Proposing a normalized Biot number: For simpler determination of Fourier exponents and for evaluating the sensitivity of the Biot number

• A normalized Biot number [Binorm] has been formulated.
• Enabling simple prediction of Fourier exponents and lag-factors.
• Easy assessment of sensitivity of the Fourier expansion.
• Graphical and tabulated misreads is eliminated.

This paper presents a normalization of the Biot number, which enables the Fourier exponents to be fitted with a simple 3rd order polynomial (R2 > 0.9999). The method is validated for Biot numbers ranging from 0.02 to ∞, and presented graphically for both the Fourier exponents and the lag factors needed in the series expansion. The lag factors and Fourier exponents are validated with an average variation coefficient (CVRMSD) less than 0.006. The resulting prediction error of the thermal response is < 0.6 °C for spheres and <0.3 °C for slabs and cylinders. The normalized Biot number also facilitates an easy investigation of the sensitivity in heat transfer calculations. The simplicity of the solution facilitates its implementation in the industry and curricula for engineers that needs crude calculation methods for thermal calculations, e.g. food science and food technology educations.