page_title: Thermal resistance
section_title: Radial Systems
hierarchical_section_title: Thermal resistance / Resistance in Composite Wall / Radial Systems
caption_attribution_description: English: Hollow cylinder with convective surface conditions in thermal conduction
context_page_description: Thermal resistance is a heat property and a measurement of a temperature difference by which an object or material resists a heat flow. Thermal resistance is the reciprocal of thermal conductance.
  thermal resistance R in kelvins per watt is a property of a particular component. For example, a characteristic of a heat sink.
  Specific thermal resistance or thermal resistivity Rλ in kelvin metres per watt, is a material constant.
  Thermal insulance has the units square metre kelvins per watt in SI units or square foot degree Fahrenheit hours per British thermal unit in imperial units. It is the thermal resistance of unit area of a material. In terms of insulation, it is measured by the R-value.
context_section_description: Spherical and cylindrical systems may be treated as one-dimensional, due to the temperature gradients in the radial direction. The standard method can be used for analyzing radial systems under steady state conditions, starting with the appropriate form of the heat equation, or the alternative method, starting with the appropriate form of Fourier's law. For a hollow cylinder in steady state conditions with no heat generation, the appropriate form of heat equation is 
            (4)
  Where  is treated as a variable. Considering the appropriate form of Fourier's law, the physical significance of treating  as a variable becomes evident when the rate at which energy is conducted across a cylindrical surface, this is represented as
            (5)
  Where  is the area that is normal to the direction of where the heat transfer occurs. Equation 1 implies that the quantity  is not dependent of the radius , it follows from equation 5 that the heat transfer rate,  is a constant in the radial direction.
  In order to determine the temperature distribution in the cylinder, equation 4 can be solved applying the appropriate boundary conditions. With the assumption that  is constant
            (6)
  Using the following boundary conditions, the constants  and  can be computed
            and          
  The general solution gives us
            and          
  Solving for  and  and substituting into the general solution, we obtain
            (7)
  The logarithmic distribution of the temperature is sketched in the inset of the thumbnail figure.
  Assuming that the temperature distribution, equation 7, is used with Fourier’s law in equation 5, the heat transfer rate can be expressed in the following form
  Finally, for radial conduction in a cylindrical wall, the thermal resistance is of the form
   such that
caption: Hollow cylinder with convective surface conditions in thermal conduction
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