Chapter 2: Review of Thermal Sciences

Thermal Sciences Overview

  • Thermodynamics
  • Heat Transfer
  • Fluid Mechanics

Application example: Solar collector design

Thermodynamics: Key Concepts

  1. First Law of Thermodynamics
  2. Second Law of Thermodynamics
  3. Energy, Enthalpy, and Specific Heat
  4. Energy Transfer: Heat and Work
  5. Steady-Flow Energy Balance

First Law of Thermodynamics

Energy balance for a system:

$E_{in} - E_{out} = \Delta E_{system}$

For steady-flow:

$\dot{E}_{in} = \dot{E}_{out}$

Second Law of Thermodynamics

  • Energy has quality and quantity
  • Processes occur in the direction of decreasing energy quality
  • Example: Heat flows from hot to cold

Energy, Enthalpy, and Specific Heat

  • Internal energy (U): Sum of all microscopic energies
  • Enthalpy (H): H = U + PV
  • Specific heat: Energy required to raise temperature of unit mass by one degree

Energy Transfer: Heat and Work

  • Heat (Q): Energy transfer due to temperature difference
  • Work (W): Energy transfer that is not heat
  • Power: Work per unit time

Steady-Flow Energy Balance

For a system with negligible kinetic and potential energy changes:

$\dot{Q} = \dot{m}\Delta h = \dot{m}c_p\Delta T$

Heat Transfer Modes

  1. Conduction
  2. Convection
  3. Radiation

Conduction Heat Transfer

Fourier's law:

$\dot{Q}_{cond} = -kA\frac{dT}{dx}$

Where:

  • k: Thermal conductivity
  • A: Heat transfer area
  • $\frac{dT}{dx}$: Temperature gradient

Convection Heat Transfer

Newton's law of cooling:

$\dot{Q}_{conv} = hA_s(T_s - T_\infty)$

Where:

  • h: Convection heat transfer coefficient
  • $A_s$: Surface area
  • $T_s$: Surface temperature
  • $T_\infty$: Fluid temperature

Radiation Heat Transfer

Stefan-Boltzmann law:

$\dot{Q}_{rad} = \varepsilon\sigma A_s(T_s^4 - T_{surr}^4)$

Where:

  • $\varepsilon$: Emissivity
  • $\sigma$: Stefan-Boltzmann constant
  • $T_s$: Surface temperature
  • $T_{surr}$: Surrounding temperature

Fluid Mechanics: Key Concepts

  1. Properties of fluids
  2. Viscosity
  3. Fluid flow in pipes

Viscosity

  • Measure of fluid's resistance to deformation
  • Dynamic viscosity (μ) and kinematic viscosity (ν)
  • Temperature dependence:
    • Liquids: Decreases with temperature
    • Gases: Increases with temperature

Fluid Flow in Pipes

Pressure drop for all types of internal flows:

$\frac{\Delta P}{L} = f\frac{L}{D}\frac{\rho V^2}{2}$

Where:

  • f: Friction factor
  • L: Pipe length
  • D: Pipe diameter
  • $\rho$: Fluid density
  • V: Average fluid velocity

Thermochemistry: Key Concepts

  1. Combustion processes
  2. Enthalpy of formation and combustion
  3. Heating values of fuels

Combustion Processes

  • Complete vs. incomplete combustion
  • Stoichiometric (theoretical) air
  • Excess air and air-fuel ratio

Enthalpy of Formation and Combustion

  • Enthalpy of formation: Energy content due to chemical composition
  • Enthalpy of combustion: Energy released during complete combustion

Heating Values of Fuels

  • Higher Heating Value (HHV)
  • Lower Heating Value (LHV)
  • Relationship: HHV = LHV + (mh_fg)_H2O

Heat Engines and Power Plants

Figure_2-35
Heat engine schematic

  • Thermal efficiency:

    $\eta_{th} = \frac{W_{net,out}}{Q_{in}} = 1 - \frac{Q_{out}}{Q_{in}}$

  • Carnot efficiency:

    $\eta_{th,Carnot} = 1 - \frac{T_L}{T_H}$

Refrigerators and Heat Pumps

Figure_2-39
Refrigerator and heat pump schematics

  • Coefficient of Performance (COP):

    • Refrigerator: $COP_{R} = \frac{Q_L}{W_{net,in}}$
    • Heat Pump: $COP_{HP} = \frac{Q_H}{W_{net,in}}$
  • Carnot COP:
    • Refrigerator: $COP_{R,Carnot} = \frac{T_L}{T_H - T_L}$
    • Heat Pump: $COP_{HP,Carnot} = \frac{T_H}{T_H - T_L}$

Conclusion

  • Thermal sciences are crucial for understanding renewable energy systems
  • Thermodynamics, heat transfer, and fluid mechanics form the foundation
  • Applications range from solar collectors to power plants and refrigeration systems