F. Alhama

Application of the network method to heat conduction processes with polynomial and potential-exponentially varying thermal properties

Nonlinear transient heat conduction in a finite slab with potential-exponential temperature-dependent specific heat and thermal conductivity is investigated numerically by using the network method. A general network model for this process is proposed, whatever the exponent of the temperature-dependent functions may be, including initial and boundary conditions. With this network model and using the electrical circuit simulation program PSPICE, time-dependent temperature and heat flux profiles at any location can be obtained. This approach allows us to solve this conduction problem by a general, efficient, and relatively simple method. To show the accuracy of the network method, a comparison is made of the present results and those obtained by other methods for a particular case.

The connection between the distributed and lumped models for asymmetric cooling of long slabs by heat convection

The unsteady cooling of a long slab by symmetric heat convection is controlled by a single Biot number Bi = hL/k applied at both surfaces. It is known that the thermal response of the long slab may be analyzed with a lumped model with a small error whenever Bi < 0.1. This paper deals with a plausible extension of the symmetric heat convection implicating an asymmetric heat convection controlled by two Biot numbers: Bi1 = Lh1/k at the left surface and Bi2 = Lh2/k at the right surface. The question that needs to be addressed is the following: under what circumstances can the unsteady cooling of a long slab by asymmetric heat convection be treated with a lumped model?

Heat conduction through a multilayered wall with variable boundary conditions

The network method has been applied to a five-layer wall with thermal conductivities and heat-transfer coefficients varying with temperature. The following boundary conditions have been assumed on the exterior: (i) periodic incident radiative heat flux; (ii) natural convection of the surrounding air, the temperature of which varies periodically; and (iii) thermal radiation to a background sink.

Numerical solution of the heat conduction equation with the electro-thermal analogy and the code PSPICE

The central objective of this paper is to provide numerical analysts with a new procedure named the network simulation method (NSM) for solving the heat conduction equation in bodies of regular shape. In principle, NSM rests on the electro-thermal analogy (loosely called the resistance-capacitance analogy or the RC analogy) that exists between the unsteady, unidirectional conduction of heat and the unsteady flow of electric current. Once the electric network model has been set up for the heat conduction equation, the numerical treatment of the analog electric circuit equation can be easily done with the computer code PSPICE. As a conceptual example, the allied numerical solution of the heat conduction equation for a large plate with symmetric surface temperatures has been carried out, demonstrating that the temperature-time histories and the heat flux-time histories can be obtained simultaneously, quickly, and accurately for the entire time domain.

An Inverse Determination of Unsteady Heat Fluxes Using a Network Simulation Method

This work addresses unsteady heat conduction in a plane wall subjected to a time-variable incident heat flux. Three different types of flux are studied (sinusoidal, triangular and step waveforms) and constant thermal properties are assumed for simplicity. First, the direct heat conduction problem is solved using the Network Simulation Method (NSM) and the collection of temperatures obtained at given instants is modified by introducing a random error: The resulting temperatures act as the input data for the inverse problem, which is also solved by a sequential approach using the NSM in a simple way. The solution is a continuous piece-wise function obtained step by step by minimising the classical functional that compares the above input data with those obtained from the solution of the inverse problem. No prior information is used for the functional forms of the unknown heat flux. A piece-wise linear stretches of variable slope and length is used for each of the stretches of the solution

Network simulation of the rapid temperature changes in the composite nozzle wall of an experimental rocket engine during a ground firing test

Abstract This paper introduces a robust computational technique named the network simulation method (NSM) that is exemplary for the numerical prediction of spatio-temporal temperatures in multi-layered composite walls in regular coordinate systems. The problem that was analyzed here deals with a composite nozzle wall of an experimental rocket engine that is fabricated with two dissimilar materials: a metallic substrate and a ceramic coating. The model involving two coupled, unidirectional nonlinear heat conduction equations in a two-material wall (ceramic coating and metallic substrate) and a convective–radiative boundary condition has been solved numerically with the NSM. NSM has its genesis in the resistance–capacitance analogy that exists between unsteady, unidirectional conduction of heat and unsteady flow of electric current. The network-simulated estimates for the temperature–time history inside the composite nozzle were performed with the code PSPICE easily, quickly, and accurately. The rapid temperature raise of the ceramic coating/metallic substrate interface from room temperature is the determining factor in this study. The time lapse to reach the melting temperature of the metallic substrate dictates the approximate duration of the ground firing test and evidently constitutes the primary design constraint.

A powerful and versatile educational software to simulate transient heat transfer processes in simple fins

Based on the network simulation method and using commercial computer codes, educational software has been developed for numerically solving and simulating lineal and non‐lineal problems of unsteady heat transfer in simple extended 1D surfaces, assuming convection and/or radiation as boundary conditions. Interface communication with the user is pleasant and immediate through the window ambient created in visual C++ source code. After introduction of the data, which includes reticulation parameters, a network model is generated whose finite difference differential equations are formally equivalent to those of the problem. Time remains a continuous variable in the model. The file is numerically run using a network simulation code, providing the transient temperature fields and heat fluxes in the whole medium. The results are shown by graphics or as tables. The program can be used as a low cost laboratory tool for teaching heat transfer or even for the design of simple fins. Students can easily determine the influence of physical parameters, such as thermal conductivity, specific heat, heat transfer coefficient, emissivity, reference temperatures, etc., in the problem.

Transient thermal behaviour of phase-change processes in solid foods with variable thermal properties

In this work we study the transient temperature fields and heat fluxes for simple or multilayer foods with planar, cylindrical or spherical geometry in one-phase or two-phase (phase-change) processes. The temperature dependencies of the thermal properties conductivity and/or specific heat are assumed to be specified as arbitrary and continuous functions. These dependencies are normally very pronounced in these products in the phase-change temperature interval. Interpolation tables or piece-wise functions, which are widely used in foods, may also be considered. Simple boundary conditions such as isothermal, convective and radiative, or any kind of compatible combination of lineal and/or non-lineal conditions may also be assumed with no special requirements. The problem, expressed by way of only one governing equation for both phases is solved numerically by the Network Simulation Method. This method, which has been recently applied to a great variety of non-lineal transport problems, only requires the use of finite-difference schemes for the spatial variable. The time remains as a continuous variable. Application to the freezing of white fish is presented.

Time-dependent heat transfer in a fin-wall assembly. New performance coefficient: thermal reverse admittance

Transient thermal fields and heat fluxes due to step-harmonic temperature excitation and their dependence on frequency are studied in a fin-wall assembly. Application of the currently used efficiency coefficient to transient-harmonic processes is discussed. A new coefficient, thermal reverse transfer admittance, and others, including the augmentation factor, have been used to characterise the behaviour of the system. In a thermal frequency response analysis, module, phase, real and imaginary components have been obtained. For the calculation a network model (whose admittance is identical to the thermal admittance of the system) has been designed for the whole system. The network simulation method provides the numerical response of the system by running the network in circuit resolution software.

Numerical simulation of Nusselt-Rayleigh correlation in Bénard cells. A solution based on the network simulation method

Purpose – Natural convection with heat transfer in porous media has been subject of extensive study in engineering due to its numerous applications. A case of particular interest is the Benard-type flow.The paper aims to discuss this issue. Design/methodology/approach – Based on the network simulation method in order to solve this problem, a numerical model is proposed. Findings – Nusselt-Rayleigh correlation is determined for a broad range of Rayleigh, the dimensionless number that influences the solution, above and below the threshold which separates the conduction and convection pure mechanisms. Originality/value – Based on the network simulation method.