. The heated oil expands and becomes less dense, rising to the top of the main tank and entering the upper openings of the cooling tubes; as it cools in the exterior tubes, it becomes denser and sinks, re-entering the main tank at the bottom.Answer
  2. B
    The heat from the core decreases the total mass of the surrounding oil, reducing its weight and causing it to be displaced upward by heavier oil, which then forces the lighter oil downward through the cooling tubes.
  3. C
    The heated oil contracts near the transformer core, becoming denser and sinking to the bottom of the tank, which displaces cooler oil and forces it up through the external tubes to dissipate accumulated heat at the top.
  4. D
    The oil remains mostly stationary inside the tank while thermal energy conducts from molecule to molecule outward into the cooling tubes, heating the exterior metal which then creates an upward draft of cold air.

Answer

The heated oil expands, becomes less dense, rises to the top of the tank, enters the top of the cooling tubes, cools/sinks, and returns to the bottom of the tank.
In a natural convection loop, the heat source must be located physically lower than the cooling area to maintain circulation. The oil heated by the transformer core expands, its density decreases, and it rises to the top of the tank. To dissipate heat, it must flow into the upper ends of the cooling radiators. As it sheds heat to the environment, it cools, contracts, becomes denser, and gravity pulls it down through the tubes. It then re-enters the bottom of the main tank to replace the oil that is rising, creating a continuous, self-sustaining flow.

Step-by-Step Solution

1
Identify the primary mechanism of heat transfer in a fluid system without pumps.
The mechanism is natural convection.
Natural convection is driven entirely by density differences caused by temperature changes within the fluid.
2
Determine how the heat from the transformer core affects the surrounding mineral oil.
The oil absorbs heat, expands in volume, and its density decreases.
Thermal expansion causes molecules to move further apart, lowering the mass per unit volume.
3
Trace the path of the heated, less dense oil.
It experiences an upward buoyant force, rising to the highest available point inside the main tank.
Less dense fluids rise above denser fluids due to gravity.
4
Trace the path of the oil as it interacts with the exterior cooling tubes.
The hot oil enters the upper connections of the exterior tubes. As it dissipates heat to the outside air, it cools, its density increases, and it sinks down the tubes to re-enter the main tank at the bottom.
This completes the continuous circulation loop required for sustained natural convection.

Key Concept

Natural convection relies on a continuous loop where a fluid is heated (becoming less dense and rising), moves to a cooler area to dissipate heat (becoming denser and sinking), and returns to the heat source.
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Topics

Heat Transfer: Convection

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