Deep-Frying French Fry Lab (2D)

What is modelled

A potato strip is lowered into hot oil. The page solves heat conduction through the strip with a moving evaporation front: the surface layer dries first and forms a crust, the front moves inward, and while there is water in a layer its temperature stays at 100 C. Bubbles in the oil follow the evaporation rate, the colour follows a surface browning reaction, and the cross-section panel shows the dried crust, the wet core or the temperature field. The strip is treated as a one-dimensional slab (depth from the nearest face), then drawn as a square.

Equations

• Heat conduction with variable properties: ρ cp(w) ∂T/∂t = ∂/∂x (k(w) ∂T/∂x), with k(w) = kcrust + (kwet − kcrust) w/w0 and the same mixing for c_p (c_wet = 3600, c_dry = 1900 J/kg/K).
• Surface boundary: q = h (Toil − Ts) in series with the half-cell resistance; centre is symmetric (zero flux).
• Evaporation (enthalpy method): when a cell would exceed 100 C and still holds water, the excess energy evaporates water instead: Δm = ρ cp (T − 100) V / Lv, L_v = 2.26 MJ/kg, and the temperature is held at 100 C until the water in that cell is gone.
• Quasi-steady Stefan estimate of the crust depth: s(t) = √( 2 kcrust (Ts − 100) t / (ρ w0 Lv) ), so the crust grows like √t.
• Surface browning extent db/dt = (1 − b) k exp[−(Ea/R)(1/Ts − 1/Tref)] (E_a = 110 kJ/mol, T_ref = 170 C), slowed while the surface is still wet.
• Oil uptake (illustrative, empirical): oil mass per initial mass = φ (w0 − w) ρoil/ρwater, a share φ of the void volume left by the evaporated water refilled while the fries cool.

Checks run in the page

• Inert slab (no boiling, constant properties, surface held at 180 C): numerical centre temperature against the exact cosine-series solution at Fo = 0.5.
• Evaporation front: crust depth after 60 s against the Stefan estimate.
• Energy balance of a 180 s fry: heat in = sensible heat + latent heat of the evaporated water.

Honest simplifications

• One-dimensional slab: corners and the strip ends are ignored; there is no vapour pressure or liquid water transport inside the potato, no shrinkage, no starch gelatinisation kinetics and no oil temperature drop when the basket goes in (oil is held at the set temperature). The heat-transfer coefficient is one number (real values vary strongly with bubbling), the thermal properties are typical textbook values, and the oil-uptake relation is an illustration, not a validated prediction. Fry size, bubbles and oil volume are drawn larger or simplified for clarity.

What to try

• Compare 6, 9 and 15 mm strips: the crust depth is the same at a given time but the core takes very different times to reach 100 C.
• Lower the oil to 140 C: the crust grows slowly, the fry stays pale and the frying time is long.
• Cut the heat-transfer coefficient (weak boiling) to see the surface lag behind the oil.
• Lift the basket and watch the core keep heating from the hot surface.