Heat Transfer Basics

Why it matters

Heat transfer is a fundamental concept in thermodynamics that plays a crucial role in various engineering applications, such as designing heat exchangers, improving energy efficiency in systems, and understanding thermal management in electronics. Mastery of heat transfer principles is essential for engineers to optimize processes and ensure safety in thermal systems.

Key ideas

• Modes of Heat Transfer: Heat can be transferred through conduction, convection, and radiation.
  • Conduction: Heat transport by microscopic interactions in solids or fluids without requiring bulk 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.
• Thermal Conductivity (k): A material property that indicates the ability of a material to conduct heat. Higher values mean better heat conduction.
• Heat Transfer Coefficient (h): Used in convection, it quantifies the heat transfer rate per unit area per unit temperature difference.
• Steady-State vs. Transient Heat Transfer: Steady-state implies no change in temperature with time, while transient involves time-dependent temperature changes.

Formulas

• 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)
• Convection: q = h·A·(T_s - T_∞)
  • q: Heat transfer rate (W)
  • h: Heat transfer coefficient (W/m²·K)
  • A: Surface area (m²)
  • T_s: Surface temperature (K)
  • T_∞: Fluid temperature away from the surface (K)
• Radiation: q = ε·σ·A·(T₁⁴ - T₂⁴)
  • q: Heat transfer rate (W)
  • ε: Emissivity (dimensionless)
  • σ: Stefan-Boltzmann constant (5.67 × 10⁻⁸ W/m²·K⁴)
  • A: Surface area (m²)
  • T₁, T₂: Absolute temperatures of the surfaces (K)

The net radiation expression assumes a diffuse-gray surface completely viewing large isothermal surroundings through a nonparticipating medium; finite surfaces require geometry and emissivity treatment. The rod example assumes steady one-dimensional conduction, constant k, no internal generation and insulated lateral surfaces. Define x so temperature increases by 100 K over 0.5 m; the resulting heat flow is in the negative x direction.

Worked example

Given: A metal rod with a thermal conductivity of k = 200 W/m·K, cross-sectional area A = 0.01 m², and a temperature difference dT = 100 K over a length dx = 0.5 m.

1. Calculate the heat transfer rate using conduction formula:

   q = -k·A·(dT/dx)

   q = -200 W/m·K · 0.01 m² · (100 K / 0.5 m)

   q = -200 W/m·K · 0.01 m² · 200 K/m

   q = -400 W

   Answer: 400 W (The negative sign indicates the direction of heat flow.)

Common mistakes

• Confusing the units of thermal conductivity and heat transfer coefficient.
• Forgetting to convert temperatures to Kelvin when using radiation formulas.
• Misapplying steady-state assumptions to transient problems.

For GATE ME

Questions often involve calculating heat transfer rates using the given formulas, understanding the differences between conduction, convection, and radiation, and applying these concepts to practical problems. Practice problems involving composite walls, fins, and heat exchangers.

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 heat transfer coefficient?

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