Heat Transfer

 

    Heat (thermal energy) is energy in transit which occurs as a result of a temperature gradient or difference. This temperature difference is thought of as a driving force that causes heat to flow.

    There are three different ways of which heat can transfer:

i) Conduction - transfer of heat by direct contact of particles of matter
ii) Convection - transfer of heat through a moving fluid at various temperature
iii) Radiation - transfer of heat through an empty space

    Temperature of an object can be measured using varius apparatus:

  • Thermometer
  • Thermocouple
  • Thermistor
  • Infrared thermometers
  • Optical pyrometer

 

Conduction

    A temperature gradient within a homogeneous substance results in an energy transfer rate within the medium can be calculated using Fourier's Law:

 

where
Q - heat transfer (W)                                        A - area (m2)
q - heat flux (Wm-1)                                         T - temperature (K)
k - thermal conductivity (Wm-1K-1)              x - distance (m)

 

i) Multi-layered wall - The resistance network analogy

 

    Can be modelled as:

 

    As the system is in steady state and no internal heat generated, the heat flow enter and exit each layer are equal:

 

ii) Polar coordinates

 

iii) Multidimensional conduction - The general conduction equation

    Consider energy conducting throught a cube:

    Rate of energy conducted into the system:

 

    Rate of energy conducted out of the system:

 

    Rate of energy generated inside the system:

    Rate of energy stored inside the system:

    Rate of heat conducted into the system + Rate of heat generated in the system = Rate of heat conducted out of the system + Rate of heat accumulated in the system

 

Convection

    Newton's Law of cooling - the rate of heat loss of a body is proportional to the difference in temperatures between the body and its surroundings

where
Q - heat transfer (W)                                                          T - temperature(K)
h - heat transfer coefficient (Wm-2K-1)

i) Time dependent cooling by natural convection

ii) Forced convection heat transfer

  • Boundary layer:

  • Reynolds Number:

where 
Re - Viscous force                                    v - Kinematic viscosity (m2s-1)
L - Characteristic length (m)                  μ - Dynamic viscosity (kgm-1s-1)
U - Free stream velocity (ms-1)             ρ - Fluid density (kgm-3)

 

  • Prandit number:

where
v - Kinematic viscosity (m2s-1)                α - Thermal diffusivity (m2s-1)

 

  • Nusselt number:

where
h - heat transfer coefficient (Wm-2K-1)            L - Characteristic length (m)
k - Thermal conductivity (Wm-1s-1) 

 

 

Radiation

  • The transfer of energy by electromagnetic waves
  • All objects emit certain amount of thermal radiation
  • There is a thermal energy component to all electromagnetic radiation - its level depends on the temperature of the body
  • No medium is required and the energy transfer is highly dependent on temperature

    Properties of radiation:

Black body is an ideal emitter and receiver (α=1)

 

    Stefan-Boltzmann Law:

where
Q - Heat radiated (W)                σ - Stefan-Boltzmann constant (Wm-2K-4)
A - Surface area (m2)                T - Body temperature (K)

    A grey body is a better approximation of real surfaces, it inviles the value ε - emissivity:

 

Contact

Larona BME

Website Administrator

 

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