Heat Transfer: Conduction & Convection – JEE & NEET Guide
Heat energy transfers spontaneously from regions of higher temperature to regions of lower temperature via three distinct physical mechanisms: conduction (microscopic collisions in solids), convection (macroscopic fluid circulation), and radiation (electromagnetic waves). In this module, we focus on conduction and convection.
1. Conduction & Fourier's Law
Conduction is the mode of heat transfer in solids where thermal energy is transmitted from particle to particle through microscopic atomic vibrations and collisions (and free electron migration in metals) without any macroscopic displacement of the medium itself.
Fourier's Law of Heat Conduction
Consider a solid slab of length L and uniform cross-sectional area A, with opposite faces maintained at steady temperatures T1 and T2 (with T1 > T2):
where:
- H = dQ/dt: Rate of heat flow / Heat current (SI unit: Watt (W) or J s−1).
- k: Coefficient of Thermal Conductivity of the material (SI unit: W m−1 K−1 or J s−1 m−1 K−1).
- dT/dx: Temperature gradient (rate of change of temperature with distance, K m−1).
| Material | Thermal Conductivity k (W m−1 K−1) | Classification |
|---|---|---|
| Diamond | ~ 2300 | Exceptional conductor (superb lattice vibration transfer) |
| Silver | 406 | Highest metallic conductor |
| Copper | 385 | Commonly used for heat sinks, utensils |
| Aluminium | 205 | Lightweight thermal conductor |
| Glass / Concrete | 0.8 – 1.2 | Moderate insulator |
| Wood | 0.12 | Good thermal insulator |
| Stagnant Air | 0.026 | Superb insulator (trapped in wool, feathers, double glass) |
2. Electrical Analogy of Heat Conduction
The mathematical similarity between Fourier's law of heat conduction and Ohm's law of electrical current flow is one of the most powerful problem-solving tools in thermal physics:
Direct Analogy Parameters
- Temperature Difference (ΔT): Analogous to Potential Difference (ΔV).
- Heat Current (H = dQ/dt): Analogous to Electric Current (I = dq/dt).
- Thermal Resistance (Rth): Analogous to Electrical Resistance (Re).
Thermal Resistance Formula
SI Unit: K W−1
Just as electrical resistance R = ρ L / A = L / (σ A), thermal resistance increases with length L and decreases with cross-section A and conductivity k.
3. Combinations of Composite Slabs (High-Yield JEE Problems)
A. Slabs in Series
Same heat current H flows through both slabs (H1 = H2 = H):
Interface Temperature (T0):
k1 A (T1 − T0)/L1 = k2 A (T0 − T2)/L2
T0 = (k1 T1 / L1 + k2 T2 / L2) / (k1/L1 + k2/L2)
B. Slabs in Parallel
Same temperature difference ΔT across both slabs; total heat current H = H1 + H2:
keq (A1 + A2) / L = (k1 A1 + k2 A2) / L
Equivalent Conductivity:
keq = (k1 A1 + k2 A2) / (A1 + A2)
4. Convection: Natural vs Forced
Convection is the mode of heat transfer in fluids (liquids and gases) by the actual bulk movement of the heated fluid medium itself. It cannot occur in solids or across a vacuum.
Natural (Free) Convection
Fluid motion is driven purely by buoyancy forces resulting from temperature-dependent density variations (gravity is indispensable for natural convection):
- Sea Breeze (Day): Land has lower specific heat, warms up faster than sea. Hot air over land rises; cool dense air over sea flows toward land.
- Land Breeze (Night): Land cools down faster than sea. Sea air is warmer and rises; cool air over land flows toward sea.
- Trade Winds: Equatorial regions receive maximum solar radiation; rising air forms large convection cells circulating toward the poles.
Forced Convection
Fluid is circulated across the heated surface by an external mechanical pump, fan, or blower:
- Human Cardiovascular System: Blood pumped by the heart carries metabolic heat from core organs to skin capillaries for dissipation.
- Automobile Radiators: Water circulated by an engine pump transfers heat to cooling fins blown by a fan.
- Computer Heat Sinks: Forced air draft from high-RPM fans expels heat from microprocessor cooling fins.
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