A. Haji-Sheikh

Comparison of some inverse heat conduction methods using experimental data

Abstract This paper compares several methods of finding the surface heat flux using transient temperature measurements inside a heat-conducting body. Experimental data is used with a known heat flux history. The methods include function specification with several future approximations, Tikhonov regularization, iterative regularization and specified functions over large time regions with Greens functions. The first three methods are used with the residual principle and the results are quite similar. If the heat flux has a simple time variation over large time regions, taking advantage of that feature can improve the results, as shown by the Greens function analysis.

On departure from local thermal equilibrium in porous media due to a rapidly changing heat source : The Sparrow number

Abstract Local thermal equilibrium is an often-used hypothesis when studying heat transfer in porous media. Examination of non-equilibrium phenomena shows that this hypothesis is usually not valid during rapid heating or cooling. The results from this theoretical study confirm that local thermal equilibrium in a fluidized bed depends on the size of the layer, mean pore size, interstitial heat transfer coefficient, and thermophysical properties. For a porous medium subject to rapid transient heating, the existence of the local thermal equilibrium depends on the magnitude of the Sparrow number and on the rate of change of the heat input.

Temperature solution in multi-dimensional multi-layer bodies

Abstract Mathematical steps leading to computation of the temperature field in multi-dimensional, multi-layer bodies are described and numerical results for two-layer bodies are presented. The presentations include boundary conditions of the first, second, and third kind. Included in this paper is a table to assist in computing eigenvalues. Also, modifications are made to account for the contribution of contact resistance. An efficient computational scheme for calculating the eigenvalues is discussed and numerical results are presented. For multi-dimensional, multi-layer bodies, the eigenfunctions may have real or imaginary eigenvalues. The complete solution must include the contribution of imaginary eigenvalues; otherwise, the information will be erroneous. A procedure is introduced that places a bound on the location of each eigenvalue.

Steady-state heat conduction in multi-layer bodies

Abstract The mathematical formulation of the steady-state temperature field in multi-dimensional and multi-layer bodies is presented. The numerical examples are for two-layer bodies and they include boundary conditions of the first, second, and third kind. This study includes tables to assist the selection of eigenfunctions and computation of the eigenvalues. The computations include the contribution of contact resistance to the temperature solution. An efficient computational scheme for calculating the eigenvalues is used. For multi-dimensional, multi-layer bodies, the eigenfunctions are real if each layer is homogeneous; they may become imaginary if layers are orthotropic.

Fully Developed Heat Transfer to Fluid Flow in Rectangular Passages Filled With Porous Materials

This is a theoretical and numerical study of fully developed forced convection in various rectangular ducts. Each duct is filled with porous materials and the Brinkman model describes the laminar fluid flow inside this fully saturated porous passage. A Fourier series solution provides the exact solution for the velocity field. Also, a Fourier series solution can produce the temperature profile for a condition of constant energy input per unit length. This includes two different wall condition: a uniform wall temperature at any axial location and a locally uniform heat flux over the boundary. The case of constant wall temperature over the entire passage is also accommodated using a special analytical/numerical solution.

Phase-change phenomena in porous media : a non-local thermal equilibrium model

Abstract An approximate theoretical enthalpy model is developed to study the phase-change process in porous media. During the melting or the freezing process, the interface within a pore remains at the phase-change temperature until the process is completed. Since the melting process is relatively slow, the assumption of local thermal equilibrium is not universally valid. This theoretical study leads to the development of working relations. An approximate two-temperature model is studied analytically. The results provide the parametric information concerning the phase-change front. Also, the conditions that would assure the existence of local thermal equilibrium are presented.

Certain Anomalies in the Analysis of Hyperbolic Heat Conduction

The hyperbolic diffusion equation is often used to analyze laser heating of dielectric materials and in thermal processing of nonhomogeneous materials. Anomalies in existing solutions of the hyperbolic heat equation are identified. In particular, the singularities associated with the interaction of a wave front and a boundary may cause a violation of the imposed boundary condition. This violation may give rise to physically unacceptable results such as a temperature drop due to heating or a temperature rise due to cooling. The development of appropriate remedies for these happenings is a major focus of this paper. In addition, the unique mathematical features of the hyperbolic heat equation are studied and set forth. Greens function solutions for semi-infinite and infinite bodies are presented. For finite bodies, it is demonstrated that the relevant series solutions need special attention to accelerate their convergence and to deal with certain anomalies

Exact Solution of Heat Conduction in Composite Materials and Application to Inverse Problems

Calculation of temperature in high-temperature materials is of current interest to engineers, e.g., the aerospace industry encounters cooling problems in aircraft skins during the flight of high-speed air vehicles and in high-Mach-number reentry of spacecraft. In general, numerical techniques are used to deal with conduction in composite materials. This study uses the exact series solution to predict the temperature distribution in a two-layer body: one orthotropic and one isotropic. Often the exact series solution contains an inherent singularity at the surface that makes the computation of the heat flux difficult. This singularity is removed by introducing a differentiable auxiliary function that satisfies the nonhomogeneous boundary conditions. Finally, an inverse heat conduction technique is used to predict surface temperature and/or heat flux

Convection cooling of microelectronic chips

Mixed natural/forced convective heat transfer in a channel with heating elements is reported. Three microelectronic chps provided the heating surfaces. An experimental study was performed to determine the influence of the Reynolds number and Grashof number on the Nusselt number. Real-time holographic interferometry with an optical crystal as the storage medium was used to visualize heat transfer from microelectronic chips. The results show that the influence of natural convection is usually negligible, even for small Reynolds numbers.<<ETX>>

PRESSURE AND HEAT TRANSFER IN CROSS FLOW OVER CYLINDERS BETWEEN TWO PARALLEL PLATES

Heat transfer and fluid flow over a row of in-line cylinders placed between two parallel plates are studied numerically. Flow is incompressible, two-dimensional, and laminar. The spacing between cylinders causes three different separation patterns. When the spacing is small, the separated flow between cylinders is stable. As the spacing increases, flow in the separated zone becomes temporal and periodic. At higher spacing, the separated flow is local and does not extend to the next cylinder. In general, the pressure drop in the flow and heat transfer to the flow are spatially periodic, indicating fully developed characteristics