Fuel has to be heated to a minimum temperature, know as kindling temperature or ignition temperature for a successful and continuous burning. We largely depend upon match sticks for creating fire. It contains combustible W (oxidisable) substance and an oxidizing (oxygen supplying) agent. We supply heat energy by rubbing the head against rough surface. Every fuel has to mix up with oxygen present in air to form a mixture of right composition for successful combustion.
The composition of the mixture can be between two limits namely lower and upper limits. Those limits are called limits of inflammability or explosive range. We should know that even when the temperature maintained is equal to kindling temperature, we cannot produce fire with fuel only or with oxygen only.
Kindling temperature depends upon the chemical nature and explosive range depends upon the volatile (vapour forming) nature of the fuel. Those two properties do not have any direct relation with size or shape of the fuel. But, of course, it seems that powdered fuel, say saw-dust in case of wood catches fire quickly rather than large log.
This difference in size or shape affects neither the kindling temperature nor the volatile nature of the fuel. The rapidity in catching fire is due to different reasons. In case of powdered fuel, small fuel particle is introduced into a large flame. That means supply of activation energy in the form of heat is very fast. In this case, availability of oxygen will also be a very high. Hence the quick ignition. But in case of logs, large mass is heated by relatively small flame. That means supply of activation energy in the form of heat is very slow.
Also, a large portion of the heat supplied to the log will be dissipated to other parts due to conduction. Chance for loss of heat energy to the surrounding cannot be also neglected. This will further slow down the process of attainment of ignition temperature.
Even when the whole log attains the ignition temperature, only the particles present on the surface can form explosive mixture combining the oxygen present, in air. Hence the delayed ignition.
Ignition temperature is specific to a substance. It is temperature at which the substance starts burning. A piece of wood catches fire quickly attain the fire point quickly. But in case of a large log when you apply flame a point of edge, the temperature transfer takes of big log a long time.