There are three basic ways of heat transfer: heat conduction, heat convection, and heat radiation. For lithium-ion batteries, their heat transfer model includes four parts: heat generation, heat conduction, convective heat transfer, and thermal radiation. That is, the total heat generated during the charging and discharging process of lithium-ion batteries is conducted inside the lithium-ion battery and ultimately to the surface of the battery, Then, on the surface of the lithium-ion battery, heat is dissipated through direct convective heat exchange with external fluids and thermal radiation from surrounding components. At the same time, some of the heat is absorbed by the internal materials of the lithium-ion battery, which will cause the temperature of the lithium-ion battery to rise.
(1) Heat conduction
Heat conduction refers to the phenomenon of heat transfer achieved through the thermal motion of microscopic particles such as molecules, atoms, and self electrons, when substances in contact with each other or substances themselves have a temperature difference and these substances do not undergo relative displacement.
For lithium-ion batteries, there is heat conduction in the electrodes, electrolytes, separators, and shell of the lithium-ion battery. According to Fourier’s law, the heat conduction flow rate is expressed as:
In the formula, λ Is the thermal conductivity coefficient, in W/(m • K); A is the cross-sectional area perpendicular to the x direction of heat conduction, in m ^ 2; T/x is the temperature gradient along the direction of heat flow on the cross-section, measured in K/m.
(2) Convective heat transfer
Convective heat transfer refers to the phenomenon of heat transfer between a fluid and a solid due to the temperature difference between the two. For lithium-ion batteries, convective heat transfer occurs on the surface of the battery, and the fluid is generally an incompressible Newtonian fluid. According to Newton’s cooling law, the convective heat transfer heat flow rate Qc is expressed as:
In the formula, h is the convective heat transfer coefficient, in units of W/(m ^ 2 • K); Z is the convective heat transfer area, in m ^ 2; Tw and Tf are the average temperatures of the wall and fluid, respectively, expressed in K.
(3) Thermal radiation
Thermal radiation refers to the phenomenon where an object with a temperature higher than absolute zero radiates energy outward, while also absorbing the energy radiated from surrounding objects. It is the radiation of electromagnetic waves by an object due to its temperature. According to Stefan Boltzmann’s law, the magnitude of radiative heat is related to the surface material and area of the object, as well as the absolute temperature difference between the two objects that undergo thermal radiation. The radiative heat transfer Qw is expressed as:
In the formula, ε Is the thermal radiation coefficient, which is the blackness of an object; σ A Boltzmann constant for Stefan, approximately 5.68xl0 ^ -8W/(m ^ 2 • K ^ 4); A1 is the area of radiation surface 1, measured in m ^ 2; F12 is the shape coefficient of radiation surface 1 to radiation surface 2; The temperatures of radiation surfaces 1 and 2, respectively, are measured in K. For the research in this article, due to the small temperature difference between lithium-ion batteries and surrounding objects, thermal radiation can be ignored.
Therefore, the external heat transfer Qe of lithium-ion batteries can be simplified as:
Since the heat generation can be expressed as a formula, the heat Qi absorbed by lithium-ion batteries is:
In the formula, m is the mass of the lithium-ion battery, in kilograms; C is the specific heat capacity of lithium-ion batteries, in J/(kg • k); Δ T is the temperature rise caused by heat absorption in lithium-ion batteries, measured in K.