we have , where G is conductance, k is conductivity, x is length, and A is cross-sectional area. For heat, where is the conductance. Fourier's law can also be stated as: analogous to Ohm's law, or The reciprocal of conductance is resistance, R, given by: analogous to Ohm's law, The rules for combining resistances and conductances (in series and parallel) are the same for both heat flow and electric current. Cylindrical shells Conduction through cylindrical shells (e.g. pipes) can be calculated from the internal radius, , the external radius, , the length, , and the temperature difference between the inner and outer wall, . The surface area of the cylinder is When Fourier's equation is applied: and rearranged: then the rate of heat transfer is: the thermal resistance is: and , where . It is important to note that this is the log-mean radius. Spherical The conduction through a spherical shell with internal radius, , and external radius, , can be calculated in a similar manner as for a cylindrical shell. The surface area of the sphere is: Solving in a similar manner as for a cylindrical shell (see above) produces: Transient thermal conduction Interface heat transfer The heat transfer at an interface is considered a transient heat flow. To analyze this problem, the Biot number is important to understand how the system behaves. The Biot number is determined by: The heat transfer coefficient , is introduced in this formula, and is measured in . If the system has a Biot number of less than 0.1, the material behaves according to Newtonian cooling, i.e. with negligible temperature gradient within the body. If the Biot number is greater than 0.1, the system behaves as a series solution. The temperature profile in terms of time can be derived from the equation which becomes The heat transfer coefficient, , is measured in , and represents the transfer of heat at an interface between two materials. This value is different at every interface and is an important concept in understanding heat flow at an interface. The series solution can be analyzed with a nomogram. A nomogram has a relative temperature as the coordinate and the Fourier number, which is calculated by The Biot number increases as the Fourier number decreases. There are five steps to determine a temperature profile in terms of time. Calculate the Biot number Determine which relative depth matters, either x