A procedure for calculating transient thermal load through multilayer cylindrical structures

This paper presents the transmission matrix and frequency characteristics of transient heat conduction through a multilayer cylindrical structure. The frequency-domain regression method [Appl. Thermal Eng. 21 (6) (2000) 683] is introduced to estimate some simple polynomial s-transfer functions from the frequency characteristics and further calculate the transient heat flow of the cylindrical structure including its thermal response factors and Z-conduction transfer function coefficients. The calculation examples and comparisons have fully demonstrated that the developed procedure is not only easy and simple, but also has high computation accuracy and efficiency.     

Short time step heat flow calculation of building constructions based on frequency-domain regression method

Short time step heat flow calculation of building constructions is often needed for practical applications. Conventional methods such as state-space method and root-finding method may produce unstable conduction transfer function (CTF) coefficients at short time steps, and thus result in unstable heat flow calculation through building constructions. Frequency-domain regression (FDR) method is a newly developed method for computing CTF coefficients efficiently by representing the real building construction system with equivalent polynomial s-transfer functions. Previous studies on this method mainly addressed CTF coefficients at the conventional time step of 3600 s and the performance of heat flow calculation using these coefficients. This paper presents the investigation on the performance of CTF coefficients at various short time steps based on FDR method, and the performance of the heat flow calculation using these coefficients. The results show that FDR method can produce stable CTF coefficients at various time steps for most building constructions, and the calculated heat flows using these coefficients are of high accuracy.     

Sensitivity analysis of transfer functions of laminar flames

The sensitivity of laminar premixed methane/air flames responses to acoustic forcing is investigated using direct numerical simulation to determine which parameters control their flame transfer function. Five parameters are varied: (1) the flame speed s_L, (2) the expansion angle of the burnt gases α, (3) the inlet air temperature T_a, (4) the inlet duct temperature T_d and (5) the combustor wall temperature T_w. The delay of the flame transfer function is computed for the axisymetric flames of Boudy et al. [1] and the slot flames of Kornilov et al. [2]. Stationary flames are first computed and compared to experimental data in terms of flame shape and velocity fields. The flames are then forced at different frequencies. Direct numerical simulations reproduce the flame transfer functions correctly. The sensitivity analysis of the flame transfer function is done by changing parameters one by one and measuring their effect on the delay. This analysis reveals that the flame speed s_L and the inlet duct temperature T_d are the two parameters controlling the flame delay and that any precise computation of the flame transfer function delay must first have proper models for these two quantities.     

Convective‐radiative fins with simultaneous variation of thermal conductivity,heat transfer coefficient,and surface emissivity with temperature

This paper is a numerical study of thermal performance of a convective‐radiative fin with simultaneous variation of thermal conductivity, heat transfer coefficient, and surface emissivity with temperature. The convective heat transfer is assumed to be a power function of the local temperature between the fin and the ambient which allows simulation of different convection mechanisms such as natural convection (laminar and turbulent), boiling, etc. The thermal conductivity and the surface emissivity are treated as linear functions of the local temperature between the fin and the ambient which provide a satisfactory representation of the thermal property variations of most fin materials. The thermal performance is governed by seven parameters, namely, convection–conduction parameter Nc, radiation–conduction parameter Nr, thermal conductivity parameter A, emissivity parameter B, the exponent n associated with convective heat transfer coefficient, and the two temperature ratios, θ_a and θ_s, that characterize the temperatures of convection and radiation sinks. The effect of these parameters on the temperature distribution and fin heat transfer rate are illustrated and the results interpreted in physical terms. Compared with the constant properties model, the fin heat transfer rate can be underestimated or overestimated considerably depending on the values of the governing parameters. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20408     

Performance rating method of thermosyphon solar water heaters

A rating method for the thermal performance of thermosyphon solar water heaters was developed. Except that the outdoor test procedure still follows the Taiwan Standard CNS B7277, a system characteristic efficiency η_s^* which is defined as the α₀ value corrected at , was derived so that η_s^* is independent of the ratio. Here, η_s^* can be evaluated by linear regression analysis of the test data. It is found from a series of tests for 31 systems that η_s^* is independent of indeed, and thus can be used to rate the thermal performance of different thermosyphon solar water heaters during the energy-collecting period. The cooling loss during the no-radiation period is rated by the system cooling time constant τ_c. The present rating method associated with the Taiwan Standard CNS B7277 has been implemented for more than three years and is accepted by the Taiwan solar industry.     

Sensitivity analysis for room thermal response

The sensitivity theory is a suitable approach for assessing the room thermal response. It results in the ‘sensitivity coefficients’ (SCs) which, as derived here, evaluate the variation of the thermal load due to a fluctuation in a given design parameter around its nominal value. In this paper the general method is presented and a number of SCs are derived to evaluate the sensitivity of the building energy demand to the window surface area, to the overall transmittance and mass thermal capacity of a given wall, and to other structural data.     

Properties of CuIn1−xGaxSe2

Polycrystalline bulk samples of CuIn_1−xGa_xSe₂ weregrown with nominal x = 0.15, 0.25 and 0.5. Mobility, conductivity and band gap were measured at room and low temperatures. Mobilities for x = 0.21 were several hundred cm² V⁻¹s⁻¹ at room temperature and for x = 0.15 were 10³ cm² V⁻¹ s⁻¹, all n type. The band gaps were estimated from the spectra of photoelectrochemical cells at room temperature (with 8.5 K photoluminescence estimates shown in brackets), as 1.10 eV (1.14) for x = 0.21, and 1.07 eV (1.093) for x = 0.15. Crystal mechanical properties as regards cracks were not as good as for CuInSe₂, using similar growth techniques.     

Simulation for flow across heated square cylinders

The thermal lattice Boltzmann method is used to examine forced convection heat transfer from six inline heated square cylinders for Re = 100 at 0.5 ≤ s/d ≤ 4.0, where s is the distance between the surfaces of two cylinders and d is the cylinder size. Such a heat transfer is transient in nature for which the present work reports heat transfer regimes such as synchronous, quasiperiodic and chaotic. For 0.5 ≤ s/d ≤ 1.5 the heat transfer is synchronous, for 1.5 ≤ s/d ≤ 3.0 it is quasiperiodic and for 3.0 ≤ s/d ≤ 4.0 it is chaotic in nature at Re = 100. These regimes are confirmed through cylinder Nusselt number signals, its power spectra, and heat wake interference. The appearance of heat transfer regimes for inline heated cylinders is similar to the appearance of flow regimes for inline unheated cylinders except for the fact that transition from synchronous to quasiperiodic regime occurs at s/d = 1.5 for heat transfer and at s/d = 1.1 for flow. The synchronous heat transfer regime is characterized by a single heat wake that envelopes all cylinders while quasiperiodic heat transfer regime is characterized by the formation of thermal blobs in the gap between cylinders. A chaotic heat transfer regime is characterized by the shedding of thermal blobs and interference of thermal blobs by downstream cylinders. Regardless of spacing, the average Nusselt number encountered by cylinders is smaller than that for the isolated cylinder. The novelty of the work is that transitions occurring in the flow of heat are considered for an understanding of heat flow from bluff bodies.     

Measurement of heat flux from steaming ground

The total thermal flux at the surface of ‘steaming ground’ consists of a convective and a conductive component, even in the absence of any visible steam discharge at the surface. The total flux and its convective component can be measured separately and directly using a water-filled ground calorimeter. The conductive component is given by the difference between the two fluxes, but can also be assessed independently using measured near-surface soil parameters and temperature gradients, retaining the thermal conductivity as parameter. The conductivity is controlled, in turn, by the thermal diffusivity and the specific moisture content of the near-surface layer. The observed total flux values range between 0.03 and 2 kW/m² at sites where boiling temperatures occur at depths of about 4 m and <0.1 m, respectively; the convective flux can reach 50% of the total flux at most sites. Analysis of various soil parameters and soil temperature sections points to a ‘heat pipe’ transfer mechanism that maintains a high conductive transfer in a thin near-surface layer where sub-surface steam condensation is enhanced. An empirical power-law function can be used to assess the total heat flux from the boiling point depth at single sites with known soil temperature profiles.     

Effect of selective surface degradation on the performance of solar water heating systems

Selective surface often degrade in the field. Their solar absorptivity α_s and thermal emittance change with time in service by some amount, say Δα_s and Δ, from their starting values. It is important to quantify the effect this degradation has on the annual fraction solar F_s. A given relative change in F_s can be caused by different combinations of Δα_s, and Δ. In this paper we use computer simulation of solar domestic hot water systems to graph these combinations, in a plot of Δα_s versus Δ, for relative changes in F_s, of 10% and 5%. The slope and intercepts of this plot, which is found to be linear, are studied for their dependence on a wide range of solar system parameters, such as geographical location, collector area, and set point temperature. We find that the slope, and - for starting values of F_s less than about 0.5 - the intercepts, are relatively insensitive to the system parameters. We show that this result is consistent with a simple model. For F_s 0.5, the intercepts rise sharply with F_s, in a way that is strongly (and to some extent, only) dependent on the geographical latitude of location. These results have direct application to projecting the useful service life of a selective surface.     

On the combined influence of Reynolds number and cylinder spacing for flow around a row of heated square cylinders

The characteristics of forced convection heat transfer across a row of heated square cylinders kept in side-by-side arrangement are numerically investigated to examine the combined effects of Reynolds number and cylinder spacing for Ri = 0, 60 ≤ Re ≤ 160, Pr = .71, and s/d = 1.0–8.0, where the space between cylinder surfaces is s and the cylinder size is d. A numerical study was carried out using the thermal lattice Boltzmann method. The goal of this work is to explore the transitions in heat transfer phenomenon that occurs behind the cylinder and to report the corresponding regimes for heat transfer namely synchronous, quasiperiodic, and chaotic. The proposed regime of heat flow is a function of Reynolds number and spacing. The synchronous heat regime is obtained for s/d ≥ 5.0 and quasiperiodic, chaotic regimes are observed for 3.0 ≤ s/d < 5.0, s/d < 3.0, respectively at Re = 100. The instantaneous isotherms, the power spectra of the corresponding Nusselt number signals, and the significance of cylinder Nusselt number frequency are used to examine these heat flow regimes. The heat transfer regimes for a row of heated cylinders and flow regimes for a row of unheated cylinders both have comparable appearances except for the fact that the heat transfer regime is synchronous at s/d ≥ 5.0 and flow is synchronous at s/d ≥ 4.0. The chaotic or quasiperiodic heat transfer regimes occur due to merging and strong interactions between thermal blobs shed from the cylinders. Heat transfer is synchronous at a higher spacing and characterized by independent thermal blobs shedded from the cylinders. It is reported that as spacing reduces and Reynolds number increases, the mean value of the Nusselt number experienced by all cylinders increases. The important outcome of the present numerical work is that for understanding heat transfer from bluff body, the transitions that occur in heat transfer are useful.     

Thermal performance testing of flat-plate collectors

Existing standards for testing the performance of flat-plate solar collectors are documented in ASHRAE 93 [ANSI/ASHRAE Standard 93-2003, 2003. Methods of Testing to Determine Thermal Performance of Solar Collectors, ISSN: 1041-2336, ASHRAE, Inc., 1791 Tullie Circle, Ne, Atlanta, GA30329], ISO 9806-1 [ISO Standard 9806-1:1994(E), 1994. Test Methods for Solar Collectors – Part 1: Thermal Performance of Glazed Liquid Heating Collectors Including Pressure Drop, ISO, Case Postale 56, CH-1211 Geneve 20, Switzerland] and EN12975-2 [European Standard EN12975-2:2001, 2001. Thermal Solar Systems and Components – Solar Collectors – Part 2: Test Methods, CEN, Rue de Stasart, 36, B-1050, Brussels]. The ASHRAE 93 standard requires an experimental determination of the steady-state collector efficiency under prescribed environmental conditions for a range of collector fluid temperatures. Each test requires a minimum of 20 min and 22 tests are required to fully characterize a collector’s thermal performance. The ASHRAE 93 testing procedure is further complicated by the fact that the prescribed weather conditions do not often occur in some locations, which prolongs the time required to conduct the performance tests for a given collector. The EN12975-2 collector test procedure provides an alternative transient test method that can be conducted over a larger range of environmental conditions. This paper compares the results obtained by applying the EN12975-2 standard with results obtained from the ASHRAE 93 steady-state tests for a well-designed single-glazed selective surface flat-plate collector. The collector thermal parameters, F_R(τα)_e and F_RU_L obtained by the two test methods show good agreement. The incident angle modifier coefficient determined in the ASHRAE method, which uses a separate test for this purpose, was found to be more accurate than that determined in the transient method according to the EN12975-2 standard, which obtains this value and all other collector parameters in the same step. This transient method, however, uses a refined collector model that includes specific terms for the wind speed dependence and the collector thermal capacitance, which are absent in the ASHRAE model. The long-term collector thermal performance as a part of a water heating system was simulated using the efficiency curves derived from each of the test methods. The solar fractions obtained by simulation are within 7% for both cases.     

Thermoelastic study of a functionally graded annular fin with variable thermal parameters using semiexact solution

Abstract

In this paper, the thermoelastic behavior of a functionally graded material (FGM) annular fin is investigated. The material properties of the annular fin are assumed to vary radially. The heat transfer coefficient and internal heat generation are considered to be functions of temperature. A closed form solution of nonlinear heat transfer equation for the FGM fin is obtained using the homotopy perturbation method (HPM) which leads to nonuniform temperature distributions within the fin. The temperature field is then coupled with the classical theory of elasticity and the associated thermal stresses are derived analytically. For the correctness of the present closed form solution for the stress field, the results are compared with the ANSYS-based finite element method (FEM) solution. The present HPM-based closed form solution of the stress field exhibits a good agreement with the FEM results. The effect of various thermal parameters such as the thermogeometric parameter, conduction-radiation parameter, internal heat generation parameter, coefficient of variation of thermal conductivity, and the coefficient of thermal expansion on the thermal stresses are discussed. The results are presented in both nondimensional and dimensional form. The dimensional stress analysis discloses the suitability of FGM as the fin material in practical applications.     

Thermal analysis of a flat-plate collector in multiphase flows, including superheat

A thermal analysis of the performance of a solar flat-plate collector operating in nonboiling, boiling, and superheated regimes is presented. The performance of the collector under these single and multiphase conditions is governed by the axial fractional channel lengths of the subcooled (nonboiling) and the superheated regions. The overall thermal loss coefficient, the dimensionless capacitance rate, and collector efficiency factors for various collector operating regions are defined. A new “Generalized Heat Removal Factor,” F_s, and a new overall thermal loss coefficient, U_L, for flat-plate collectors under any operation mode are developed. The thermal efficiency a flat-plate collector, whether under nonboiling, boiling, or superheated conditions, is evaluated using, F_s and U_L. It is shown that the value of F_s decreases and the value of U_L increases as the degree of superheat increases. Current applications of flat-plate collectors having multiphase flows are represented by those charged with refrigerants.     

Mathematical representation of a few chosen weather parameters of the capital zone ‘Damascus’ in Syria

This work presents a mathematical representation of a few chosen weather parameters of the capital zone ‘Damascus’ in Syria.Seasonal models, as an alternative to the use of hourly historical weather data, were suggested and used to generate synthetic weather data for the following parameters:

– relative humidity;

– atmospheric pressure;

– wind speed;

– global solar radiation intensity.

Such mathematical models were derived for the heating season (November to April) and for the air-conditioning season (June to September) in the zone involved. Moreover, daily sunshine-hours rate was also represented by single model throughout a year. These models were developed based on long time records of data.The choice of the best model was based on three statistical parameters: the coefficient of determination R², the mean relative error e_m and the t-test.The predicted values along with the recorded data were plotted on the same scale in order to consider a visual comparison between them. It is visually noticeable that good agreement between the predicted and observed data values was obtained.The question of whether both, the stochastic and deterministic components of the analyzed weather parameters have to be included in building thermal performance calculation was investigated. It was demonstrated that on an hour-to-hour basis, the stochastic component may be disregarded in building thermal performance calculations without significantly affecting the results.     

A computational method for determining segmental and overall geothermal gradients and geothermal heat flow values

A new computational method is presented which calculates geothermal heat flow values and geothermal gradients with more precision than permitted by previously published techniques. The data required are: geothermal temperature at a known depth, mean surface temperature, the rock types in the stratigraphic column and the thermal resistivity values for the different types of rocks. This method is valuable in areas that have no measured gradient values. Basic equation used was the Fourier heat transfer equation where is heat flux in μcal/(cm² s), ρ_i is thermal resistivity (°C s cm/μcal) and ∂T/∂x is the x component of the temperature gradient (°C/cm). The thermal resistivity was allowed to vary linearly with temperature ρ_i = ρ_i^o [1 + K_i (T − 30)] where ρ_i is thermal resistivity of the lithographic segment «iå at a temperature T, ρ_i^o is thermal resistivity at 30°C and K_i is the temperature coefficient of thermal resistivity. The procedure consisted of integrating the combined equation for heat flux in terms of temperature dependent resistivity.Two iterative solutions were used to simplify the calculations: exact and approximate. The heat flux for each well was assumed to be 1.0 HFU and segmental temperatures were calculated from the bottom (arbitrarily) up, until a surface temperature was obtained. The calculated surface temperature could then be compared with the mean surface temperature (MST). Correction in the heat flux value was made until the calculated surface temperature and MST agreed. An analysis of three deep Appalachian test wells was made and the results showed the critical importance of lithographic ordering and the temperature dependence of thermal resistivity upon calculated geothermal quantities.     

Thermal–electrical–luminous model of multi-chip polychromatic LED luminaire

This paper proposed a thermal–electrical–luminous dynamic model of red–green–blue (RGB) light-emitting diode (LED) luminaire for lighting control. The thermal–electrical–luminous model consists of three parts, namely, electrical–thermal (E–T), electrical–luminous (E–L), and thermal–luminous (T–L) models. Using step response method, the electrical–thermal (E–T) model G(s) is derived as a first-order bi-proper system. The electrical–luminous (E–L) and thermal–luminous (T–L) models are zeroth order model with a constant gain since the luminous response to electric or thermal input is much faster. The thermal–electrical–luminous model shows that the luminous intensity is proportional to input power and inversely proportional to junction temperature. The dynamic response of luminous intensity is dominated by the electrical–thermal model G(s).The whole thermal–electrical–luminous model can be further divided into a constant gain and a first-order bi-proper system. The constant gain causes the instantaneous response at power switch on; the first-order system represents the luminous variation due to junction temperature change which is mainly related to the heat sink design. The complete model can accurately describe luminous dynamic behavior and be used in control system design of RGB LED lighting luminaire.     

Simulation numérique des transferts thermiques entre une cavite enterrée et le sol : méthode des fonctions de transfert bidimensionnelles et sous-structuration

Numerical simulation of heat transfer between an earth-sheltered cavity and the soil: two-dimensional transfer functions method and subdivision. This paper describes the use of the two-dimensional transfer functions method for predicting the heat transfer between an earth-sheltered cavity and the surrounding ground. This method is first, applied for the generation of the transfer function coefficients for the system formed by the whole “earth-sheltered cavity–soil”. Then, the latter is decomposed into different layers. Each layer is characterised by its inputs and outputs and by its appropriate transfer functions coefficients. This technique allows a significant reduction in the computation time required to generate the transfer function coefficients of the cavity coupled to the soil. These methods are tested by comparing their results with those of the alternative directions implicit method (ADI) for various situations. The influence of parameters that have large effects on heat transfer such as the cavity depth, the thermal insulation, the nature and the thickness of the cavity walls are studied in typical climates.     

Investigation of twisted tape inserted solar water heaters—heat transfer, friction factor and thermal performance results

Heat transfer in a solar water heater could be enhanced by means of twisted tapes, inserted inside the fluid flow tubes, which induce swirl flow and act as turbulence promoters. Experimental investigations for a solar water heater with twisted tape inserts having twist pitch to tube diameter ratio ranging from 3–12 have been carried out for varying mass flow rates. The results on heat transfer and friction data have been found to compare well with available results. Within the range of investigated parameters, the heat transfer in the twisted tape insert collectors has been found to increase by 18–70%, whereas the pressure drop increased by 87–132%, as compared to plane collectors. An expression correlating the Nusselt numbers in twisted tape and plane collectors, the twist pitch ratio has been developed in the form of Nu_s/Nu=1.3+2.88/y, which predicts the heat transfer within the range of the present investigation. Results conclude that such collectors would be preferable for higher grade energy collection as it is also at higher rate.Solar water heaters having twisted tape inserts inside the flow tubes perform better than the plane ones. It has been observed that heat losses are reduced (due to the lower value of the plate temperature) consequently increasing the thermal performance by about 30% over the plane solar water heaters under the same operating conditions. The effect of twisted-tape geometry, flow Reynolds number and intensity of solar radiation on the thermal performance of the solar water heater has been presented. It has been found that the twisted-tape collectors perform remarkably better in the lower range of flow Reynolds number (Re≈12,000), beyond which the increase in thermal performance is monotonous. It has also been found that such collectors might perform even better at higher values of intensity of solar radiation.     

Analysis of the effective thermal conductivity of fractal porous media

Several types of fractals are generated to model the structures of porous media, and heat conduction in these structures is simulated by the finite volume method (FVM). The influences of the thermal conductivity of solid k_s, the thermal conductivity of fluid k_f, the porosity ε, the size and spatial distribution of pores on the effective thermal conductivity k_e of these structures are analysed in detail. The calculated results indicate that the relation of effective thermal conductivity k_e with thermal conductivity of solid k_s and thermal conductivity of fluid k_f conforms to a power function, and the relation of effective thermal conductivity k_e with porosity ε conforms to an exponential function. The porosity ε is the most important factor that determines the effective thermal conductivity of fractal porous media, but the size and spatial distribution of pores, especially the spatial distribution of the bigger pores, do have substantive influence. The numerical results are analysed by comparing with the available empirical formulas from literatures, and provide verification of these empirical formulas.