An analysis has been performed to study the problem of the thermal performance of a continuously moving convective-radiative rod with variable thermal conductivity. Highly accurate semi-analytical methods called the least Square method (LSM) and the Galerkin method (GM) are introduced and then used to obtain a nonlinear temperature distribution equation in a fin that allows for more accurate measurements that could make the investigation stand out. This research investigated the influence of various parameters on heat transfer in a continuously moving convective-radiative rod. The parameters examined include the convective-conductive factor (Ncc), dimensionless thermal conductivity coefficients (a), radiative-conductive parameter (Nrc), Peclet number (Pe), dimensionless convective (θc), and radiative sink temperatures (θr). An increase in the dimensionless thermal conductivity coefficient (a) led to higher dimensionless temperatures within the rod, indicating an amplification of conductive heat transfer. The convective-conductive parameter (Ncc) demonstrated a direct relationship with heat loss. In contrast, the radiative-conductive parameter (Nrc) exhibited an inverse relationship between radiative heat transfer and local temperature within the fin. A rise in the Peclet number was associated with higher dimensionless temperatures, indicating a faster-moving rod. Additionally, variations in dimensionless convective and radiative sink temperatures affected temperature profiles, with higher sink temperatures resulting in increased dimensionless temperatures. Notably, the dimensionless radiative sink temperature was found to have a more significant impact on overall dimensionless temperature than the convective sink temperature. These findings underscore the intricate interplay of factors governing heat transfer and temperature distribution in the moving rod system. The importance of this work lies in its comprehensive analysis of the intricate interplay of parameters affecting heat transfer and temperature distribution in continuously moving convective-radiative rods, providing valuable insights for optimizing industrial processes and engineering applications.

The present work inspects the entropy generation on radiative heat transfer in the flow of variable thermal conductivity optically thin viscous Cu–water nanofluid with an external magnetic field through a parallel isothermal plate channel. Our approach uses the power series from the governing non-linear differential equations for small values of thermal conductivity variation parameter which are then analysed by various generalizations of Hermite- Pade approximation method. The influences of the pertinent flow parameters on velocity, temperature, thermal conductivity criticality conditions and entropy generation are discussed quantitatively both numerically and graphically. A stability analysis has been performed for the rate of heat transfer which signifies that the lower solution branch is stable and physically acceptable, whereas the upper solution branch is unstable.

The intent of this analysis is to explore the influence of thermal radiation paired with variable thermal conductivity on MHD micropolar fluid flow over an upper surface. The novelty of the present model is to consider the fluid flow along an upper horizontal surface of a paraboloid of revolution (uhspr) with the porous medium. This physical phenomenon is described by a set of coupled non-linear ODEs by using suitable scaling analysis. The ODEs along with the boundary conditions are solved numerically. Influence of various flow parameters on momentum, thermal and concentration boundary layers is discussed graphically. It is noticed that the variable thickness of the surface has a leading consequence on the boundary layer progression along the surface. Moreover, the results of this study are not only useful for industrial applications but also present a basic understanding of the physical model.

In this article, the thermoelastic interactions in an isotropic and homogeneous semi-infinite medium with variable thermal conductivity caused by an ultra-short pulsed laser heating based on the linear nonlocal theory of elasticity has been considered. We consider that the thermal conductivity of the material is dependent on the temperature. The surface of the surrounding plane of the medium is heated by an ultra-short pulse laser. Basic equations are solved along with the corresponding boundary conditions numerically by means of the Laplace transform technique. The influences of the rise time of the laser pulse, as well as the nonlocal parameter on thermoelastic wave propagation in the medium, have also been investigated in detail. Presented numerical results, graphs and discussions in this work lead to some important deductions. The results obtained here will be useful for researchers in nonlocal material science, low-temperature physicists, new materials designers, as well as to those who are working on the development of the theory of nonlocal thermoelasticity.

The lattice Boltzmann method (LBM) was used to analyze two-dimensional (2D) non-Fourier heat conduction with temperature-dependent thermal conductivity. To this end, the evolution of wave-like temperature distributions in a 2D plate was obtained. The temperature distributions along certain parts of the plate, which was subjected to heat generation and constant thermal conductivity conditions, were also derived and compared. The LBM results are in good agreement with those reported in other works. Additionally, the temperature contours at four different times in which steady state conditions can be achieved were analyzed. The results showed that thermal conductivity increased with rising temperature. Given the material’ s considerable effectiveness in transferring heat energy under heat generation conditions, the temperature gradient of the plate decreased to a level lower than that observed under constant thermal conductivity.

Application of feed pellets in animal and aquatic farming industries has grown because of both the physical and the nutritional benefits it provides. Development of feed pellets manufacturing industry is also considerable. Steam conditioning process, which plays an important role in pelleting production, includes heating feed particles, adding moisture, and mixing the mash. Pellets cooling and drying processes are also involved in heat transfer phenomena. In this study, thermal conductivity of feed pellets was determined at different temperatures ranging from 25 to 85oC and moisture contents of 11.8 to 18.2% wb. It was measured by the transient technique using the line heat source method assembled in a thermal conductivity probe. It turned out that decreasing moisture contents from 18.2 to 11.8% (wb) produced non-linear reduction in thermal conductivity.The average values of thermal conductivity changed from 0.1509 to 0.2143 W m-1 oC-1 at different moisture contents. Tests conducted on two pellet size categories (based on nominal diameter) revealed a significant difference in thermal conductivity between these categories. The thermal conductivities of the first category (minor than nominal dia.) appeared to be 8.5% higher than those of the second category (superior to nominal dia.).Average values of thermal conductivity changed from 0.1538 to 0.2333 W m-1 oC-1 for the first category and from 0.1235 to 0.2456 W m-1 oC-1 for the second category (in 25oC). In addition, some empirical models were developed to express thermal properties as a function of moisture content and temperature.