Introduction to Heat Transfer

Why it matters

Heat transfer is crucial in various engineering applications, from designing efficient thermal systems like heat exchangers to ensuring the safety and performance of mechanical components. Understanding heat transfer principles helps engineers optimize energy use and improve system reliability.

Key ideas

• Heat Transfer Modes: Heat can be transferred via conduction, convection, and radiation. Each mode has distinct mechanisms and governing equations.
• Conduction: Energy transfer by microscopic interactions in solids or fluids, without requiring bulk material motion. Governed by Fourier's law.
• Convection: Transfer of heat between a solid surface and a fluid (liquid or gas) in motion. Described by Newton's law of cooling.
• Radiation: Transfer of heat in the form of electromagnetic waves, which can occur in a vacuum. Governed by Stefan-Boltzmann law.
• Thermal Conductivity: A material property indicating how well a material conducts heat.
• Heat Flux: The rate of heat energy transfer per unit area.

Formulas

• Fourier's Law of Conduction: q = -k·A·(dT/dx)
  • q: Heat transfer rate (W)
  • k: Thermal conductivity (W/m·K)
  • A: Cross-sectional area (m²)
  • dT/dx: Temperature gradient (K/m)
• Newton's Law of Cooling: q = h·A·(T_s - T_∞)
  • q: Heat transfer rate (W)
  • h: Convective heat transfer coefficient (W/m²·K)
  • A: Surface area (m²)
  • T_s: Surface temperature (K)
  • T_∞: Fluid temperature (K)
• Stefan-Boltzmann Law: q = ε·σ·A·(T⁴ - T₀⁴)
  • q: Radiative heat transfer rate (W)
  • ε: Emissivity (dimensionless)
  • σ: Stefan-Boltzmann constant (5.67 × 10⁻⁸ W/m²·K⁴)
  • A: Surface area (m²)
  • T: Absolute temperature of the surface (K)
  • T₀: Absolute temperature of the surroundings (K)

The net radiation expression assumes a diffuse-gray surface viewing large isothermal surroundings through a nonparticipating medium. General finite-surface exchange also needs view factors and surface properties. Conduction example assumptions are steady one-dimensional transfer through a plane wall with constant k and no internal heat generation.

Worked example

Problem: Calculate the heat transfer rate through a 0.5 m² wall with a thermal conductivity of 0.8 W/m·K, where temperature rises by 10 K in the positive x direction across the wall and the wall thickness is 0.1 m.

1. Identify the formula: Use Fourier's Law of Conduction.

   q = -k·A·(dT/dx)

2. Substitute the given values:

   q = -0.8 W/m·K · 0.5 m² · (10 K / 0.1 m)

3. Calculate:

   q = -0.8 · 0.5 · 100

   q = -40 W

4. Interpret the result: The negative sign indicates the direction of heat flow. The magnitude of the heat transfer rate is 40 W.

Common mistakes

• Confusing the direction of heat flow, especially in conduction problems.
• Incorrectly applying the temperature difference in convection problems.
• Neglecting the emissivity factor in radiation calculations.

For GATE ME

Questions often involve calculating heat transfer rates using the basic formulas for conduction, convection, and radiation. Practice problems that require identifying the correct mode of heat transfer and applying the appropriate formula.

Quick check

1. What is the primary mode of heat transfer in a vacuum?
2. Which property measures a material's ability to conduct heat?
3. What is the unit of the convective heat transfer coefficient?

Answers: 1. Radiation 2. Thermal conductivity 3. W/m²·K