Summary of "Heat Transfer | Maha Revision | Mechanical"

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.

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.

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 (Ts - 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.

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.

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.

Series connection: Walls arranged one after another.
- Equivalent thermal resistance: Req = R1 + R2 + ... + Rn
- 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 / Req = 1 / R1 + 1 / R2 + ... + 1 / Rn
- Equivalent Thermal Conductivity depends on area fractions and conductivities.
Combination of series and parallel connections possible.