Fourier's law is a famous French scientistFourier An article proposed in 1822Thermodynamic law。This law refers to the amount of heat conduction per unit time through a given section in the process of heat conduction,ProportionalThe sum of temperature change rate andCross-sectional area, andHeat transferAnd the direction of temperature rise is opposite.[1]
The law of heat conduction, also known as Fourier's law, indicates the heat passing through a given section in unit time,Positive proportionThe sum of temperature change rate andCross-sectional area, andHeat transferAnd the direction of temperature rise is opposite.We can express this law in two equivalent forms: the overall form andDifferenceForm.
NewtonianCooling lawIs a discrete generalization of Fourier's law, andOhm's lawIs an electrical generalization of Fourier's law.[2]
Text expression of Fourier's law: in the phenomenon of heat conduction, the heat passing through a given section in unit time,Positive proportionThe sum of temperature change rate andCross-sectional areaThe direction of heat transfer is opposite to the direction of temperature rise.
Fourier's LawHeat fluxJTThe expression is as follows:
It can be used to calculate the heat conduction.Wherein, heat flow densityJT(W·m-2）Is on the unit area perpendicular to the transmission directionxDirectionalHeat transfer rate。It is different from thetemperature gradientdT/dxIs proportional.Proportional constantκIs a transport characteristic calledThermal conductivity(also known asthermal conductivity）, the unit is (W · m-1·K-1)。It can also be expressed as follows:
Where dQ/dt(QPrevious point) isThermal conduction rate(or recorded asIT）, in W
Fourier's law
AIs the heat transfer area, in mtwo
TIs the temperature, in K
xIs the coordinate on the heat conduction surface, in m
Where:JTIs onrThe heat flux in the direction perpendicular to the isothermal surface.The heat flux is a vector, which can also be decomposed into several components.
In the above formulaminus signIt indicates that the heat transfer direction is opposite to the temperature gradient direction.[4]
[Physical analogy] The thermal conductivity and heat flux in heat can be compared to the conductivity and current density in electricityJ=σE。rememberET=dT/dxIs the temperature field intensity, then the heat flux can be written asJT=-κET。If the temperature difference ofInverse number-ΔTRecorded as temperature pressure difference ΔUT, then Δ can be deducedUT=RTIT, which is called heatOhm's law。amongITIs the thermal conductivity rate (see the above formula),RTRepresents thermal resistance, which can be deducedRT=ρTL/A, which is calledLaw of thermal resistance, whereρT=1/κIs the thermal resistance. The thermal resistance is also similar to the resistanceparallel connectionRules.[5]
In addition, as mentioned above, Fourier's law is a vector expression.Heat fluxIs perpendicular toIsothermal surfaceAnd along the direction of temperature decrease.Fourier's law applies to all substances, regardless of their state (solid, liquid or gas).
Functional significance
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Application of heat and mass movement and transfer
Heat energy (particles) possessed by matterRandom movementKinetic energy) is matterEnergy formOne is that it corresponds to the thermal mass of matter and can be regarded as the mass of pyron gas.In the process of heat conduction of objectsHeat transportIt corresponds to the transport of thermal mass (hot gas mass).Different from convective transport, heat and mass transport belongs to molecular transport or diffusion transport.It can use the macroscopic velocity of hot gas（Drift velocity）To describe.
Descriptivemechanical movement, we need to haveMass of object、Movement speedandaccelerationetc.physical quantityas well asNewton's law of motion。Similarly, in order to describe and study the macro motion of the hot gas, it is necessary to establish physical quantities such as the velocity and acceleration of the hot gas motion.In order to determine the thermionic gasmotion state The change of and the non-equilibrium applied on the hot gasForceWe need to establish the relationship between heat and massLaw of motion。
We are based on Fourier's law and neglectinertia forceThermionic gasconservation equation , the above thermionic gas is obtainedViscous forceExpression for.At the same time, it can be seen from the formula that the Fourier heat conduction law reflects the pressure and viscosity of the hot gasForce balance, is thermionic gasmomentum equation An approximation that ignores inertial forces.
It is found that the Fourier heat conduction law essentially ignores the heat carrier gas under the condition of inertial forcePressure gradientViscousequilibrium equation ；When the inertia force can be neglected, the momentum conservation equation of the hot gas degenerates into the Fourier heat conduction law.At extremely low temperature or extremely high heat flux, Fourier heat conduction law is no longer applicable.
