Thermal Convective Coefficient Research Articles

Performance and optimization analysis of a constructal T-shaped fin subject to variable thermal conductivity and convective heat transfer coefficient

In the present study, an exercise has been devoted to establish an analytical model for thermal performance and optimization of a constructal fin subject to variable thermal conductivity of fin material and convective heat transfer coefficient over the fin surface. For the adaptation of these considerations, the governing energy equation for the stem as well as the flange becomes nonlinear. A new analytical scheme based on the Adomian decomposition method has been established for the solution process. As the present study is an analytic, it can be extended to the analysis for determining the optimum dimensions of fins satisfying either the maximization of rate of heat transfer for a given fin volume or the minimization of fin volume for a desired heat transfer rate. From the results, it can be highlighted that the present model predicts the fin performance always an under value in comparison with that the published results whereas the optimum heat transfer rate determined by using the present analysis gives an over value. The effect of different geometric and thermophysical parameters on both the fin performance and optimization has been studied. For a comparative study, the present and published results are executed for a wide range of thermogeometric parameters.

Convective heat transfer characteristics of nanofluids under laminar and turbulent flow conditions

To investigate the effect of nanofluids on convective heat transfer, an experimental study was performed through a circular straight tube with a constant heat flux condition in the laminar and turbulent flow regime. Stable nanofluids, which were water-based suspensions of alumina and amorphous carbonic nanoparticles, were prepared by two- and one-step methods. The effects of thermal conductivity and supernatant nanoparticles of the nanofluids on convective heat transfer were investigated under different flow regimes. In alumina nanofluids containing 3 vol% of suspended particles, the increment of thermal conductivity and convective heat transfer coefficient was 8% and 20%, respectively. For amorphous carbonic nanofluids, the thermal conductivity was similar to that of water, and the convective heat transfer coefficient increased by only 8% in laminar flow. In a comparison of thermal conductivity and convection, the enhancement of the convective heat transfer was much higher than that of the thermal conductivity of nanofluids. The movements of nanoparticles enhanced the convective heat transfer at the entrance region.

Heat transfer and flow behaviour of aqueous suspensions of titanate nanotubes (nanofluids)

Titanate nanotubes of an aspect ratio of ~ 10 are synthesized, characterised and dispersed in water to form stable nanofluids containing 0.5, 1.0 and 2.5 wt.% of the nanotubes. Experiments are then carried out to investigate the effective thermal conductivity, rheological behaviour and forced convective heat transfer of the nanofluids. The results show a small thermal conductivity enhancement of ~ 3% at 25 °C and ~ 5% at 40 °C for the 2.5 wt.% nanofluid. The nanofluids are found to be non-Newtonian with obvious shear thinning behaviour with the shear viscosity decreasing with increasing shear rate at low shear rates. The shear viscosity approaches constant at a shear rate higher than ~ 100–1000 s − 1 depending nanoparticle concentration. The high shear viscosity is found to be much higher than that predicted by the conventional viscosity models for dilute suspensions. Despite the small thermal conduction enhancement, an excellent enhancement is observed on the convective heat transfer coefficient, which is much higher than that of the thermal conductivity enhancement. In comparison with nanofluids containing spherical titania nanoparticles under similar conditions, the enhancement of both thermal conductivity and convective heat transfer coefficient of the titanate nanotube nanofluids is considerably higher indicating the important role of particle shape in the heat transfer enhancement. Possible mechanisms are also proposed for the observed enhancement of the convective heat transfer coefficient.

Estimation of parameters in multi-mode heat transfer problems using Bayesian inference – Effect of noise and a priori

Parameter estimation problems and heat source/flux reconstruction problems are some of the most frequently encountered inverse heat transfer problems. These problems find their application in many areas of science and engineering. The primary focus of this paper is on the heat transfer parameter estimation for a two-dimensional unsteady heat conduction problem with (a) convection boundary condition and (b) convection and radiation boundary condition. The paper demonstrates the effect of a priori model on the performance of the algorithm at different noise levels in the measured data. The inverse problem is solved using three different a priori models namely normal, log normal and uniform. The posterior PDF is sampled using the Metropolis–Hastings sampling algorithm. Both single-parameter estimation and multi-parameter estimation problems are addressed and the effects of corresponding a priori models are studied. It was found that the mean and maximum a posteriori estimates for thermal conductivity and the convection heat transfer coefficient were insensitive to the a priori model at all the considered noise levels for the single-parameter estimation problem. At high noise levels in the two-parameter estimation problem, the estimates for thermal conductivity and convection coefficient were sensitive to the a priori model. It was also found that the standard deviation of the samples was correlated to the error in estimation in the single-parameter estimation case. In three parameter estimation case, alternate solutions to the same problem were retrieved due to a strong correlation between the convection coefficient and the emissivity. However, a more informative a priori model could address this issue.

A review on simultaneous determination of thermal diffusivity and heat transfer coefficient

Mathematical simulation studies for thermal food processes require knowledge of thermal diffusivity and convective heat transfer coefficient. There have been different experimental and empirical approaches reported in the literature for determination of these parameters where different approximations were applied. One of the most applied approaches is to assume an infinite convective heat transfer coefficient at the surface boundary when analytical solutions for infinite slab, infinite cylinder and sphere are used for further determinations. Since this approach results in certain errors in results, it would be an important task to determine thermal diffusivity and convective heat transfer coefficient simultaneously. Therefore, the objective of this study was to review the literature for determination of thermal diffusivity and mathematically apply optimization methodologies for simultaneous determination of heat transfer coefficient. For this purpose, constrained optimization methodologies, based on analytical solutions of infinite slab, infinite cylinder and sphere were defined, and results were discussed intensively. The results showed that a precise determination of thermal diffusivity and convective heat transfer coefficient is a difficult task, but knowing the location where the experimental time–temperature was obtained would really simplify this problem.

세라믹 분말을 이용한 오일 기지 나노유체의 열적거동 평가

Oil-based nanofluids were prepared by dispersing spherical and fiber shaped <TEX>$Al_2O_3$</TEX> and AlN nanoparticles in transformer oil. Two hydrophobic surface modification processes using oleic acid (OA) and polyoxyethylene alkyl acid ester (PAAE) were compared in this study. The dispersion stability, viscosity and breakdown voltage of the nanofluids were also characterized. <TEX>$(Al_2O_3+AlN)$</TEX> mixed nanofluid was prepared to take an advantage of the excellent thermal conductivity of AlN and a good convective heat transfer property of fiber shaped <TEX>$Al_2O_3$</TEX>. For <TEX>$(Al_2O_3+AlN)$</TEX> particles with 1 % volume fraction in oil, the enhancement of thermal conductivity and convective heat transfer coefficient was nearly 11 % and 30 %, respectively, compared to pure transformer oil. The nanofluid, containing <TEX>$Al_2O_3+AlN$</TEX>, successfully lowered the temperature of the heating element and oil itself during a natural convection test using a prototype transformer.

Heat transfer of gas flow through a packed bed

This paper reports an experimental study of both the transient and steady-state heat transfer behaviour of a gas flowing through a packed bed under the constant wall temperature conditions. Effective thermal conductivities and convective heat transfer coefficient are derived based on the steady-state measurements and the two-dimensional axial dispersion plug flow (2DADPF) model. The results reveal a large temperature drop at the wall region and the temperature drop depends on the axial distance from the inlet. The 2DADPF model predicts the axial temperature distribution fairly well, but the prediction is poor for the radial temperature distribution. Length-dependent behaviour of the effective heat transfer parameters and non-uniform flow behaviour are proposed to be responsible. A comparison with previously published correlations and data in the literature shows that the relationships proposed by Bunnell et al. and Demirel et al. agree well with the measured effective radial thermal conductivity, whereas the wall–fluid heat transfer coefficient is better represented by the Li–Finlayson correlation.

Determination of thermal conductivity and convective heat transfer coefficient during deep fat frying of “Kroštula” dough

In this study, the influence of oil temperature, water migration and surface temperature of “Krostula” dough on convective heat transfer coefficient was investigated. The convective heat transfer coefficient during deep fat frying was determined at temperatures 160, 170, 180 and 190±1 °C. Heat transfer coefficient was the highest at the start of deep fat frying process; 579.12±2.46, 583.88±1.81, 597.05±1.10 and 657.91±0.95 W/m2 K for 160, 170, 180 and 190 °C of oil temperature, respectively. The smallest heat transfer coefficient was in the case of setting up a uniform period of water migration from sample, which corresponded to surface temperatures slightly higher than 100 °C; 26.53±0.63, 14.42±0.56, 56.78±0.49 and 37.52±0.54 W/m2 K for 160, 170, 180 and 190 °C of oil temperature, respectively. Higher oil temperature for deep fat frying increased values of heat transfer coefficient. A steady-state method was used to determine thermal conductivity of “Krostula” dough in temperature range of 40–70±1 °C. The thermal conductivity first increased with temperature and then after reaching maximum values decreased. The maximum value 0.5985±0.0196 W/(m K) was determined at 47.5 °C. The minimal value 0.4723±0.0192 W/(m K) was determined at 65 °C.

Easy and rapid computation of the transfer of heat from annular fins of nearly optimal profile with the finite‐difference technique and the shooting method

It is undeniable that the annular fin of hyperbolic profile with constant thermal conductivity and uniform convective coefficient is important in many applications of heat transfer engineering. The importance of this fin configuration stems from its close resemblance to the annular fin of optimal cross section capable of delivering maximum heat transfer for a given volume of material. This paper addresses two simple numerical procedures for solving the generalized Bessel equation that governs the temperature variation in annular fins of hyperbolic profile, one is the finite‐difference technique with an uncharacteristic coarse mesh and the other is the shooting method. Certainly, the central objective here is to avoid the evaluation of the elegant, but intricate exact analytic temperature distributions and companion fin efficiencies containing modified Bessel functions of fractional order.

Avenues for Computing the Heat Transfer from a Circular Fin of Hyperbolic Cross-Sectional Profile

The circular fin of hyperbolic profile with constant thermal conductivity and uniform convective coefficient is of remarkable importance in heat transfer engineering. This particular fin resembles the optimal circular fin of convex parabolic profile, which delivers the maximum heat transfer for a given volume of material. The circular fin of hyperbolic profile is governed by a two-term differential equation of second order with one variable coefficient which, via a transformation, can be converted into a Bessel equation. Setting aside the use of Bessel functions, the present paper addresses three elementary computational procedures that are amenable to heat transfer education: the power series method, the finite-difference technique and the shooting method. With the second technique, the system of algebraic equations was solved by the elimination of unknowns, or the Gauss elimination method. With the third method, a fourth-order Runge—Kutta integration algorithm was paired with a linear interpolation formula for solving the system of two differential equations of first order. The three computational procedures are capable of producing approximate temperature distributions and approximate heat transfer rates of high quality. All analytical and numerical calculations were carried out on a personal computer.

Effect of variable material properties and environmental conditions on thermomechanical phase transformations in shape memory alloy wires

This paper reports a computational study of the impact of variable material properties and environmental conditions (thermal boundary conditions and convection coefficients) on shape memory alloy wires undergoing (i) zero-stress, thermally-induced phase transformations, and (ii) stress-induced phase transformations at constant stress rates. A finite difference numerical approach has been employed, and has been validated by comparing with two analytical solutions. The results have been all given in non-dimensional form, and within the context of the range of parameters that have been studied, the following recommendations can be made for shape memory alloys (SMA) actuator design: (i) an uncertainty in the thermal boundary condition is not as important as long as the design process allows for a full transformation back to martensite at the end of a cycle of martensite–austenite–martensite thermal transformation, (ii) uncertainties in the thermal boundary condition, convection coefficient and thermal material properties are not as important when the phase transformation in a SMA is induced by stress.

Transient laminar forced convection with arbitrary variation in the wall heat flux

The aim of the work is to present a detailed numerical study of the transient forced laminar convection flow over a flat plate, when thermal conditions are due to arbitrary wall heat flux variations in space. The energy governing equation is modelled using the Karman–Pohlhausen integral approach in the wide range of Prandtl numbers. The influence of both the thermal problem nature (transient heating and/or cooling processes) and the wall flux function on the resulting mathematical expressions is evidenced and the thermal boundary layer thickness behaviour is discussed. In addition, a particular attention has been focused on both the change in sign of the flux and the duration of the transient heating and cooling. Detailed thermal responses and convective heat coefficient evolutions due to the change of wall conditions are presented.

Kinetic parameters for thermal inactivation of cut green beans lipoxygenase calculated using unsteady‐state methods

SummaryKinetic parameters describing lipoxygenase inactivation during heating of cut green beans were determined using two unsteady‐state procedures. The model used an analytical solution for heat conduction in a finite cylinder to predict time–temperature profiles, and a trial and error and a non‐linear regression of experimental lipoxygenase retentions to estimate kinetic parameters. Thermal diffusivity and convective heat transfer coefficient were determined experimentally, but thermal conductivity was estimated. Mean values obtained, with standard deviations between parenthesis, were k76°C=27.2 (9.4) s–1; k82°C=92.9 (7.5) s–1; k88°C=212.1 (52.7) s–1; k94°C=407.8 (56.7) s–1; Ea=160.7 (8.1) KJ mol−1 using the trial and error procedure; k85°C=150 (26.3) s–1 and Ea=164 (4.7) KJ mol−1 using the non‐linear regression method. Predicted and observed lipoxygenase retentions showed good agreement.

Prediction of thermal protection of walls by blowing with different fluids

This work concerns the modelling of heat and mass transfer in the boundary layer and inside a plane porous plate which is below a hot fluid flow and submitted to cold fluid blowing. A preliminary study of the heat transfer rates in the boundary layer without blowing permits us to validate, comparing with experimental results, the RNG κ-ϵ model. The RNG κ-ϵ model, with kinematic and thermal laws for the wall, linked with a model of blowing, is then used to study the heat and mass transfer rates at the wall when the main flow and the injected fluids are the same species - air - but at different temperatures. The comparison between calculated friction factors, Stanton numbers and published results confirms the validity of our model. We also show the strong influence of the injection rate on the thermal convective coefficient of the wall. In the last part, results on cooling by blowing with water vapour in a main flow of air are given. Comparisons of the evolution of Stanton numbers and friction factors show that blowing with water vapour is more efficient than air injection in terms of momentum transfer and thermal protection of walls.

Cutting Tool Temperatures in Contour Turning: Transient Analysis and Experimental Verification

This paper describes a model for predicting cutting tool temperatures under transient conditions. It is applicable to processes such as contour turning, in which the cutting speed, feed rate, and depth of cut may vary continuously with time. The model is intended for use in process development and trouble shooting. Therefore, emphasis is given in the model development to enable rapid computation and to avoid the need to specify parameters such as thermal contact resistances and convection coefficients which are not known in practice. Experiments were conducted to validate the predictive model. The model predictions with two different boundary conditions bound the experimental results. An example is presented which shows the utility of the model for process planning.

Selective cooling of biological tissues: application for thermally mediated therapeutic procedures

The ability to control the degree and spatial distribution of cooling in biological tissues during a thermally mediated therapeutic procedure would be useful for several biomedical applications of lasers. The authors present a theory based on the solution of the heat conduction equation that demonstrates the feasibility of selectively cooling biological tissues. Model predictions are compared with infrared thermal measurements of in vivo human skin in response to cooling by a cryogen spurt. The presence of a boundary layer, undergoing a liquid-vapour phase transition, is associated with a relatively large thermal convection coefficient ( approximately=40 kW m-2 K-1), which gives rise to the observed surface temperature reductions (30-40 degrees C). The degree and the spatial temporal distribution of cooling are shown to be directly related to the cryogen spurt duration.

Loss-at-source thermal modelling in salient pole alternators using 3-dimensional finite difference techniques

A method of calculating the temperature rise in the core, conductors, insulation, and cooling air of the stator and rotor of a salient pole alternator is described, with emphasis on the development of a finite-difference model of sufficiently reduced complexity to allow reasonably economic computation. The electrical losses arising in each metal element of the 3-D mesh are derived from loss-at-source computations described elsewhere, while thermal properties and convection coefficients are obtained by experiment or from standard characteristics. The results of temperature rise predictions are presented and compared with measured values.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Power-temperature dependence of elements in hybrid circuits

This paper presents a simple method of approximate calculation of the thermal conductivity for a hybrid circuit element. The method is to calculate the effective surface area of the element and to multiply it by the thermal conductivity coefficient. The effective area is equal to the sum of the element surface area and the surrounding element margin which has a constant width. The margin width depends on the thermal convection coefficient, on the thermal conductance of the substrate and on the substrate thickness-d.

Estimating friction factors in a fouled annulus

AbstractFouling of heat transfer surfaces modifies the associated conductive thermal resistance and convective heat transfer coefficient. Often, the latter varies as a result of changes in the roughness of the deposition surface. If fouling is being studied in an annular heat exchanger, deposits may form on both surfaces of the annular cross section, and an estimation of the friction factors of each fouled surface is needed. In order to evaluate these factors a simple method can be used as described in this paper, based on pressure drop measurements and current equations. Experimental results are reported and appear to support the method.

Prediction of temperature distribution along a thin heated wire of finite length

An exact elliptic-integral solution is given for the temperature distribution of a thin, heated wire between two supports. The solution includes the variation of thermal conductivity, electrical resistivity, convective coefficient, and emissivity of the wire with temperature. The complete fourth-order (and higher) temperature effects of thermal radiation can be included in the general solution. The hot-wire-anemometer case is evaluated numerically and is successfully compared with measured wire-temperature distributions. The exact theoretical temperature distribution is also compared with a first-order hyperbolic solution.