The Time Delay for a Perceptible Thermal Disturbance in a Slab

Abstract

If a thermal disturbance such as a step change in temperature is applied at each surface of a homogeneous slab of thickness 2L, the effect of cooling at x = +L at first has no effect at x = −L but is clearly evident after a time described by a Fourier number F0 = λt/ρcpL2 of around 0.2. To establish the time of a perceptible change the minimum value of φi − (φ1 + (φ2) is sought, where φ1 is the flux into a semi-infinite solid and φ1 and φ2 are the first and second eigenfunction contributions to the solution for a slab of finite thickness. Cooling throughout the slab is determined virtually by the first eigenfunction alone after F0 = 0.22. For a fluid-cooled slab these values are larger.