Inclusion of unsteady heat conduction in regular bodies subject to uniform surface heat flux in a heat transfer course

Abstract

The present study is concerned with the analysis of unsteady heat conduction in regular bodies (large plane wall, long cylinder, and sphere) with constant initial temperature, prescribed surface heat flux and thermal properties of the solid that are invariant with temperature. Surprisingly, this important topic is absent in textbooks on heat transfer. The exact evaluation of the dimensionless surface temperatures varying with the dimensionless time in the regular bodies over the entire dimensionless time domain $0<\tau <\mathrm{\infty }$ is carried out with a symbolic algebra code. Thereafter, regression analysis is applied to the data gathered for the dimensionless surface temperatures varying with the dimensionless time of the regular bodies inside the dimensionless “small time” time sub-domains $0<\tau \le {\tau }_{\mathrm{th}}$ . The dimensionless threshold time ${\tau }_{\mathrm{th}}$ is a decisive parameter that establishes the borderline between the “small time” sub-domain $\tau \to 0$ and the “large time” sub-domain $\tau \gg 0$ comprising the entire dimensionless time domain $0<\tau <\mathrm{\infty }$ . Based on regression analysis, compact asymptotes are constructed for the dimensionless surface temperatures varying with the dimensionless time inside the dimensionless “small time” sub-domain $0<\tau \le {\tau }_{\mathrm{th}}$ . At the end, agreements with the dimensionless exact, analytical surface temperature distributions (the baseline solutions) valid for the dimensionless time sub-domain $0<\tau <\mathrm{\infty }$ . are considered of excellent quality.