A method of fundamental solutions for transient heat conduction

In this paper we investigate an application of the method of fundamental solutions (MFS) to transient heat conduction. In almost all of the previously proposed MFS for time-dependent heat conduction the fictitious sources are located outside the time-interval of interest. In our case, however, these sources are instead placed outside the space domain of interest in the same manner as is done for stationary heat conduction. A denseness result for this method is discussed and the method is numerically tested showing that accurate numerical results can be obtained. Furthermore, a test example with boundary singularities shows that it is advisable to remove such singularities before applying the MFS.

A comparative study on applying the method of fundamental solutions to the backward heat conduction problem

We investigate an application of the method of fundamental solutions (MFS) to the backward heat conduction problem (BHCP). We extend the MFS in Johansson and Lesnic (2008) [5] and Johansson et al. (in press) [6] proposed for one and two-dimensional direct heat conduction problems, respectively, with the sources placed outside the space domain of interest. Theoretical properties of the method, as well as numerical investigations, are included, showing that accurate and stable results can be obtained efficiently with small computational cost.

A method of fundamental solutions for transient heat conduction in layered materials

In this paper we investigate an application of the method of fundamental solutions (MFS) to transient heat conduction in layered materials, where the thermal diffusivity is piecewise constant. Recently, in Johansson and Lesnic [A method of fundamental solutions for transient heat conduction. Eng Anal Boundary Elem 2008;32:697–703], a MFS was proposed with the sources placed outside the space domain of interest, and we extend that technique to numerically approximate the heat flow in layered materials. Theoretical properties of the method, as well as numerical investigations are included.

Recovering boundary data in planar heat conduction using boundary integral equation method

We consider a Cauchy problem for the heat equation, where the temperature field is to be reconstructed from the temperature and heat flux given on a part of the boundary of the solution domain. We employ a Landweber type method proposed in [2], where a sequence of mixed well-posed problems are solved at each iteration step to obtain a stable approximation to the original Cauchy problem. We develop an efficient boundary integral equation method for the numerical solution of these mixed problems, based on the method of Rothe. Numerical examples are presented both with exact and noisy data, showing the efficiency and stability of the proposed procedure and approximations.

Computer methods for the heat conduction equation

The merits of various numerical methods for the solution of the one and two dimensional heat conduction equation with a radiation boundary condition have been examined from a practical standpoint in order to determine accuracies and efficiencies. It is found that the use of five increments to approximate the space derivatives gives sufficiently accurate results provided the time step is not too large; further, the implicit backward difference method of Liebmann (27) is found to be the most accurate method. On this basis, a new implicit method is proposed for the solution of the three-dimensional heat conduction equation with radiation boundary conditions. The accuracies of the integral and analogue computer methods are also investigated.

A method of fundamental solutions for radially symmetric and axisymmetric backward heat conduction problems

We propose and investigate an application of the method of fundamental solutions (MFS) to the radially symmetric and axisymmetric backward heat conduction problem (BHCP) in a solid or hollow cylinder. In the BHCP, the initial temperature is to be determined from the temperature measurements at a later time. This is an inverse and ill-posed problem, and we employ and generalize the MFS regularization approach [B.T. Johansson and D. Lesnic, A method of fundamental solutions for transient heat conduction, Eng. Anal. Boundary Elements 32 (2008), pp. 697–703] for the time-dependent heat equation to obtain a stable and accurate numerical approximation with small computational cost.

A domain decomposition based algorithm for non-linear 2D inverse heat conduction problems

Inverse heat conduction problems (IHCPs) appear in many important scientific and technological fields. Hence analysis, design, implementation and testing of inverse algorithms are also of great scientific and technological interest. The numerical simulation of 2-D and –D inverse (or even direct) problems involves a considerable amount of computation. Therefore, the investigation and exploitation of parallel properties of such algorithms are equally becoming very important. Domain decomposition (DD) methods are widely used to solve large scale engineering problems and to exploit their inherent ability for the solution of such problems.

A Distributed algorithm for 1-D non-linear heat conduction with an unknown point source

Abstract not available

Comparison between one-dimensional uncoupled and convection-conduction conjugated approaches in finned surface heat transfer

This work studies the forced convection problem in internal flow between concentric annular ducts, with radial fins at the internal tube surface. The finned surface heat transfer is analyzed by two different approaches. In the first one, it is assumed one-dimensional heat conduction along the internal tube wall and fins, with the convection heat transfer coefficient being a known parameter, determined by an uncoupled solution. In the other way, named conjugated approach, the mathematical model (continuity, momentum, energy and K-epsilon equations) applied to tube annuli problem was numerically solved using finite element technique in a coupled formulation. At first time, a comparison was made between results obtained for the conjugated problem and experimental data, showing good agreement. Then, the temperature profiles under these two approaches were compared to each other to analyze the validity of the one-dimensional classical formulation that has been utilized in the heat exchanger design.

Experimental investigations of heat transfer coefficients of cutting fluids in metal cutting processes: analysis of workpiece phenomena in a given case study

This paper reports an experimental method to estimate the convective heat transfer of cutting fluids in a laminar flow regime applied on a thin steel plate. The heat source provided by the metal cutting was simulated by electrical heating of the plate. Three different cooling conditions were evaluated: a dry cooling system, a flooded cooling system and a minimum quantity of lubrication cooling system, as well as two different cutting fluids for the last two systems. The results showed considerable enhancement of convective heat transfer using the flooded system. For the dry and minimum quantity of lubrication systems, the heat conduction inside the body was much faster than the heat convection away from its surface. In addition, using the Biot number, the possible models were analyzed for conduction heat problems for each experimental condition tested.

AIR SIDE HEAT TRANSFER ENHANCEMENT IN HEAT EXCHANGERS UTILIZING INNOVATIVE DESIGNS AND THE ADDITIVE MANUFACTURING TECHNIQUE

Over the last decade, rapid development of additive manufacturing techniques has allowed the fabrication of innovative and complex designs. One field that can benefit from such technology is heat exchanger fabrication, as heat exchanger design has become more and more complex due to the demand for higher performance particularly on the air side of the heat exchanger. By employing the additive manufacturing, a heat exchanger design was successfully realized, which otherwise would have been very difficult to fabricate using conventional fabrication technologies. In this dissertation, additive manufacturing technique was implemented to fabricate an advanced design which focused on a combination of heat transfer surface and fluid distribution system. Although the application selected in this dissertation is focused on power plant dry cooling applications, the results of this study can directly and indirectly benefit other sectors as well, as the air-side is often the limiting side for in liquid or single phase cooling applications. Two heat exchanger designs were studied. One was an advanced metallic heat exchanger based on manifold-microchannel technology and the other was a polymer heat exchanger based on utilization of prime surface technology. Polymer heat exchangers offer several advantages over metals such as antifouling, anticorrosion, lightweight and often less expensive than comparable metallic heat exchangers. A numerical modeling and optimization were performed to calculate a design that yield an optimum performance. The optimization results show that significant performance enhancement is noted compared to the conventional heat exchangers like wavy fins and plain plate fins. Thereafter, both heat exchangers were scaled down and fabricated using additive manufacturing and experimentally tested. The manifold-micro channel design demonstrated that despite some fabrication inaccuracies, compared to a conventional wavy-fin surface, 15% - 50% increase in heat transfer coefficient was possible for the same pressure drop value. In addition, if the fabrication inaccuracy can be eliminated, an even larger performance enhancement is predicted. Since metal based additive manufacturing is still in the developmental stage, it is anticipated that with further refinement of the manufacturing process in future designs, the fabrication accuracy can be improved. For the polymer heat exchanger, by fabricating a very thin wall heat exchanger (150μm), the wall thermal resistance, which usually becomes the limiting side for polymer heat exchanger, was calculated to account for only up to 3% of the total thermal resistance. A comparison of air-side heat transfer coefficient of the polymer heat exchanger with some of the commercially available plain plate fin surface heat exchangers show that polymer heat exchanger performance is equal or superior to plain plate fin surfaces. This shows the promising potential for polymer heat exchangers to compete with conventional metallic heat exchangers when an additive manufacturing-enabled fabrication is utilized. Major contributions of this study are as follows: (1) For the first time demonstrated the potential of additive manufacturing in metal printing of heat exchangers that benefit from a sophisticated design to yield a performance substantially above the respective conventional systems. Such heat exchangers cannot be fabricated with the conventional fabrication techniques. (2) For the first time demonstrated the potential of additive manufacturing to produce polymer heat exchangers that by design minimize the role of thermal conductivity and deliver a thermal performance equal or better that their respective metallic heat exchangers. In addition of other advantages of polymer over metal like antifouling, anticorrosion, and lightweight. Details of the work are documented in respective chapters of this thesis.

Contribution to dynamic characteristics of the cutting temperature in the drilling process considering one dimension heat flow

The machining of hardened steels has always been a great challenge in metal cutting, particularly for drilling operations. Generally, drilling is the machining process that is most difficult to cool due to the tool`s geometry. The aim of this work is to determine the heat flux and the coefficient of convection in drilling using the inverse heat conduction method. Temperature was assessed during the drilling of hardened AISI H13 steel using the embedded thermocouple technique. Dry machining and two cooling/lubrication systems were used, and thermocouples were fixed at distances very close to the hole`s wall. Tests were replicated for each condition, and were carried out with new and worn drills. An analytical heat conduction model was used to calculate the temperature at tool-workpiece interface and to define the heat flux and the coefficient of convection. In all tests using new and worn out drills, the lowest temperatures and decrease of heat flux were observed using the flooded system, followed by the MQL, considering the dry condition as reference. The decrease of temperature was directly proportional to the amount of lubricant applied and was significant in the MQL system when compared to dry cutting. (C) 2011 Elsevier Ltd. All rights reserved.

A transient three-dimensional heat transfer model of the human body

The objective of this work is to develop an improved model of the human thermal system. The features included are important to solve real problems: 3D heat conduction, the use of elliptical cylinders to adequately approximate body geometry, the careful representation of tissues and important organs, and the flexibility of the computational implementation. Focus is on the passive system, which is composed by 15 cylindrical elements and it includes heat transfer between large arteries and veins. The results of thermal neutrality and transient simulations are in excellent agreement with experimental data, indicating that the model represents adequately the behavior of the human thermal system. (C) 2009 Elsevier Ltd. All rights reserved.

Experimental and numerical investigation of dynamic heat transfer parameters in packed bed

Dynamic experiments in a nonadiabatic packed bed were carried out to evaluate the response to disturbances in wall temperature and inlet airflow rate and temperature. A two-dimensional, pseudo-homogeneous, axially dispersed plug-flow model was numerically solved and used to interpret the results. The model parameters were fitted in distinct stages: effective radial thermal conductivity (K (r)) and wall heat transfer coefficient (h (w)) were estimated from steady-state data and the characteristic packed bed time constant (tau) from transient data. A new correlation for the K (r) in packed beds of cylindrical particles was proposed. It was experimentally proved that temperature measurements using radially inserted thermocouples and a ring-shaped sensor were not distorted by heat conduction across the thermocouple or by the thermal inertia effect of the temperature sensors.

Analysis of steady-state heat transfer through mid-crustal vertical cracks with upward throughflow in hydrothermal systems

We conduct a theoretical analysis of steady-state heat transfer problems through mid-crustal vertical cracks with upward throughflow in hydrothermal systems. In particular, we derive analytical solutions for both the far field and near field of the system. In order to investigate the contribution of the forced advection to the total temperature of the system, two concepts, namely the critical Peclet number and the critical permeability of the system, have been presented and discussed in this paper. The analytical solution for the far field of the system indicates that if the pore-fluid pressure gradient in the crust is lithostatic, the critical permeability of the system can be used to determine whether or not the contribution of the forced advection to the total temperature of the system is negligible. Otherwise, the critical Peclet number should be used. For a crust of moderate thickness, the critical permeability is of the order of magnitude of 10(-20) m(2), under which heat conduction is the overwhelming mechanism to transfer heat energy, even though the pore-fluid pressure gradient in the crust is lithostatic. Furthermore, the lower bound analytical solution for the near field of the system demonstrates that the permeable vertical cracks in the middle crust can efficiently transfer heat energy from the lower crust to the upper crust of the Earth. Copyright (C) 2002 John Wiley Sons, Ltd.