TY - JOUR

T1 - Compact Algebraic Asymptotes for Small and Large Time Surface Temperatures for Regular Solid Bodies Heated with Uniform Heat Flux

T2 - Scrutiny of New Critical Fourier Numbers

AU - Delgado-Torres, Agustín M.

AU - Campo, Antonio

AU - Masip-Macia, Yunesky

N1 - Publisher Copyright:
© 2020 by ASME.

PY - 2021/6/1

Y1 - 2021/6/1

N2 - The alternate infinite series at "small time"have been used to analyze the time variation of surface temperatures (φs) in regular solid bodies heated with uniform heat flux. In this way, compact algebraic asymptotes are successfully retrieved for φs 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 φs for the plate, cylinder, and sphere are τcr obtained, respectively, with the "small time"- "large time"approximation using a traditional approach to fix the τcr value. An alternative approach to set the τcr 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.

AB - The alternate infinite series at "small time"have been used to analyze the time variation of surface temperatures (φs) in regular solid bodies heated with uniform heat flux. In this way, compact algebraic asymptotes are successfully retrieved for φs 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 φs for the plate, cylinder, and sphere are τcr obtained, respectively, with the "small time"- "large time"approximation using a traditional approach to fix the τcr value. An alternative approach to set the τcr 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.

KW - Conduction

KW - heat and mass transfer

UR - http://www.scopus.com/inward/record.url?scp=85091960660&partnerID=8YFLogxK

U2 - 10.1115/1.4047939

DO - 10.1115/1.4047939

M3 - Article

AN - SCOPUS:85091960660

SN - 1948-5085

VL - 13

JO - Journal of Thermal Science and Engineering Applications

JF - Journal of Thermal Science and Engineering Applications

IS - 3

M1 - 031001

ER -