How does fire spread on a piece of paper? If one lights the corner of a piece of paper with a matc

I don't know a simple expression for the speed of the spread, I can think of an easy way to simulate the problem that should give you the answer. We assume the paper is lying horizontally on a table, so that gravitation and convection can be neglected.
Quantities needed:
$\mathrm{\kappa <!--\; \kappa \; -->}$: thermal conductivity of paper
$E_B$: Total energy released from burning a given mass of paper
$\mathrm{\rho <!--\; \rho \; -->}$: density of paper
$\mathrm{\ell <!--\; \ell \; -->}$: thickness of paper
$t_B$: time it takes to burn a small square of paper
$T_c$: temperature at which paper burns
$C$: specific heat of paper
$\mathrm{\sigma <!--\; \sigma \; -->}$: Stefan-Boltzmann constant
Paper burns when it reaches temperature $T_c$. The temperature distribution is determined by the heat equation with a source:
$\frac{dT}{dt}=\mathrm{\kappa <!--\; \kappa \; -->}{\mathrm{\nabla <!--\; \nabla \; -->}}^{2}T+\frac{Q}{C\mathrm{\rho <!--\; \rho \; -->}}$
So we'll divide our paper into tiny area elements of area $A$, and set boundary conditions to be $T_c$ for one of the corners and room temperature for the rest of the border. Initial conditions should be room temperature everywhere except for the corner that's already at $T_c$. Additionally, for each area element, assign a "burn-time" counter, setting all counters initially to zero.
Suppose we choose a time step $\mathrm{\Delta <!--\; \Delta \; -->}t$
For each area element, calculate the increment in temperature over the time step according to the heat equation, using the usual numerical methods to handle the Laplacian. As for the handling of the $Q$ term, if the element's temperature is above $T_c$ and its "burn-time" counter is below $t_B$, then set $Q=E_B\mathrm{\rho <!--\; \rho \; -->}\mathrm{\ell <!--\; \ell \; -->}A\frac{\mathrm{\Delta <!--\; \Delta \; -->}t}{t_B}+\mathrm{\sigma <!--\; \sigma \; -->}A{T}^4\mathrm{\Delta <!--\; \Delta \; -->}t$ and increment the "burn-time" counter by $\mathrm{\Delta <!--\; \Delta \; -->}t$. Otherwise, $Q=\mathrm{\sigma <!--\; \sigma \; -->}A{T}^4\mathrm{\Delta <!--\; \Delta \; -->}t$
This should generate a reasonably realistic simulation of burning paper. I accounted for the fact that a burning area element should produce heat, but also should eventually burn out, not producing heat anymore (hence the "burn-time" counter). I assumed the power output of the combustion reaction was constant during burning, which is probably inaccurate, but anything more precise is beyond my expertise. Because of the boundary conditions, the simulation will be most accurate in the center, or for large pieces of paper.