Questions: Convective Heat Transfer: Natural and Forced

Question 1

You are cooling a circuit board with a fan blowing air at 5 m/s. You replace the fan with a more powerful one blowing at 20 m/s. What happens to the convection coefficient h?

• A. h stays the same — h is a property of air and doesn't depend on flow speed
• B. h decreases — faster air has less time to absorb heat from the surface
• C. h increases — higher velocity improves convective heat transfer
• D. h is undefined for forced convection — it only applies to natural convection

Answer: (C)

The convection coefficient h is not a fixed material property — it depends on flow conditions including velocity. Higher velocity reduces the thermal boundary layer thickness, increasing heat transfer. Empirical correlations for forced convection express Nu (and thus h) as a function of the Reynolds number, which increases with velocity: Nu = C Re^m Pr^n. Option A is the most common misconception: treating h like thermal conductivity k, which is a fixed material property. h encodes the geometry, flow pattern, velocity, and fluid properties all together.

Question 2

What drives fluid motion in natural convection?

• A. An external pump or fan imposing a flow on the fluid
• B. The temperature gradient alone, which directly pushes fluid from hot to cold regions
• C. Density differences in the fluid caused by temperature-dependent expansion
• D. Pressure differences imposed by the geometry of the enclosure

Answer: (C)

Natural convection is driven by buoyancy: a heated fluid expands, becomes less dense, and rises — while cooler, denser fluid sinks to replace it. The buoyancy force is ρgβΔT (thermal expansion coefficient β times the temperature difference). Option B is subtly wrong: temperature gradient alone doesn't move fluid; it must first cause a density change, which then creates buoyancy. This is why the governing dimensionless number is the Grashof number Gr = gβΔTL³/ν² — it explicitly contains β, the link between temperature and density.

Question 3

Newton's law of cooling states that the rate of convective heat transfer is proportional to the surface area and the temperature difference between the surface and the surrounding fluid.

• T. True
• F. False

Answer: True

Newton's law of cooling is Q̇ = hA(T_s − T_∞), where A is surface area and (T_s − T_∞) is the temperature difference between the surface and the bulk fluid. This proportionality is the defining relationship for convection analysis, with h encoding everything about how efficiently the flow removes heat. Doubling the area or doubling the temperature difference doubles the heat transfer rate (holding h constant).

Question 4

The convection coefficient h is a fixed property of the fluid material, like thermal conductivity, and can be looked up from standard tables given the fluid type.

• T. True
• F. False

Answer: False

This is a critical distinction: thermal conductivity k is a material property (a number like 0.6 W/m·K for water at 20°C), but the convection coefficient h is a system property. It depends on the fluid, yes, but also on flow velocity, surface geometry, whether flow is laminar or turbulent, and the size of the surface. Typical h values span three orders of magnitude: ~10 W/(m²·K) for still air, ~100 for forced air, ~1000 for flowing water, and ~10,000 for boiling water. There is no single 'h for air' — only h for air under specific conditions.

Question 5

What is the convection coefficient h, and why is it fundamentally different from thermal conductivity k?

Model answer: The convection coefficient h (W/m²·K) quantifies the effectiveness of convective heat transfer between a surface and a fluid, encoding all the complexity of the flow — velocity, turbulence, fluid properties, and geometry — into a single number for use in Newton's law of cooling: Q̇ = hA(T_s − T_∞). Thermal conductivity k (W/m·K) is a material property: a fixed constant for a given material at a given temperature, governing heat diffusion through a stationary medium via Fourier's law. The key difference is that k is intrinsic to the material and does not change with flow conditions, while h is extrinsic — it characterizes the flow situation and can vary by orders of magnitude for the same fluid depending on velocity and geometry.

The Nusselt number Nu = hL/k_fluid bridges the two: it expresses the ratio of total (convective + conductive) heat transfer to what pure conduction through the fluid would give. Empirical correlations for Nu as a function of Re and Pr allow engineers to determine h from measurable flow conditions.