Effects of temperature-dependent thermal conductivity with variable Biot number on a fully developedflow in a porous channel using LTNE (local thermal nonequilibrium) model

Abstract

The thermal conductivity of the porous materials is dependent on the temperature in a range of applications, including nuclear reactors and fossil fuel sources. The LTNE (local thermal nonequilibrium) model is widely used to study the thermal interactions between solid and fluid phases inside the porous media. The majority of the prior LTNE models assumed the constant thermal conductivities of both the fluid and solid phases, but in actual practice, the thermal conductivities depend on the temperature variations. In the current study, the effective thermal conductivities of the fluid and solid phases in the porous channel are considered as the functions of the respective temperatures by implementing the LTNE model. The Biot number is assumed to vary linearly, quadratically and sinusoidally along with the channel height. The thermal conductivity variation parameter [Formula: see text], porosity [Formula: see text] the ratio of fluid and solid phase thermal conductivities [Formula: see text] and heat generation parameter [Formula: see text] are considered as the main operating parameters. A system of ordinary differential equations has been derived and solved numerically under the above-mentioned conditions which is the generalization of the constant thermal conductivities of both the phases. The present results are validated with the already published results for the constant thermal conductivity and variable Biot number with the LTNE model. The obtained results show that the maximum heat transfer between the two phases is observed by taking [Formula: see text] as the linear increasing function of [Formula: see text] i.e., [Formula: see text] and correspondingly, it provides the highest values of Nusselt number. The Nusselt number increases with the decrement in thermal conductivity variation parameter [Formula: see text], heat generation parameter [Formula: see text] and ratio of fluid to solid phase conductivities [Formula: see text] A complex relationship has been observed between the porosity and the Nusselt number.