Compact Algebraic Asymptotes for Small and Large Time Surface Temperatures for Regular Solid Bodies Heated With Uniform Heat Flux: Scrutiny of New Critical Fourier Numbers

The alternate infinite series at “small time” have been used to analyze the time variation of surface temperatures (ϕ_s) in regular solid bodies heated with uniform heat flux. In this way, compact algebraic asymptotes are successfully retrieved for ϕ_s in a plate, cylinder, and sphere in the “small time” sub-domain extending from 0 to the critical dimensionless time or critical Fourier number. For the “large time” sub-domain, the exact solution is approximated in two ways: with the “one-term” series and with the simple asymptotes corresponding to extreme “large time” conditions. Maximum relative errors of 1.23%, 6.24%, and 0.96% in ϕ_s for the plate, cylinder, and sphere are τ_cr obtained, respectively, with the “small time”—“large time” approximation using a traditional approach to fix the τ_cr value. An alternative approach to set the τ_cr is proposed to minimize the maximum relative error of the approximated solutions so that values of 1.19%, 3.93%, and 0.16% are then obtained for the plate, cylinder, and sphere, respectively, with the “small time”—“large time” approximation. For the “small time”—“one-term” approximation maximum relative errors of 0.024%, 1.33%, and 0.004% for the plate, cylinder, and sphere are obtained, respectively, with this approach.