Transient Conduction Heat Transfer Problems Research Articles

A double distribution lattice Boltzmann scheme for unsteady Conjugate Heat Transfer: The DD-CHT LB method

In this paper, we propose an innovative formulation of the “well-known” thermal lattice Boltzmann method for solving transient conduction heat transfer problems in heterogeneous media: the DD-CHT LB method for Double Distribution – Conjugate Heat Transfer. The main idea of this new formulation is to bring out a second distribution function that represent the effect of thermal inertia and its variation in a heterogeneous media. By adopting this original formulation we achieved several goals, mainly conservation of local properties of the studied media and ensuring the stability of the proposed formulation by avoiding any alteration of the “well-known” TLBM collision step. Validation of the formulation is fulfilled through three different benchmark conduction heat transfer problems in heterogeneous media. All results are compared with those obtained by the Control Volume Method (CVM) and excellent agreements were found.

Thermal Diffusivity Determination of High-Temperature Levitated Oblate Spheroidal Specimen by a Flash Method

In extending the range of applicability of a recently developed method, a single-step containerless flash technique for determining the thermal diffusivity of levitated oblate spheroidal oblate spheroidal samples is proposed. The flash method is modeled as an axisymmetric transient conduction heat transfer problem within the oblate spheroid. It is shown that by knowing the sample geometric parameters and recording the temperature rise history at least at two different points on the surface simultaneously, the thermal diffusivity can be determined without knowing needed for determining the thermal diffusivity of oblate spheroidal samples are provided.

Containerless Thermal Diffusivity Determination of High-Temperature Levitated Spherical Specimen by Extended Flash Methods: Theory and Experimental Validation

In order to determine the thermal diffusivity of materials, especially solids and liquids at high temperatures, two extended containerless flash techniques that are applicable to levitated spherical specimen are proposed. The extended flash methods are modeled as an axisymmetric transient conduction heat transfer problem within the sphere. For the “single-step” method, analytic expressions for the temperature history on the surface of the sphere are obtained that are independent of the incident energy and the absorption layer thickness. It is shown that by knowing the sample diameter and recording the temperature transient history at least at two different points on the surface simultaneously, the thermal diffusivity can be determined. A detailed discussion of the effects of the various parameters is presented. For the “two-step” analysis the problem of nonlinearity of the radiative heat transfer boundary condition is overcome by replacing it with the measured time-dependent surface temperature data. Upon obtaining the temperature field the determination of the thermal diffusivity turns into a minimization problem. In performing the proposed two-step procedure there is a need to undertake a cool-down experiment. Results of an experimental study directed at determining the thermal diffusivity of high-temperature solid samples of pure Nickel and Inconel 718 superalloy near their melting temperatures using the single-step method are discussed. Based on close agreement with reliable data available in the literature, it is concluded that the proposed techniques can provide reliable thermal diffusivity data for high-temperature materials.

Laplace-variational method for transient multidimensional temperature distributions

An analytical method has been developed which will provide closed form approximate temperature distributions for two-dimensional transient conduction heat transfer problems. It is referred to a s a Laplace-variational method since it utilizes a Laplace transformation along with methods from the calculus of variations. The Laplace-variational method can be applied to bodies with or without heat generation. Application of the method to both of these types of two-dimensional problems is shown in this paper. Also, some one-dimensional and three-dimensional transient conduction heat transfer problems can be analyzed by the Laplace-variational method even though the method was formally prepared for two-dimensional problems. The procedure used to approach such problems by this method is outlined. Use of the Laplace-variational method in heat transfer problems means that the thermal properties of a material must be constant and also that a radiation boundary condition cannot be considered. Utilization of the technique in this paper has also been restricted to problems involving regular geometry.