Investigating the Significance of Material Grading on Transient Thermal Characteristics of a Longitudinal Fin
Abhishek Sahu, Shubhankar BhowmickABSTRACT
This manuscript investigates the transient thermal characteristics of graded longitudinal fins subjected to boundary conditions of a step change in root temperature and convective tip at the extremities of fin. Herein, the spatially varying heat conductivity of graded fin is treated as a polynomial function of temperature, and the convection coefficient of environment fluid is considered as a power law function of temperature. The non‐linear governing equation is explicitly solved to determine the numerical solution using the mesoscale Lattice Boltzmann (LB) solver coupled with in‐house source code. The transient thermal characteristics , namely instantaneous temperature , steady‐state temperature, threshold time , and instantaneous efficiency of homogeneous material ( HM ) and linearly graded material ( LGM ) fins, have been investigated. The threshold time ( τ th ) required to attain the steady‐state temperature (θ ss ) is obtained for a stipulated location for HM and graded LGM longitudinal fins. The reported results reveal that owing to their tailored material composition, LGM quickly dissipates the heat as compared to the uniform composition of HM material for the same value of equivalent thermal conductivity. Increasing the value of the grading factor ( β ) from β = 1.0 to β = 3.0 significantly enhances the magnitude of the relative improvement percentage ( ϕ th ) for instantaneous normalized temperatures ( ϕ in ) approximately from 2.324% to 13.178 and steady‐state temperature ( ϕ ss ) from 2.314% to 11.051%, whereas it decreases the threshold time ( ϕ th ) from 2.500% to 15.789%. Consequently, the relative improvement percentage(ϕ th ) of ( IE ) can be improved up to 12.598%. Rapid attainment of a steady state indicates that LGM fins quickly dissipate the heat, consequently lessening the impact of thermal deformation and stress on the material. Hence, comprehending the material grading significance facilitates material selection for applications wherein temperature management is paramount. The reported data set can be utilized as design references for practicing engineers.