Summary of Heat Transfer | Maha Revision | Mechanical

Summary of "Heat Transfer | Maha Revision | Mechanical"

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Main Ideas, Concepts, and Lessons Conveyed

1. Introduction and Exam Preparation

• The session is a comprehensive revision on Heat Transfer for mechanical students, also useful for chemical and PK students.
• Announcement of a live mock test on YouTube scheduled for 31st January at 2:30 PM following the GATE exam pattern (MCQ format).
• The revision covers the entire syllabus with a focus on important concepts and problem-solving strategies.

2. Basics of Heat Transfer

• Heat Transfer is energy transfer due to temperature difference between a system and its surroundings.
• Modes of energy transfer:
  • Heat Transfer (energy transfer due to temperature difference)
  • Work transfer
  • Mass transfer
• Heat Transfer is governed by the Second Law of Thermodynamics, which dictates the direction of heat flow from higher to lower temperature.

3. Modes of Heat Transfer

• Conduction: Heat Transfer through a solid medium.
  • Governed by Fourier’s Law of Heat Conduction.
  • Rate of Heat Transfer is proportional to temperature difference and cross-sectional area, inversely proportional to thickness.
  • Mathematical form:
    Q̇ = -k A dT/dx
    where k = Thermal Conductivity.
  • Heat flux form:
    q = -k dT/dx
  • Thermal Conductivity unit: W/m·K.
  • Temperature gradient (dT/dx) is the slope of the temperature profile.
  • Problems include slab, cylindrical, and spherical coordinates.
  • General heat conduction equation and its forms (Laplace, Poisson, Diffusion equations) depending on steady/unsteady state and internal heat generation.
• Convection: Heat Transfer between a solid surface and a fluid.
  • Governed by Newton’s Law of Cooling:
    Q̇ = h A (T_s - T_∞)
    where h = convective Heat Transfer coefficient.
  • Convective coefficient depends on:
    • Type of convection (free or forced)
    • Flow regime (laminar or turbulent)
    • Fluid properties (liquid or gas)
    • Surface roughness and orientation
• Radiation: Heat Transfer through electromagnetic waves.
  • Governed by Stefan-Boltzmann Law for black bodies:
    E = σ T⁴
    where σ = Stefan-Boltzmann constant.
  • For non-black bodies, emissivity (ε) modifies the radiation:
    E = ε σ T⁴
  • Radiation heat exchange between two bodies involves view factors (configuration factors) and emissivities.
  • Medium between bodies can be participating or non-participating in radiation.

4. Heat Conduction in Different Geometries

• Cartesian coordinates for slab/wall problems.
• Cylindrical and spherical coordinates for pipes and spheres.
• Heat conduction problems classified into:
  • Steady state without internal heat generation (Laplace equation)
  • Steady state with internal heat generation (Poisson equation)
  • Transient conduction (Diffusion equation)
• Thermal diffusivity α = k / (ρ c) explains the rate of heat conduction relative to heat storage.

5. Thermal Properties of Materials

• Thermal Conductivity highest in diamond (non-metal), followed by metals (silver highest, then copper, gold, aluminum, iron).
• Thermal Conductivity depends on free electron movement and lattice vibration.
• Metals: Thermal Conductivity decreases with temperature (except aluminum and uranium).
• Gases: Thermal Conductivity increases with temperature due to increased molecular velocity.
• Liquids: generally Thermal Conductivity decreases with temperature (exceptions like mercury).
• Specific heat and heat capacity concepts explained with units.

6. Heat Transfer Through Composite Walls

• Series connection: Walls arranged one after another.
  • Equivalent thermal resistance:
    R_eq = R₁ + R₂ + ... + R_n
  • Equivalent Thermal Conductivity calculated based on total thickness and sum of individual resistances.
  • Intermediate temperature can be calculated using energy balance and thermal resistances.
• Parallel connection: Walls arranged side by side.
  • Equivalent thermal resistance:
    1 / R_eq = 1 / R₁ + 1 / R₂ + ... + 1 / R_n
  • Equivalent Thermal Conductivity depends on area fractions and conductivities.
• Combination of series and parallel connections possible.

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Educational

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