Constant Convective Heat Transfer Coefficient Research Articles

Theoretical modeling of heat transfer in a multilayer rectangular body with spatially-varying convective heat transfer boundary condition

Theoretical analysis of heat transfer in a multilayer body is relevant for several engineering applications where heat transfer occurs through a stack of thermally dis-similar materials. In most of such literature, a constant convective heat transfer coefficient is assumed as a boundary condition at one end of the body. In contrast, there is a lack of work to model a problem with spatial variation in the convective heat transfer coefficient. This paper presents an analytical solution for thermal conduction in a multilayer rectangular body with spatially varying convective heat transfer coefficient at one end. In addition, this solution also accounts for internal heat generation and inter-layer thermal contact resistance and spatially varying heat flux on the other end of the body. The solution is derived in a series form, and it is shown that the coefficients of the series can be determined by solving a well-defined set of linear algebraic equations. The analytical solution is verified by comparison with numerical simulations, as well as with standard solution for a simplified special case. The impact of spatially varying cooling provided by jet impingement is analyzed using the analytical solution. A resource optimization problem pertaining to the optimal use of jet cooling is solved. Results presented here may benefit thermal management analysis of a broad variety of engineering applications involving heat transfer in multi-layer bodies.

Experimental characterization and modeling of boundary conditions and flame spread dynamics observed in the UL-94V test

Abstract To characterize the UL-94 vertical burning test (UL-94 V), temperature, oxygen content, and heat flux of the burner flame were measured using an R-type thermocouple, oxygen analyzer, and water-cooled Schmidt–Boelter gage, respectively. To account for sample geometry, mock samples from Kaowool PM insulation board were used during the burner measurements. Temperature and heat flux measurements were used to express the heat flux of the burner as a linear, piecewise function of burner flame temperature and a constant convective heat transfer coefficient. UL-94 V tests were conducted using 0.27 cm thick poly(methyl methacrylate) (PMMA) samples with and without insulated sides to investigate edge effects. All UL-94 V tests were recorded on video using a 900-nm narrow-band filter to focus on emissions from soot for tracking flame length over time. In some of these tests, a heat flux gage was embedded into the sample to measure PMMA flame heat flux to verify a previously developed laminar wall flame heat feedback submodel. PMMA flame heat fluxes of insulated samples confirmed the wall flame submodel, while non-insulated samples had significantly greater heat fluxes; the flame submodel was scaled accordingly. The burner and wall flame heat flux submodels were combined with an independently developed pyrolysis model of PMMA to conduct two-dimensional, time-resolved simulations of the UL-94 V test. Burner flame oxygen content was measured to be about 5 vol% and was found to enhance PMMA decomposition. Inclusion of the oxygen effect was essential to predict ignition. The simulation predicted flame length and spread on insulated UL-94 V samples reasonably well, validating the submodels. However, the simulation underpredicted flame length on the non-insulated samples; discrepancies were attributed to burning and spread on the edges which were not modeled explicitly. The developed model can be applied to non-charring polymeric solids with no to moderate amount of dripping. Its applicability for charring and intumescent materials will be explored in the future.

Temperature distribution in a multi-layer cylinder with circumferentially-varying convective heat transfer boundary conditions

Theoretical modeling of thermal conduction in a multilayer cylinder has been studied in multiple past papers due to its significance in engineering applications such as nuclear engineering, energy storage and sensing. Most past papers have assumed a constant convective heat transfer coefficient on the outer surface of the cylinder. However, a circumferentially varying heat transfer coefficient may be appropriate in several applications due to the distributed nature of fluid flow around the cylinder. This paper presents a theoretical model for steady-state thermal conduction in a multilayer cylinder with circumferentially-varying convective heat transfer coefficient on the cylinder surface. The theoretical model is presented for both solid and annular cylinders. A series solution is derived for the temperature distribution in each layer by using the convective boundary condition(s) to derive a set of linear algebraic equations for the coefficients of the inner-most layer. Results are shown to be in good agreement with numerical simulations and with closed-form solutions for special cases. The impact of various problem parameters, such as internal heat generation rate and thermal contact resistances on the temperature distribution is analyzed. It is expected that the results presented in this work will improve the theoretical understanding of multilayer heat transfer and be of practical use in multiple engineering applications.

Numerical investigation of thermal performance of extended surfaces for a novel heat exchanger

AbstractThe present paper provides a thorough numerical study of variation in geometrical parameters that affect the performance of the novel finned‐tube type heat exchanger design. The finite volume method was employed to discretize and solve the governing partial differential equations of heat conduction. A wide range of constant convective heat transfer coefficient (5 < h < 200 W/m2 K) is chosen to reduce the computational time and power, which covers thermal applications of latent thermal energy storage, refrigeration & air‐conditioning, etc. The effects of the ratio of fin spacing of fins to the outer diameter of the tube (0.1 ≤ δ* ≤ 8), the material of fins (copper and stainless steel) and the ratio of fin thickness to the outer diameter of the tube (0.0333 ≤ t* ≤ 0.4) on the performance parameters namely efficiency (η) and effectiveness (ε) of the fins were studied. Temperature contours for a wide range of geometries were depicted. The maximum effectiveness of copper fins is 304.62, whereas that for steel fin is 219.33 with the optimum dimensionless fin thickness reported to be t* = 0.1666. Furthermore, the maximum overall efficiencies of fins were 99.98% and 99.62% for copper and steel fins, respectively.

Estimation of thermal conductivity of low thermal conductive solid materials using the jet flush method

A novel and practical transient-type technique named as “Jet Flush” is proposed for measuring temperature-dependent thermal conductivity of solid materials with low thermal conductivity. In order to estimate thermal conductivity of the sample, its surface is exposed to an impinging air jet flow with higher (or lower) temperature than the sample for a short period of time, while an infrared thermometer records the heated (or cooled) surface temperature history. A nonlinear 1D inverse heat conduction problem with constant convective heat transfer coefficient on the boundary condition is then employed for determining the temperature-dependent thermal conductivity using the measured temperatures. As a requirement for solving the inverse problem, the convective coefficient on the surface of the sample is measured in a separate experiment with the same flow condition using a standard sample. Sensitivity and error analyses are performed to discuss the effects of the estimation points (the temperatures in which the thermal conductivity is to be estimated), and the simplification assumption of constant convective heat transfer coefficient (with respect to time) on the solution of the inverse problem and the accuracy of the estimated results. In order to demonstrate the applicability of the proposed method, the thermal conductivities of three polymer-type materials (HDPE, PMMA and PA6) are measured over the temperature range of ~22–62 °C, and the results are found to be in good agreement with literature data. Moreover, the uncertainty analysis performed in this study showed that the accuracy of the proposed method can be better than 5% for an appreciable temperature range.

What is the Required Level of Details to Represent the Impact of the Built Environment on Energy Demand?

A full coupling between a CFD code, a thermo-radiative model and a building energy simulation model enables Solene-microclimat software to calculate both building thermal behavior and urban microclimate with the retroaction of buildings on microclimate. However, this full coupling is time consuming and it is legitimate to wonder if it is always necessary to perform such detailed simulations. In the framework of the MERUBBI project, simulations were carried out to answer this question. A set of simulations was designed to explore different kinds of configurations: three cities in France (Nantes, Paris and Strasbourg), three levels of density (from an isolated building to an implementation in the dense city center) and three kinds of buildings (an individual house in Paris, a residential building in Nantes and an office building in Strasbourg). To study the sensitivity of energy demand to the coupling detail, for each thermal flux at the external surfaces of the building, several levels of details were taken into account. For the impact of wind on convection, three modalities were considered: a constant convective heat transfer coefficient, calculated from the wind velocity at 10m; a convective heat transfer coefficient calculated from a vertical wind profile; a convective heat transfer coefficient calculated from the local wind velocity simulated with a CFD code. For the impact of air temperature on convection, two modalities are considered the use of the temperature measured at the nearest meteorological station; a local temperature calculated with the CFD simulation. For the impact of long-wave radiative exchanges, three modalities: the building exchanges with the sky without taking into account the masks of the environment and the long-wave radiative exchanges with the other surfaces; the building exchanges with the sky, taking into account the mask effects but not the exchanges with the surrounding surfaces; long-wave exchanges are taken into account with all kinds of surfaces in function of view factors. For the impact of short-wave radiations, two modalities: only direct and diffuse solar fluxes are taken into account; inter-reflections are considered. The results indicate that if the calculation of air temperature and convective heat transfer coefficient have few impacts in all the cases, the way of calculating long-wave and short wave radioactive fluxes has to be carefully considered, in winter as in summer. More detailed recommendations are given according to the density of the site in which the building will be implemented.

Thermal Analysis in Gas Insulated Transmission Lines Using an Improved Finite-Element Model

In this paper, an improved finite element (FE) model is proposed to investigate the temperature distribution in gas insulated transmission lines (GILs). The solution of joule losses in eddy current field analysis is indirectly coupled into fluid and thermal fields. As is different from the traditional methods, the surrounding air of the GIL is involved in the model to avoid constant convective heat transfer coefficient, thus multiple species transport technique is employed to deal with the problem of two fluid types in a single model. In addition, the temperature dependent electrical and thermal properties of the materials are considered. The steady-state and transient thermal analysis of the GIL are performed separately with the improved model. The corresponding temperature distributions are compared with experimental results reported in the literature. DOI: http://dx.doi.org/10.11591/telkomnika.v11i1.1247 Full Text: PDF

Thermal Analysis of a Novel Compact Packaged Passively Cooled Laser Diode Array

The temperature of a laser diode array chip must be maintained under a safe level during operation in order to achieve satisfactory performance and lifetime. In this paper, 3-D thermal analysis on diode heatsink is presented. The boundary condition at the bottom of heatsink is constant convective heat transfer coefficient. In addition, heat transfer in thermal-entry region of tubes is accounted for to calculate the convective heat transfer coefficient. Moreover, a 12 mm times 37 mm times 7 mm passively cooled laser diode array cooled by a base heatsink is demonstrated. Up to 62 W output power with an electrical-to-optical conversion efficiency of 49.2% are achieved. System thermal resistance of 0.77 K/W is obtained when the flow rate through the base heatsink with 0.8-mm-wide, 2-mm-high and 20-mm-long channels is 25 cm3/s.

Numerical Modeling of Droplet Transient Heating and Evaporation

Several approaches to numerical modelling of liquid droplet heating and evaporation by convection and radiation from the surrounding hot gas are discussed. The finite thermal conductivity of liquid, recirculation in droplets, and time dependence of gas temperature and the convection heat transfer coefficient are taken into account. For the constant and almost constant convection heat transfer coefficient the new analytical solutions of the heat conduction equation inside droplets are incorporated into the numerical code. For the abitrary convection heat transfer coefficient the numerical solution of the latter equation is replaced by the numerical solution of the Volterra integral equation of the second kind. Direct comparison between these approaches shows that the solution based on the assumption of constant convective heat transfer coefficient is the most computer efficient for implementation into numerical codes. The results of the application of this approach to the numerical modelling of fuel droplet heating and evaporation in conditions relevant to diesel engines are briefly discussed. This approach is more effective than the approach based on the numerical solution of the discretised heat conduction equation inside the droplet, and more accurate than the solution based on the parabolic temperature profile model. The relatively small contribution of thermal radiation to droplet heating allows us to take it into account using a simplified model, which does not consider the variation of radiation absorption inside droplets.

Effect of variable heat transfer coefficient on tissue temperature next to a large vessel during radiofrequency tumor ablation

BackgroundOne of the current shortcomings of radiofrequency (RF) tumor ablation is its limited performance in regions close to large blood vessels, resulting in high recurrence rates at these locations. Computer models have been used to determine tissue temperatures during tumor ablation procedures. To simulate large vessels, either constant wall temperature or constant convective heat transfer coefficient (h) have been assumed at the vessel surface to simulate convection. However, the actual distribution of the temperature on the vessel wall is non-uniform and time-varying, and this feature makes the convective coefficient variable.MethodsThis paper presents a realistic time-varying model in which h is a function of the temperature distribution at the vessel wall. The finite-element method (FEM) was employed in order to model RF hepatic ablation. Two geometrical configurations were investigated. The RF electrode was placed at distances of 1 and 5 mm from a large vessel (10 mm diameter).ResultsWhen the ablation procedure takes longer than 1–2 min, the attained coagulation zone obtained with both time-varying h and constant h does not differ significantly. However, for short duration ablation (5–10 s) and when the electrode is 1 mm away from the vessel, the use of constant h can lead to errors as high as 20% in the estimation of the coagulation zone.ConclusionFor tumor ablation procedures typically lasting at least 5 min, this study shows that modeling the heat sink effect of large vessels by applying constant h as a boundary condition will yield precise results while reducing computational complexity. However, for other thermal therapies with shorter treatment using a time-varying h may be necessary.

New approaches to numerical modelling of droplet transient heating and evaporation

New approaches to numerical modelling of droplet heating and evaporation by convection and radiation from the surrounding hot gas are suggested. The finite thermal conductivity of droplets and recirculation in them are taken into account. These approaches are based on the incorporation of new analytical solutions of the heat conduction equation inside the droplets (constant or almost constant h) or replacement of the numerical solution of this equation by the numerical solution of the integral equation (arbitrary h). It is shown that the solution based on the assumption of constant convective heat transfer coefficient is the most computer efficient for implementation into numerical codes. This solution is applied to the first time step, using the initial distribution of temperature inside the droplet. The results of the analytical solution over this time step are used as the initial condition for the second time step etc. This approach is applied to the numerical modelling of fuel droplet heating and evaporation in conditions relevant to diesel engines, but without taking into account the effects of droplet break-up. It is shown to be more effective than the approach based on the numerical solution of the discretised heat conduction equation inside the droplet, and more accurate than the solution based on the parabolic temperature profile model. The relatively small contribution of thermal radiation to droplet heating and evaporation allows us to take it into account using a simplified model, which does not consider the variation of radiation absorption inside droplets.

An analytical solution of thermal resistance of cubic heat spreaders for electronic cooling

A three-dimensional analytical solution using the method of Fourier expansion is developed for determination of the spreading thermal resistance of a cubic heat spreader for electronic cooling applications. The model assumes that the heat spreader is receiving a uniform heat flux centroidally with a projected heating area from the heat source. Heat is conducted inside the heat spreader in a three-dimensional coordinate, then transferred to a heat sink with a constant convective heat transfer coefficient. Dimensionless expressions in the form of infinite series are provided to compute the maximum spreading thermal resistance, the surface temperature fields and the heat flux distribution as a function of relative projected heating area, plate thickness and Biot number. The correlation developed herein is effective and accurate to predict the spreading thermal resistance.

An inverse thermal field problem based on noisy measurements: comparison of a genetic algorithm and the sequential function specification method

Draws a comparison between the use of a genetic algorithm and the sequential function specification method for the solution of a one‐dimensional linear inverse thermal field problem, based on the use of noisy measurements. In solving this problem aims to estimate the value of a single constant convective heat transfer coefficient. Documents the findings that both approaches can provide estimates within 1 per cent of the target solution and that the sensitivity and robustness of each approach to measurement location, time step size and measurement errors are markedly different.

Transient heat conduction in a glass with chemically deposited SnSCu xS solar control coating

The transient thermal performance of a chemically deposited thin film on a glass substrate is presented. Differential energy balances for the glass are set up assuming a one-dimensional transient state for normal incidence of the air mass to solar radiation. Using the reported properties of a SnS-Cu xS thin film as a specific example, the net energy flow through a glass and the specific film were calculated for a time period. The effect of absorption in the film is specifically considered. The theoretical time histories of the surface temperatures of the glass plus solar control coating and the clear glass are plotted for an exterior temperature range of 0–50°C. The redistribution to the interior and exterior of the absorbed component of the solar radiation as well as the shading coefficient in time are evaluated for a constant convective heat transfer coefficient for ambient temperatures of 30 and 20°C. Also, the time constant of the system is given.

An exact solution for one-dimensional acoustic fields in ducts with an axial temperature gradient

Abstract In this paper an approach is presented for obtaining exact analytical solutions for sound propagation in ducts with an axial mean temperature gradient. The one-dimensional wave equation for ducts with an axial mean temperature gradient is derived. The analysis neglects the effects of mean flow, and therefore the solutions obtained are valid only for mean Mach numbers that are less than 0.1. The derived wave equation is then transformed to the mean temperature space. It is shown that by use of suitable transformations, the derived wave equation can be reduced to analytically solvable equations (e.g., Bessel’s differential equation). The applicability of the developed technique is demonstrated by obtaining a solution for ducts with a linear temperature profile. This solution is then applied to investigate the dependence of sound propagation in a quarter wave tube upon the mean temperature profile. Furthermore, the developed analytical solution is used to extend the classical impedance tube technique to the determination of admittances of high temperature systems (e.g., flames). The results obtained using the developed analytical solution are in excellent agreement with experimental as well as numerical results. Analytical solutions were also obtained for a duct with an exponential temperature profile and also for a temperature profile that corresponds to a constant convective heat transfer coefficient at the wall.

Contribution to the study of thermal erosion on Mars

Similar to the coldest terrestrial periglacial regions like Yakutia (Siberia), the planet Mars exhibits wide outflow channels. This analogy and the presence of permanent ground ice suggest that thermal erosion have existed during Martian fluvial outbursts 3000 m.y. ago. Thermal erosion here is considered to be the result of ground thawing produced by heat transfer between the water flow and the frozen ground, followed by a transport of unfrozen sediments. This paper proposes a qualitative explanation of thermal erosion with the help of some physical models. From the quantitative point of view, two thermal mathematical models are proposed and discussed. The zones undergoing the most efficient erosion are river banks. The first model studied here describes extreme thermomechanical actions: a constant thermal flux on the ground surface produces ground thaw, and the unfrozen sediments are immediately removed by water flow. It is an ablation model. It allows a theoretical evaluation of the river bank recession. Validity of theoretical estimations is acquired by comparing the calculations to the observed backwearing of the banks of some Siberian rivers which can reach 25 m yr−1. Thermal erosion acting upon the bottom of wide rivers (on Mars or in Siberia as well) is a very complex mechanism. Indeed, the mathematical modeling requires the study of interaction between thermal processes and transport of sediments laws. These laws are not yet well defined and are very difficult to establish. Thus another model presented in this paper concerns only one‐dimensional thermal actions of water flow upon the bottom of wide rivers. It considers fluvial flow at positive Celsius temperature producing a thermal flux from the bottom to the initially frozen semi‐infinite ground. This model considers a constant convective heat transfer coefficient and allows an estimation of the thickness of the thawed ground beneath the river (talik). Calculated thickness of the melted ground is given in the paper for different periods of time.

Thermal performance of an architectural window with chemically deposited SnSCu xS solar control coating

A mathematical model enabling the prediction of the thermal performance of solar control glazings employing chemically deposited solar control coatings with or without a transparent protective polymer coating is presented. Differential energy balance for the glazing is set up assuming one-dimensional steady state case for normal incidence of air mass 2 solar radiation and by considering conductive heat transfer within the glazing and convective and radiative heat transfer into the interior and exterior of the building. Using the specific example of the optical properties of the already reported SnSCu x S solar control coatings, the redistribution of the absorbed component of the solar radiation is evaluated for constant convective heat transfer coefficient and temperature in the interior and for exterior temperatures in the 0–50°C range. The results yield shading coefficient versus exterior temperature curves for two specific SnSCu x S coatings without and with a protective transparent varnish and offering transmittance in the visible region of 27 and 21%.

Local Heat Transfer Behavior and Its Impact on a Single-Row, Annularly Finned Tube Heat Exchanger

Experimental studies of the local mass transfer characteristics of annularly finned tubes in crossflow are presented. Variations due to boundary layer development, forward-edge separation, the tube wake, horseshoe vortices, and tip vortices are discussed. In addition, regularly located local maxima in mass transfer rates associated with the horseshoe vortex system are found, and conjecture as to their mechanism is offered. Inferring heat transfer behavior from the mass transfer results, we find that the true fin efficiency is always less than that obtained with an assumed constant convective heat transfer coefficient. The difference is 3–7 percent for high-conductivity materials such as aluminum alloys, and 9–17 percent for low-conductivity materials such as mild steels.

Boundary Perturbation Method for Free Boundary Problem in Convectively Cooled Continuous Casting

Novel mathematical techniques are here used to treat general boundary conditions in convectively cooled continuous ingot casting problems, applying a constant convective heat transfer coefficient at the ingot sides (so that the temperature distribution along the sides is unknown). The problem is first inverted to treat the physical coordinates as dependent variables of temperature and heat flow, mapping the ingot into a region that is nearly rectangular. A boundary perturbation method is then used to obtain an analytical solution in this near-rectangular region. Solidification interface shapes depend on two dimensionless parameters: one is a function of the casting velocity, while the other is dependent on the convective heat transfer coefficient at the cooled wall.