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Thermal convection

Explore convection using Newton’s cooling law, the heat-transfer coefficient and links to conduction and radiation.

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  • University Physics Year 1
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Why this matters + quick links

This page gives the UY1 working model/result for Convection. You reuse it when you turn thermal intuition into calculable models (energy balances, process reasoning, and kinetic/statistical links), with careful sign/units checks.

At a glance

  • Prerequisites: temperature difference, fluid motion basics.
  • Outcomes: use Newton’s cooling law and interpret convection coefficient h.
  • Key result: Q dot = hA(Tₛ-T_∞).
  • Common trap: treating h as a universal constant independent of flow and geometry.

Setup

Surface at temperature Tₛ in fluid at bulk temperature T_∞.

  • Natural convection: buoyancy-driven flow.
  • Forced convection: fan/pump-driven flow.

Convention:

Q dot = hA(Tₛ-T_∞),

positive when heat leaves a hotter surface to cooler fluid.

Physical interpretation:

  • Convection is “heat transfer assisted by fluid motion.” The fluid motion continually brings new fluid to the surface, which keeps the near-surface temperature gradient large.
  • The coefficient h is a lumped boundary-layer parameter: it packages fluid properties, geometry, and flow regime into one number.

Bridge note (overlap topic):

  • Conduction law uses internal gradient in a solid.
  • Convection law uses an empirical boundary coefficient linking surface to moving fluid.
  • UY1 upgrade is to combine both via thermal resistances.

Core derivation / explanation

Newton’s cooling form is a constitutive model, not a first-principles universal law:

q'' = h(Tₛ-T_∞), Q dot = q''A.

The coefficient h depends on:

  • fluid properties,
  • flow speed/regime,
  • orientation and geometry,
  • temperature range.

For engineering calculations, treat convection as boundary thermal resistance:

R_conv = 1/hA, Q dot = (Δ T)/R_conv.

Units check:

[h] = W m⁻²K⁻¹, [hAΔ T] = W.

Physical sanity/sign checks:

  • If Tₛ > T_∞, Q dot > 0 (heat leaves surface).
  • If Tₛ = T_∞, Q dot = 0.
  • Stronger airflow usually increases h, so heat transfer increases.

Limit checks:

  • h → 0 gives Q dot → 0 (nearly insulated boundary).
  • Very large h makes the surface temperature approach the bulk fluid temperature (small boundary resistance).
Pitfalls (convection)
  • h is not a universal constant for a material; it depends on flow/geometry/orientation and must often come from correlations or measurement. - Use the correct temperatures: Tₛ is the surface temperature; T_∞ is the bulk fluid temperature away from the boundary layer. - Celsius vs kelvin: for convection you use a temperature difference, so Δ T is the same in K and °C, but keep the sign consistent.

Cooling a hot plate with a fan

Worked example 1

Effect of forced airflow

Problem

A plate has exposed area 0.40 m² and surface temperature 80°C in air at 20°C. Find its convective heat-loss rate for h = 12 W m⁻²K⁻¹ and for h = 30 W m⁻²K⁻¹ with a fan. Keep both temperatures fixed.
Show full solution

  1. Find the initial convective loss

    Method

    Use Q dot = hA(Tₛ-T_∞) with a 60 K temperature difference.

    Reason

    The coefficient relates the surface to the bulk fluid. A Celsius temperature difference has the same numerical value in kelvin.

    Working

    Answer

    Q dot = hA(Tₛ-T_∞) = 12(0.40)(60) = 288 W.

  2. Compare the fan-assisted rate

    Working

    Answer

    Without the fan, Q dot = 288 W. With the fan, Q dot = 30(0.40)(60) = 720 W. The rate rises by 30/12 = 2.5 because area and temperature difference are fixed.

Practice set

Check your understanding 1

A surface has h = 8 W m⁻²K⁻¹, area 2.0 m² and temperature 15 K above the bulk fluid. Find its convective heat-loss rate.

Show hint
Multiply h, exposed area and the surface-to-fluid temperature difference.
Show answer
Q dot = hAΔ T = 8(2.0)(15) = 240 W. The positive rate denotes heat leaving the warmer surface.

Check your understanding 2

At fixed exposed area, what happens to R_conv when h doubles?

Show hint
Use R_conv = 1/(hA).
Show answer
It halves: 1/(2hA) = R_conv/2. For a fixed temperature difference this doubles the convective heat rate.

Check your understanding 3

Why can a fan increase convective cooling of a hot electronic component?

Show hint
Consider how replacing warm near-surface fluid affects h.
Show answer
Forced flow replaces warmed air near the surface and usually increases h. This lowers 1/(hA) and increases heat removal for the same surface-to-air temperature difference.

Summary + next steps

  • Convection links heat transfer to fluid transport near surfaces.
  • h is context-dependent and usually obtained from experiments/correlations.
  • Resistance form makes coupling with conduction straightforward.

Next steps:

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Syllabus and review details

No official syllabus alignment is listed for this lesson.

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