Fourier number is a measure of heat conducted through a body relative to heat stored. Thus, a large value of the Fourier number indicates faster propagation of heat through a body.

To understand physical significance we can refer below figure.

Fourier number at time t can be viewed as the ratio of the rate of heat conducted to the rate of heat stored at that time.

$τ=\frac{αt}{L^2} =\frac{the rate at which heat is conducted across L of a Body of Volume L^3}{The rate at which heat is stored in a body of@volume L^3 }$

The Biot number is the ratio of the internal resistance of a body to heat conduction to its external resistance to heat convection. Therefore, a small Biot number represents small resistance to heat conduction, and thus small temperature gradients within the body.

The Biot number can be viewed as the ratio of the convection at the surface to conduction within the body.

Physical significance: Lumped system analysis assumes a uniform temperature distribution throughout the body, which will be the case only when the thermal resistance of the body to heat conduction (the conduction resistance) is zero. Thus, lumped system analysis is exact when Bi = 0 and approximate when Bi≥0. Of course, the smaller the Bi number, the more accurate the lumped system analysis.

Bi=$\frac{(Conduction resistance within the body)}{(Convection resistance at the surface of the body)}$=$\frac{\frac{L_c}{k}}{\frac{1}{h}}$=$\frac{(hL_c)}{k}$