Unsteady State Heat Transfer Equation Research Articles

Topological Asymptotic Expansion for a Thermal Problem

In this paper, we propose an approach based on the topological sensitivity notion for solving an inverse design problem. The presented procedure can be applied for finding the optimal design of cooling holes in a turbine blade. Our proposed method uses a simplified and rigorous mathematical analysis related to the unsteady state heat transfer equation. We start our analysis by establishing a preliminary estimate describing the asymptotic behavior of the heat equation solution with respect to the presence of small hole. The obtained estimate will play a crucial role in the derivation of a topological asymptotic formula valid for a large class of design functions. Based on the derived theoretical results, we build a one-iteration numerical algorithm for solving an inverse design problem. To point out the efficiency and accuracy of the proposed approach, some numerical experiments are presented.

Topological sensitivity analysis based method for solving a geometry reconstruction problem

This paper is concerned with the topological sensitivity analysis for a parabolic type operator. We consider the unsteady-state heat transfer equation as a model problem and we develop the topological asymptotic expansion valid for a large class of cost functions. The obtained theoretical results are based on a simplified mathematical analysis involving the elliptic part of the operator. In the numerical part, we proposed a simple and fast geometry reconstruction algorithm. The proposed algorithm is applied for recovering internal cooling holes in a turbine blade by minimizing various error functions measuring the difference between the current and actual temperature fields.

Application of Unsteady-State Heat Transfer Equations to Thermal Process ofMorcela de arrozfromMonchiqueRegion, a Portuguese Traditional Blood Sausage

Morcela de Arroz (MA) is a popular cooked blood and rice sausage produced following empirical procedures in the Monchique region, south of Portugal. Presenting high pH (about 6.5) and water activity (around 0.97), it is commercialized without preservatives, unpacked and with restricted commercialization period (1 week at 0C–5C). The aim of this study was (i) to assess the adequacy of unsteady-state heat transfer equations (USHTE) using Heisler charts to predict temperature in the centre of the product and the time needed to attain the temperature needed for cooking and (ii) to determine if the thermal treatment traditionally applied complies with the recommendations for refrigerated processed foods of extended durability (REPFEDs). A very good fit of USHTE to the experimental time/temperature data was observed. MA thermal process complies with the REPFEDs recommendations. Bacillus cereus and Clostridium perfringens were not detected in any of the tested samples. Practical Applications The USHTE model used allows the adjustment of cooking time and medium temperature to product dimension, without the need for the continuous monitoring of MA internal temperature. The model can easily be used to predict the adequacy of MA thermal process in terms of food safety. The traditional thermal process applied to MA exceeds the most conservative safe harbor of 90C/10 min allowing the extension of its refrigerated shelf life.

Numerical Analysis of Cold Storage System with Array of Solid-Liquid Phase Change Module

This paper is the fundamental study for the application of cold storage system to the transportation equipment by sea and land. This numerical study presents the solid-liquid phase change phenomenon of calcium chloride solution of 30wt %. The governing equations are 1-dimensional unsteady state heat transfer equations of order partial differential equations. This type of latent heat storage material is often usable in fishery vessel for controlling the temperature of container with constant condition. The governing equation was discretized with finite difference method and the program was composed with Mathcad program. The main parameters of this solution were the initial temperature of heat storage material, ambient temperature of cold air and the velocity of cold air. The data of boundary layer thickness becomes thin with the increasing of cold air flowing velocity and also the heat storage completion time become shorten.

An Investigation of the Radiative Heat Transfer through Nonwoven Fibrous Materials

In this study, the surface-to-surface radiation model of the Fluent CFD code is used to investigate the response of a fibrous material to the radiative heat transfer. The unsteady state heat transfer equation is solved for the temperature and heat flux in and around the fibers that constitute a nonwoven fibrous material. For a fixed fiber diameter, it was shown that the higher the fabric's Solid Volume Fraction (SVF), the slower is the material's average temperature rise. Our simulation results also indicate that for a fixed SVF, fiber diameter has a negligible influence on the unsteady transfer of heat through the media. Of particular interest in this paper is the effect of material's thickness on the heat penetration. It is shown that the transient heat transfer exponentially decreases by increasing the material's thickness for fixed SVFs and fiber diameters. The above finding is also in agreement with our experimental study.

Modelling Work-Roll Temperature Variations in Hot Strip Rolling

Prediction of temperature distribution within work-rolls during the hot strip rolling process is of great importance to mill designers because of the significant role it plays in the product's dimensional accuracy and roll life. The present article employs the unsteady state heat transfer equation with time-dependent boundary conditions, as well as a two-dimensional finite element method, to determine work-roll temperature variations during continuous hot strip rolling. To achieve an accurate temperature field, the authors consider the effects of different factors, including work-roll and metal thermal relationship, idling work-roll revolutions, and the effects of various process parameters such as rolling speed, interface heat transfer co-efficient, and the amount of thickness reduction at each deformation pass. A comparison of the predicted and published experimental results shows the validity of the mathematical model.

Modelling the work-roll temperature variation at unsteady state condition

In this paper, the unsteady state heat transfer equations with time dependent boundary conditions are coupled with a two-dimensional finite element method to predict the work-roll temperature distribution during the continuous hot slab rolling process. To achieve an accurate temperature field, the effects of various factors including the thermal relationship of the work-roll and the metal slab, the idling work-roll revolutions, the rolling speed, the slab/roll interfacial heat transfer coefficient, and the magnitude of the thickness reduction of the slab at each deformation pass are taken into account. Comparisons between the predicted and published experimental results are used to illustrate the validity of the mathematical model.

Unsteady state work-roll temperature distribution during continuous hot slab rolling

Predicting temperature distributions in the work-rolls during the hot slab rolling process is of great importance to mill designers. This is because the temperature distribution and the dimensional accuracy of the slab being rolled are both dependent on the work-roll temperature. In addition, the life of the roll is also a function of its own temperature distribution. In this paper, the unsteady state heat transfer equations with time dependent boundary conditions are coupled with a two-dimensional finite element method to predict the work-roll temperature distribution during the continuous hot slab rolling process. To achieve an accurate temperature field, the effects of various factors including the thermal relationships of the work-roll and the metal slab, the idling work-roll revolutions, the rolling speed, the slab/roll interfacial heat transfer coefficient, and the magnitude of the thickness reduction of the slab at each deformation pass are taken into account. Comparisons between the predicted and published experimental results are used to illustrate the validity of the mathematical model.

Computer simulation of ice recrystallization in ice cream during storage

The effect of storage conditions on ice recrystallization in vanilla ice cream was investigated using a simulation program. Changes in mean size and coefficient of variance of the ice-crystal size distribution were determined from data in the literature. Thermal diffusivities during heating and cooling of ice cream were found experimentally. The unsteady state heat transfer equation for a finite cylinder was solved simultaneously with the recrystallization kinetics equation. Good agreement was found between experimental and simulation results. Simulation of typical storage conditions gave final ice-crystal mean size of ≈46 μm and coefficient of variance of 0.58. Recrystallization rate was high during the initial stages of storage. Storage temperature fluctuations had a greater influence near the containers' surface, resulting in higher mean size closer to the surface at the end of the storage. Very low storage temperatures (≈ −30 °C) during initial steps of storage decreased the recrystallization rate significantly. High heat transfer coefficient of cooling medium inhibited recrystallization at storage stages involved initial cooling and low amplitude temperatures.

Modeling Heat Transfer During Oven Roasting of Unstuffed Turkeys

ABSTRACTA finite element method was used to solve the unsteady state heat transfer equations for heating of turkeys in a conventional electric oven. Breast, and thigh and wing joint temperature in 5.9, 6.8, 8.6, 9.5, and 10.4 kg turkeys were simulated. A surface heat transfer coefficient of 19.252 W/m2K determined by transient temperature measurements in the same oven, was used. Thermal conductivity measured using a line heat source probe from 0 to 80°C was 0.464 W/mK. Simulated temperatures were within 1.33, 1.47, and 1.22°C of experimental values of temperature in the breast, thigh, and wing joint, respectively. Initial temperature 1,2, and 3°C lower than 4°C required additional baking time of 16,22, and 27 min., respectively for the thigh joint to reach the target endpoint temperature.

A finite element model for conduction errors in thermocouples during thermal sterilization of conduction‐heating foods

SummaryErrors in temperature measurement due to heat conduction along thermocouples employed in heat penetration studies of food which is heated by conduction have been quantified, using a finite element numerical solution of the unsteady state heat transfer equation. For a 0.56‐mm (24s.w.g.) Type T thermocouple, temperature at the centre of a can may be overestimated by over 2°C in the heating phase of a typical process. The errors are much larger for thicker thermocouples. The orthodox conservative design strategy for thermal processes, relying on the lethal effect of the heating phase and treating the cooling phase as a safety margin, may not be a ‘safe’ strategy. The conduction errors result in an overestimate of the heating‐phase lethality and an underestimate of the cooling‐phase lethality. The application of a correction to the lag factor is not adequate to compensate for the derestimation of the lethality during the cooling stage. The errors in the determination of the thermal diffusivity from heat‐penetration data are much lower than the errors in the determination of the sterilization effect delivered by a particular process. The silicon elastomer used to experimentally validate the model employed in this study, is shown to be an ideal material to model food which is heated by conduction.