Heat Generation in a Cell

Heat generation in a cell can be defined quite simple for the case where the cell is operating within it’s normal limits. The following expression gives the heat flow [W]:

heat generation in a cell

Where: I = current [A], Voc = open circuit voltage [V], Tref = reference temperature [K], T = cell temperature [K]

The first part of this equation is the irreversible Joule heating term:

joule heating term for a battery cell

The second part is the reversible entropy term or Reaction heat terms:

entropy heating term for a battery cell

A comparison of these two terms is shown based on the experimental analysis [1] of a power type
prismatic LMO-G (lithium manganese oxide/graphite) with nominal capacity 8 Ah. The battery has a maximum discharge current rate of 20C and maximum charge current rate of 10C.

heat generation in a battery cell
A comparison of Joule heating and Reaction heating (entropy) at 1C discharge rate and different temperatures [Reference 1].

From these graphs you see that the entropy term can be endothermic under certain conditions. When charging this cell the entropy term becomes very significant, especially at low SoC. Charging the fully discharged cell shows that it will cool down even further until it reaches around 20% SoC.

This shows how important it is to fully characterise the thermal behaviour of a cell in order to properly model and then design a battery pack to optimise charging.

heat generation in a battery cell
A comparison of Joule heating and Reaction heating (entropy) under charge and discharge conditions [Reference 1].

At high discharge rates the joule heating term dominates, as expected. It is under high discharge rates that often the heating is approximated as just I2Rint. Where Rint is the internal resistance of the cell.

References


Thermal conductivity of a cell

Thermal Conductivity of the Active Layers

If we look at the active layers of a cell the thermal conductivity in the plane of the layers is approximately 10x to 100x that through the planes.

This should not be unexpected as the electrodes are made from sheets of aluminium and copper. Two of the best materials for thermal conductivity.

These values though have a large range [Ref 1]:

  • 15 to 160 W/mK In-Plane
  • 0.2 to 8 W/mK Through-Plane

Specific Heat Capacity of Lithium Ion Cells

The specific heat capacity of lithium ion cells is a key parameter to understanding the thermal behaviour. From literature we see the specific heat capacity ranges between 800 and 1100 J/kg.K

Heat capacity is a measurable physical quantity equal to the ratio of the heat added to an object to the resulting temperature change. Specific heat is the amount of heat per unit mass required to raise the temperature by kelvin (one degree Celsius).

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