Answer:
Conduction is how heat travels through solid especially metals. A wide squat pan provides more basal surface area and a shorter path of travel for the heat to travel to its upper limits, thereby heating up pretty fast. A tall narrow pot puts a lot of distance between the heat source and its upper limits and a small basal surface area and hence spends a comparatively longer time to be completely heated up. Also factors like convection cooling of the pots due to the sorrounding air will be much more easier and faster in the tall narrow pot since it's top is farther away from the heat source.
According to Fourier's equation of conduction we can see that an increase in the depth or lenght of heat travel will reduce the rate of heat transfer. Also a larger heated surface area provides more area for heat conduction increasing the heat transfer rate. From
P = kA(dt/dx)
Where P is the heat transfer rate,
K is the conductivity of the metal,
dt is the temperature difference between the two ends of the metal,
dx is the depth or lenght of heat travel which in this case is the height of the pot,
A is the area of the heated surface.
If we assume both pot to be made of the same material, then from the above we can see that the wide stout pot has more basal area and a shorter height for heat travel when compared to the tall narrow pot.
