Unit 6.4: Thermal Conductivity

Definition

Thermal Conductivity:
Thermal conductivity is the ability of a material to conduct or transmit heat through it.

It indicates how easily heat flows through a material from a high-temperature region to a low-temperature region.

Thermal conductivity is represented by the symbol k.

The basic relation governing heat conduction is given by Fourier’s Law of Heat Conduction:

$$q = -kA\frac{dT}{dx}$$

Where:

• $q$ = Rate of heat transfer

• $k$ = Thermal conductivity

• $A$ = Area through which heat flows

• $\frac{dT}{dx}$ = Temperature gradient

The negative sign indicates that heat flows from higher temperature to lower temperature.

Core Concept Explanation

Heat transfer in materials occurs mainly by conduction.

When one part of a material is heated:

1. Atoms in that region gain energy and vibrate faster.

2. These vibrations transfer energy to neighboring atoms.

3. Heat moves through the material from hot region to cold region.

Materials differ in their ability to conduct heat.

• Metals conduct heat very well.

• Insulators conduct heat poorly.

Thermal conductivity measures this ability.

Important Classifications

1. Good Thermal Conductors

These materials allow heat to pass through them easily.

Examples:

• Copper

• Aluminum

• Silver

• Brass

Used in heat exchangers, radiators, cooking utensils.

2. Poor Thermal Conductors (Insulators)

These materials resist heat flow.

Examples:

• Wood

• Glass

• Rubber

• Air

Used for thermal insulation.

Key Principles / Concepts

1. Heat Transfer by Conduction

Heat transfer occurs due to molecular vibration and free electrons.

Metals conduct heat mainly due to free electrons.

2. Temperature Gradient

Heat flow depends on the temperature difference between two points.

Greater temperature difference → greater heat transfer.

3. Material Structure

Thermal conductivity depends on:

• Atomic structure

• Crystal lattice

• Presence of free electrons

Metals have high conductivity, while non-metals have low conductivity.

Important Comparisons

Properties / Characteristics

Typical thermal conductivity values:

Observations:

• Metals generally have high thermal conductivity.

• Non-metals have low thermal conductivity.

Applications in Engineering

1. Heat Exchangers

Materials like copper and aluminum are used because of high conductivity.

2. Radiators

Used in automobile cooling systems to transfer heat efficiently.

3. Cooking Utensils

High conductivity metals allow uniform heat distribution.

4. Thermal Insulation

Materials with low conductivity are used in:

• Refrigerators

• Boilers

• Buildings

Exam-Focused Points

Important points frequently asked in JE/AE exams:

• Thermal conductivity measures ability to conduct heat.

• Represented by k.

• SI unit = W/m·K.

• Metals have high thermal conductivity.

• Insulators have low thermal conductivity.

• Heat conduction follows Fourier’s Law.

Common Exam Traps

Trap 1

Confusing thermal conductivity with thermal expansion.

• Thermal conductivity → heat flow

• Thermal expansion → change in size due to temperature

Trap 2

Assuming all solids conduct heat well.

Correct concept:

• Only metals are good conductors.

Trap 3

Ignoring units.

Correct SI unit:

W/m·K

Example Competitive Exam Questions

Question: What is thermal conductivity?
Answer: The ability of a material to conduct heat.

Question: Which type of materials have high thermal conductivity?
Answer: Metals.

Question: What is the SI unit of thermal conductivity?
Answer: Watt per meter Kelvin (W/m·K).

Question: Which metal is widely used in heat exchangers due to high thermal conductivity?
Answer: Copper.

Question: Which law governs heat conduction in materials?
Answer: Fourier’s Law of Heat Conduction.

Quick Revision Summary

• Thermal conductivity = ability of material to conduct heat.

• Symbol = k.

• SI unit = W/m·K.

• Heat flows from high temperature to low temperature.

• Metals → high thermal conductivity.

• Insulators → low thermal conductivity.

• Governed by Fourier’s Law of heat conduction.