temperature, the variation can be small over a significant range of temperatures for some common materials. In anisotropic materials, the thermal conductivity typically varies with orientation; in this case is represented by a second-order tensor. In non-uniform materials, varies with spatial location. For many simple applications, Fourier's law is used in its one-dimensional form, for example, in the direction: In an isotropic medium, Fourier's law leads to heat equation with a fundamental solution famously known as heat kernel. Integral form By integrating the differential form over the material's total surface , we arrive at the integral form of Fourier's law: where (including the SI units): is the amount of heat transferred per unit time (in W), is an oriented surface area element (in m2). The above differential equation, when integrated for a homogeneous material of 1-D geometry between two endpoints at constant temperature, gives the heat flow rate as where is the time interval during which the amount of heat flows through a cross-section of the material, is the cross-sectional surface area, is the temperature difference between the ends, is the distance between the ends. This law forms the basis for the derivation of the heat equation. Conductance Writing where is the conductance, in W/(m2 K). Fourier's law can also be stated as: The reciprocal of conductance is resistance, is given by: Resistance is additive when several conducting layers lie between the hot and cool regions, because and are the same for all layers. In a multilayer partition, the total conductance is related to the conductance of its layers by: or equivalently So, when dealing with a multilayer partition, the following formula is usually used: For heat conduction from one fluid to another through a barrier, it is sometimes important to consider the conductance of the thin film of fluid that remains stationary next to the barrier. This thin film of fluid is difficult to quantify because its characteristics depend upon complex conditions of turbulence and viscosity—but when dealing with thin high-conductance barriers it can sometimes be quite significant. Intensive-property representation The previous conductance equations, written in terms of extensive properties, can be reformulated in terms of intensive properties. Ideally, the formulae for conductance should produce a quantity with dimensions independent of distance, like Ohm's Law for electrical resistance, , and conductance, . From the electrical formula: , where ρ is resistivity, x is length, and A is cross-sectional area,