1,721,149 research outputs found
Transient heat conduction in one-dimensional composite slab. A 'natural' analytical approach
No full textThe transient response of one-dimensional multilayered composite conducting slabs to sudden Variations of the temperature of the surrounding fluid is analysed. The solution is obtained applying the method of separation of variables to the heat conduction partial differential equation. In separating the variables, the thermal diffusivity is retained on the side of the modified heat conduction equation where the time-dependent function is collected. This choice is the essence of composite medium analysis itself. In fact, it 'naturally' gives the relationship between the eigenvalues for the different regions and then yields a transcendental equation for the determination of the eigenvalues in a less complex form than the ones resulting from the application of traditional techniques. A new type of orthogonality relationship is developed by the author and used to obtain the final complete series solution. The errors, which develop when the higher terms in the series solution are neglected, are also investigated. Some calculated results of a numerical example are shown in a graphical form, by using dimensionless groups, and therefore discussed
Initial guesses for computing eigenvalues of Sturm-Liouville problems of multi-dimensional multi-layer unsteady heat conduction
No full textThe paper analyses the transverse eigenvalue problem of Sturm-Liouville type associated with the time-dependent heat conduction in two-component rectangular domains. In particular, it describes how the physical insight of a ‘homogeneous rectangular region’ thermally and geometrically equivalent to the considered 2-D two-layered region in the transverse direction is capable of providing useful and reasonably accurate information about the initial guesses for the roots (eigenvalues) of the transverse eigencondition. This information, in fact, enables one to establish starting points for a root-finding iteration (e.g., Müller's method) so that convergence of the iteration may absolutely be guaranteed. Representative test examples are computed to illustrate the accuracy, reliability, and efficiency of the proposed fully automated solution algorithm when the two layers have the same thermal diffusivity and are perfectly jointed
Calculation of the Thermodynamic properties of R407C and R410A by the martin-Hou equation of state. Part II. Technical interpretation
No full textResults are technically interpreted that follow from the theoretical analyses and numerical calculations of the thermodynamic properties of vapour R407C and R410A in terms of the Martin-Hou equation of state. All aspects of the theoretical approach derived in the first part of this study are investigated. In particular, the influence of temperature on either thermodynamic property of the HFC-refrigerant mixtures here under consideration is established, together with the overriding influence of the pressure (that accounts for the gas compressibility effects) in characterising these properties
Unsteady heat conduction in two-dimensional two slab-shaped regions. Exact closed-form solution and results
No full textThe unsteady heat conduction analysis for multi-directional piecewise-homogeneous bodies is generally held to be complex and demanding, possibly explaining why practical guidelines for thermal field calculation are few and far between. The proposed solution method represents an extension of the new, ÔnaturalÕ analytic approach derived in companion papers for solving one-dimensional multi-layer problems of time-dependent heat conduction. As the ap- proach is new, it is presented in full, together with the complete temperature double-series solution prepared for computer implementation. By setting thermal diffusivity ratio unitary and assuming a uniform distribution of initial temperature, it emerges that, all other things being equal, the transient thermal response can be expressed as the product of two, separated, one-directional solutions, one across the layers and the other along the composite slab. The for- mulation deals properly with thermal conductivity ratios of all magnitudes. An efficient and accurate procedure of computing eigenvalues is given. Graphical and numerical output is presented and discussed
An analytic approach to the unsteady heat conduction processes in one-dimensional composite media
No full textThe transient heat conduction problems in one-dimensional multi-layer solids are usually solved applying con- ventional techniques based on Vodicka’s approach. However, if the thermal diffusivity of each layer is retained on the side of the heat conduction equation modified from the application of the separation-of-variables method where the time-dependent function is collected, then the modified heat conduction equation by itself represents a transparent statement of the physical phenomena involved. This ‘natural’ choice so simplifies unsteady heat conduction analysis of composite media that thermal response computation reduces to a matter of relatively simple mathematics when compared with traditional techniques heretofore employed
Multi-layer transient heat conduction using transition time scales
No full textThe solution of multi-layer transient heat conduction problems may be simplified by analyzing the different transition times of the various layers of a composite slab. These transition times, in fact, allow the ‘disturbance’ effect of each layer on the eigenvalues of the composite slab to
be analyzed and estimated. It was found that the eigenvalues may be obtained in the first approximation by merging in increasing order the suitable
corrected eigenvalues of each layer for which explicit equations are available. The errors in the resulting dimensionless temperatures are of one
order of magnitude larger than the deviations between the exact and approximate eigenvalues. In particular, when one of the two outer boundaries
is kept at constant temperature and the transition times of the layers are quite different, the eigenvalues may be written down very simply as the
eigenvalues of the layer whose exposed surface is not at prescribed temperature. In this paper the temperature solution for the case of a two-layer
slab with interlayer thermal contact resistance is presented
Transverse eigenproblem of steady-state heat conduction for multi-dimensional two-layered slabs with automatic computation of eigenvalues
No full textThe paper analyses the transverse eigenvalue problem of nonconventional Sturm–Liouville type associated to the
steady-state heat conduction in 3-D two-component slabs with imperfect thermal contact. In particular, it describes
how the physical insight deriving from the transverse direction of six suitable homogeneous parallelepipeds’ inherent to
the considered two-layered parallelepiped is capable of providing useful and reasonably accurate information about the
best bracketing bounds (lower and upper) for the roots (eigenvalues) of the transverse eigencondition. This information,
in fact, enables one to establish starting points (initial guesses) for a root-finding iteration (e.g., M€uller’s method) so
that convergence of the iteration may absolutely be guaranteed. Representative test examples are computed to illustrate
the accuracy, reliability, and efficiency of the proposed fully automated solution algorithm
Thermal Analysis of the Heat Exchangers and Regenerator in Stirling Cycle Machine
No full textA closed-form expression for the effectiveness of the heat exchangers and regenerator of a Stirling cycle machine is given. This result may be used in a simple way to evaluate their effect on the machine performance. The proposed method allows the actual cycle gas temperatures in the heater and cooler to be obtained readily, once the geometry of the heater, cooler, and regenerator is known and some quantities characterizing the engine dynamics (strokes, frequency, and phase angle of the moving elements) and its heat-exchange processes (inlet temperatures of the heating and cooling fluids and their volumetric flow rates) are measured. Thus, an immediate indication about the effectiveness of the heat exchangers and regenerator as well as about the machine thermal efficiency may be obtained. The availability of a closed-form expression for the heater, regenerator, and cooler effectiveness is useful especially for those engines, like the free-piston Stirling engines, whose design requires the application of analytically based optimization criteria. The obtained relations have been applied to the well-known Space Power Research Engine
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