Heat Transfer

Heat Transfer

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Conduction

\[Q = \frac{k A (T_2 - T_1)}{d}\]

Properties & Key Points:

  • Conduction is the process of heat transfer through a solid material from the region of higher temperature to the region of lower temperature.
  • \( Q \): Heat transferred.
  • \( k \): Thermal conductivity of the material.
  • \( A \): Area of the cross-section through which heat flows.
  • \( T_2 - T_1 \): Temperature difference between the two ends.
  • \( d \): Thickness of the material.
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Convection

\[Q = h A (T_s - T_\infty)\]

Properties & Key Points:

  • Convection is the process of heat transfer through a fluid (liquid or gas) by the motion of the fluid itself.
  • \( Q \): Heat transferred.
  • \( h \): Heat transfer coefficient.
  • \( A \): Area through which heat is transferred.
  • \( T_s \): Temperature of the surface.
  • \( T_\infty \): Temperature of the surrounding fluid.
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Radiation

\[Q = \sigma A \epsilon (T^4 - T_0^4)\]

Properties & Key Points:

  • Radiation is the transfer of heat in the form of electromagnetic waves, primarily in the infrared spectrum. It does not require a medium.
  • \( Q \): Heat transferred.
  • \( \sigma \): Stefan-Boltzmann constant.
  • \( A \): Surface area of the object emitting radiation.
  • \( \epsilon \): Emissivity of the surface.
  • \( T \): Temperature of the emitting body.
  • \( T_0 \): Temperature of the surroundings.
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Newton's Law of Cooling

\[\frac{dT}{dt} = -k (T - T_s)\]

Properties & Key Points:

  • Newton's Law of Cooling describes the rate at which the temperature of an object decreases due to the surrounding medium.
  • \( \frac{dT}{dt} \): Rate of change of temperature.
  • \( T \): Temperature of the object.
  • \( T_s \): Temperature of the surrounding medium.
  • \( k \): Cooling constant.
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Heat Capacity

\[C = \frac{Q}{\Delta T}\]

Properties & Key Points:

  • Heat capacity is the amount of heat required to change the temperature of an object by one degree Celsius.
  • \( C \): Heat capacity.
  • \( Q \): Heat absorbed or released.
  • \( \Delta T \): Change in temperature.
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Specific Heat Capacity

\[Q = mc \Delta T\]

Properties & Key Points:

  • Specific heat capacity is the amount of heat required to change the temperature of one unit mass of a substance by one degree Celsius.
  • \( Q \): Heat absorbed or released.
  • \( m \): Mass of the substance.
  • \( c \): Specific heat capacity of the substance.
  • \( \Delta T \): Change in temperature.
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Latent Heat

\[Q = m L\]

Properties & Key Points:

  • Latent heat is the amount of heat required to change the phase of a substance without changing its temperature.
  • \( Q \): Heat absorbed or released.
  • \( m \): Mass of the substance.
  • \( L \): Latent heat (latent heat of fusion for melting, latent heat of vaporization for boiling).
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Stefan-Boltzmann Law

\[P = \sigma A T^4\]

Properties & Key Points:

  • Stefan-Boltzmann law describes the power radiated by a black body in terms of its temperature.
  • \( P \): Power radiated by the body.
  • \( \sigma \): Stefan-Boltzmann constant.
  • \( A \): Surface area of the body.
  • \( T \): Absolute temperature of the body.
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Thermal Conductivity

\[k = \frac{Q d}{A (T_2 - T_1) t}\]

Properties & Key Points:

  • Thermal conductivity is a material property that indicates how well a material conducts heat.
  • \( k \): Thermal conductivity of the material.
  • \( Q \): Heat transferred.
  • \( d \): Thickness of the material.
  • \( A \): Area of the cross-section.
  • \( T_2 - T_1 \): Temperature difference.
  • \( t \): Time taken for the heat transfer.
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Thermal Expansion

\[\Delta L = \alpha L_0 \Delta T\]

Properties & Key Points:

  • Thermal expansion refers to the increase in the size of a material when its temperature is increased.
  • \( \Delta L \): Change in length.
  • \( \alpha \): Coefficient of linear expansion.
  • \( L_0 \): Original length of the material.
  • \( \Delta T \): Change in temperature.
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Joule's Law of Heating

\[Q = I^2 R t\]

Properties & Key Points:

  • Joule's law states that the heat produced by an electric current is proportional to the resistance of the conductor and the square of the current.
  • \( Q \): Heat produced.
  • \( I \): Current through the conductor.
  • \( R \): Resistance of the conductor.
  • \( t \): Time for which the current flows.
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