README.md

Pouch-Cell Through-Thickness Thermal Gradient

This base-MATLAB example resolves a pouch cell as a one-dimensional slab of finite thermal volumes. It connects uniform internal heat generation to through-thickness conduction and independent convection conditions at the two broad faces.

Engineering Question

When the two pouch-cell faces see different cooling conditions, where does the hot spot move, how large is the through-thickness temperature gradient, and does the numerical model conserve energy?

Model Topology

left fluid <-> [CV 1] - [CV 2] - ... - [CV N] <-> right fluid
                  uniform volumetric heat generation

The default cell uses 15 equal, cell-centered control volumes.

Element	Meaning	Illustrative value
L	Cell thickness	8 mm
A	Broad-face area	0.015 m2
rho	Effective density	2200 kg/m3
cp	Effective specific heat	900 J/(kg K)
kz	Effective through-plane conductivity	0.45 W/(m K)
hleft	Left-face heat-transfer coefficient	35 W/(m2 K)
hright	Right-face heat-transfer coefficient	12 W/(m2 K)
Qcell	Applied whole-cell heat profile	0 to 12 W

These values are deliberately illustrative. A real layered pouch cell is anisotropic and requires geometry-, compression-, SOC-, and temperature-qualified properties.

Finite-Volume Relations

For node i, the thermal state follows:

Cnode * dTi/dt =
    Qcell / N
    + Gz * (Ti-1 - Ti)
    + Gz * (Ti+1 - Ti)

where:

Cnode = rho * cp * A * dx
Gz = kz * A / dx

At each boundary, the half-control-volume conduction resistance and convection resistance are combined:

Gboundary = A / (dx / (2*kz) + 1/h)
Qboundary = Gboundary * (Tboundary-node - Tfluid)

Positive boundary heat denotes heat removed from the cell. Internal interface flows cancel exactly when all control-volume balances are summed.

Included Files

examples/pouch-cell-thermal-gradient/
  README.md
  pouch_cell_thermal_default_parameters.m
  pouch_cell_thermal_default_profile.m
  simulate_pouch_cell_thermal_model.m
  run_pouch_cell_thermal_model.m
  check_pouch_cell_thermal_model.m

Requirements

• MATLAB R2026a is the verified release.
• The example uses base MATLAB only.
• No Simulink, Simscape, PDE, or additional toolbox is required.

How To Run

From this folder:

run_pouch_cell_thermal_model

For deterministic no-plot validation:

check_pouch_cell_thermal_model

Expected output:

Pouch-cell thermal-gradient check passed.
Peak node temperature: 43.83 degC at 5.60 mm and 1800 s
Peak through-thickness node spread: 3.09 degC
Symmetric steady center error: 0.003 degC
Medium-to-fine grid center difference: 0.0024 degC

The simulator accepts native irregular timestamps or a requested uniform sample time:

profile = pouch_cell_thermal_default_profile();
parameters = pouch_cell_thermal_default_parameters();
result = simulate_pouch_cell_thermal_model( ...
    profile, parameters, 0.5);

Key outputs include every node temperature, inferred surface temperatures, center and volume-average temperature, every interface heat flow, both boundary heat-removal rates, hot-spot position, spatial temperature spread, and node-level and whole-cell energy-balance diagnostics.

Validation Checks

The no-plot script verifies that:

• uniform heat allocation sums to the prescribed whole-cell heat;
• internal interface heat cancels from the whole-cell balance;
• every node and the complete slab close their discrete energy balances;
• inferred surface temperatures close both convection relations;
• asymmetric cooling creates a bounded gradient and shifts the hot spot;
• a zero-heat isothermal case remains exactly at equilibrium;
• equal boundary conditions preserve mirror symmetry;
• a long symmetric run approaches the continuous slab steady-state solution;
• center temperature converges as the spatial grid is refined;
• native irregular timestamps remain unchanged;
• malformed inputs and unstable explicit time steps are rejected; and
• repeated simulations are deterministic.

Continuous Steady-State Reference

For uniform volumetric heat qdot, equal convection coefficient h on both faces, and common fluid temperature Tinf, the continuous symmetric slab has:

Tcenter - Tinf = qdot * L / (2*h) + qdot * L^2 / (8*kz)

The check compares the finite-volume transient against this independent reference after the thermal response has settled.

Limitations

• Parameters are educational placeholders and are not fitted to a particular cell or cooling plate.
• The model resolves only the through-thickness direction. It omits in-plane gradients, tabs, edge cooling, current-collector detail, and layer-by-layer properties.
• Heat generation is spatially uniform and externally prescribed rather than calculated from an electrochemical model or calorimetry data.
• Material properties and heat-transfer coefficients are constant.
• Contact resistance is represented only through the effective boundary coefficients and is not separated from convection.
• The explicit solver rejects time steps outside a conservative monotonic stability bound; perform temporal and spatial refinement studies for new parameter sets.
• Phase change, gas generation, thermal runaway, propagation, and safety controls are outside the model scope.
• Calibrate and validate against spatial temperature or heat-flux measurements before using the model for design or safety decisions.