Physics · Molecular physics and thermodynamics · Grade 7

Tandoor and sandal: heat

Why is a tandoor built of clay, and why is the flatbread baked on its wall?

The situation

At dawn the baker stacks firewood in the tandoor and lights it. After about an hour the inner wall is so hot that dough stuck to it turns into baked, browned flatbread in a few minutes, while the outer wall stays much cooler. In winter the family gathers around the sandal: a small heater underneath keeps the space under the quilt warm for hours. By what routes does heat travel from the fire to the bread, and why is a tandoor built of clay rather than steel?

Topic

Types of heat transfer. Tandoor and sandal: conduction, convection, radiation

Key ideas

Thermal conduction
Convection
Radiation

Formulas

q = - k \frac{d T}{d x}

Fourier's law (heat conduction): $k$ is the thermal conductivity, W/(m·K).

ρ c \frac{\partial T}{\partial t} = \frac{1}{r} \frac{\partial}{\partial r} (k r \frac{\partial T}{\partial r})

The heat equation in a cylindrical wall — in the model the wall is divided into 31 layers (finite differences) and solved.

q_{r a d} = ε σ (T_{1}^{4} - T_{2}^{4})

Radiation (the Stefan–Boltzmann law): $σ = 5.67 \cdot 10^{- 8}$ W/(m²·K⁴), $ε$ is the emissivity. Temperature in kelvin!

q_{c o n v} = h (T_{s} - T_{a i r})

Convection (Newton's law of cooling): for still air outside $h \approx 10$ W/(m²·K).

R = \frac{d}{k}, τ \approx \frac{d^{2}}{α}, α = \frac{k}{ρ c}

The thermal resistance of the wall (per 1 m²) and the order of magnitude of its heating time.

Theory

Three routes

Heat is transferred in three ways. Conduction — through collisions of particles inside a substance: from the inner wall heated by the fire to the outer wall (the coloured layers in the section). Convection — a stream of heated air: hot air rising from the fire, and yard air cooling the outer wall. Radiation — infrared electromagnetic waves: the embers and the hot wall heat the bread from a distance, with no need for air.

Why is a tandoor made of clay?

Clay has a low thermal conductivity ( $k \approx 1$ W/(m·K)) and a large heat capacity. A thick clay wall stores the energy of the fire and releases it slowly to the outside — flatbread can be baked even after the fire has died down. Steel conducts heat about 45 times better: its outer surface heats almost as much as the inner one and the heat goes off into the yard. The heating time of an 8 cm clay wall is $τ \approx d^{2} / α \approx 3$ hours — that is why the outer wall stays quite cool even after an hour of fire.

How is bread baked?

The side of the dough touching the wall is heated by conduction, the open side by radiation from the opposite wall and the embers, and by convection from the hot air. First the water in the dough evaporates: the wet layer does not heat above 100 °C. Once the surface has dried the temperature rises, and above about 150 °C the bread browns. In the model the bread is baked in 5–8 minutes when the wall is at about 300–400 °C; a wall that is too hot (above about 450 °C) burns the bottom of the bread.

The sandal and the limits of the model

In a sandal the quilt ( $k \approx 0.04$ W/(m·K)) conducts heat poorly and keeps the power of the small heater under the quilt: the temperature rises until $Δ T = P / (U A)$ . A sandal with burning charcoal in a closed room creates a risk of poisoning by carbon monoxide (CO). The model is simplified: the tandoor is a cylinder with an inner radius of 35 cm and a height of 90 cm; half of the fire's power is absorbed by the wall; the power of the embers is 20 % of the fire's, their temperature about 700 °C; the dough is 1.2 cm thick and 40 % water; the degree of browning is calculated by an empirical formula.

Steady and unsteady conduction

After the fire is lit the wall heats unsteadily: the temperature of each layer changes with time, and the flow entering the inner surface is much greater than that leaving the outer surface — the difference goes into heating the wall ( $ρ c \partial T / \partial t$ ). This regime lasts about $τ \approx d^{2} / α$ ; the curve on the profile graph straightens during this time. Then a steady state sets in: the temperature no longer depends on time, the flows entering and leaving become equal (compare them in the HUD), and the profile in a flat wall is a straight line: $q = k Δ T / d$ (in a cylindrical wall — a logarithmic curve). The thermal conductivity $k$ is the heat that passes in 1 s through a 1 m² layer 1 m thick at a temperature difference of 1 K, W/(m·K): copper ≈ 400, steel ≈ 45, clay ≈ 1, cotton ≈ 0.04. To study thermal conduction (Grade 7): compare a clay and a steel wall in the same fire, then different thicknesses.

Solar collector

A flat solar collector is a black absorber plate with water pipes soldered to it, glass on top and thermal insulation behind. Solar radiation $G$ passes through the glass and is absorbed by the plate (radiation), passes through the pipe wall into the water (conduction), and the flowing water carries it away (forced convection). The hot plate emits infrared, but glass hardly lets this radiation through and holds in the hot air — the greenhouse effect, so a glazed collector has a small loss coefficient $U_{L}$ . The useful power is $Q_{u} = \dot{m} c (T_{o u t} - T_{i n})$ , the efficiency $η = Q_{u} / (G A)$ ; in the steady state $η = η_{0} - U_{L} (T_{m} - T_{a}) / G$ , where $T_{m}$ is the mean water temperature: the hotter the water, the greater the loss. Laboratory: measure $η$ at different inlet temperatures and record it in the log; on the graph of $η$ against $(T_{m} - T_{a}) / G$ the intercept of the straight line with the $η$ axis gives $η_{0}$ , and its slope gives $- U_{L}$ . Model: a 2 m² collector, $η_{0}$ and $U_{L}$ are approximate typical values, the water temperature rises linearly along the collector, air $T_{a}$ = 20 °C.

Did you know?

The tandoor is an ancient oven widespread in Central Asia, the Caucasus, Iran and India. Its name is pronounced differently in the languages of the region: tandoor, tonir, tannur.
Radiated power is proportional to the fourth power of the absolute temperature: embers at about 700 °C (973 K) radiate about 8 times more strongly than a wall at 300 °C (573 K): ${(973 / 573)}^{4} \approx 8.3$ .

Inside the experiment

The experiment starts from a real-life situation: you predict the result, change the controls, run the experiment and draw a conclusion. Inside are missions, theory, a quiz and a guided tour in which the camera moves and explains the key points.

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