A numerical approach to model non-isothermal viscous flow through fibrous media with free surfaces

A numerical simulation is presented to predict the free surface and its interactions with heat transfer and cure for flow of a shear-thinning resin through the fibre preform the flow part of the simulation is based on the finite element/control volume method. Since the traditional control volume approach produces an error associated with a mass balance inconsistency, a new method which overcomes this issue is proposed, the element control volume method. The heat transfer and cure analysis in the simulation are based on the finite difference/control volume method. Since heat conduction is dominant in the through-thickness direction and most of the heat convection is in-plane, heat transfer and cure are solved in fully three-dimensional form. A simple concept of the boundary condition constant is introduced which models a realistic mould configuration with a heating element located at a distance behind the mould wall. The varying viscosity throughout the mould associated with the strain rate, temperature and degree of cure distribution may be accounted for in calculating the mould-filling pattern. This introduces a two-way coupling between momentum and energy transport in fibrous media during mould filling.     

An analytical solution to non-axisymmetric heat transfer with viscous dissipation for non-Newtonian fluids in laminar forced flow

Forced convection heat transfer in a non-Newtonian fluid flow inside a pipe whose external surface is subjected to non-axisymmetric heat loads is investigated analytically. Fully developed laminar velocity distributions obtained by a power-law fluid rheology model are used, and viscous dissipation is taken into account. The effect of axial heat conduction is considered negligible. The physical properties are assumed to be constant. We consider that the smooth change in the velocity distribution inside the pipe is piecewise constant. The theoretical analysis of the heat transfer is performed by using an integral transform technique – Vodicka’s method. An important feature of this approach is that it permits an arbitrary distribution of the surrounding medium temperature and an arbitrary velocity distribution of the fluid. This technique is verified by a comparison with the existing results. The effects of the Brinkman number and rheological properties on the distribution of the local Nusselt number are shown.     

Global heat transfer analysis in Czochralski silicon furnace with radiation on curved specular surfaces

Numerical analysis of global heat transfer with coupled thermal radiation and heat conduction is investigated in Czochralski silicon crystal growth furnace with curved diffuse and specular surfaces. The finite element method and the radiation element method are adopted to solve the global heat transfer and the radiative heat exchange, respectively. The emphasis focuses on the discussion of the influence of silicon surface radiative characteristics, i.e., either diffuse or specular, on the global heat transfer and the crystal growth process. When the specular character of the silicon crystal and melt surfaces is considered, it is found that the temperature of the melt is obviously decreased and the crystal pulling rate is enhanced. Received on 7 August 1998     

Experimental study on axial wall heat conduction for convective heat transfer in stainless steel microtube

Distilled water and nitrogen gas used as the working fluids flow through the stainless steel microtube with inner diameter 168 μm outer diameter 406 μm. Using the Joule heating, the wall temperature field photos of the microtube is acquired by employing an IR camera and the temperature and the volume flow rate of the inlet and the outlet of microtube are measured. A correlation between the axial wall heat conduction and the convective heat transfer is obtained by theoretical analysis based on the experimental results. The investigative results clearly show that the axial heat conduction can reduce the convective heat transfer in the stainless steel microtube and the decrement may reach 2% compared to the convective heat transfer when the working fluid is nitrogen gas, however, the decrement can be neglected for distilled water as the working fluid.     

Heat transfer from horizontal tubes in pool boiling: influence of three-dimensional heat conduction in the wall of the evaporator tube—a finite element analysis

In pool boiling, the electrically heated tube releases the energy non-uniformly to the liquid, due to different surface roughness and flowing liquid. The heat transfer coefficient therefore varies with axial and azimuthal position on the tube. Hence a finite element analysis has been carried out on a horizontal 1in. copper tube for evaporation in pool boiling for three-dimensional conduction heat transfer. A test tube has been made with different surface structures, tested and analysed for heat conduction effects. It has been observed that significant amount of heat flows in azimuthal and axial directions in addition to the heat flow in radial direction.     

Three-dimensional melting of ice around a liquid-carrying tube

Three-dimensional melting of ice around a liquid-carrying tube placed in an adiabatic rectangular cavity is investigated mainly by means of a numerical analysis. Natural convection in the melt layer enhances melting by about 1.2 times compared with the approximate solution of a conduction mode derived from London and Seban and Hausen. The morphology of the melt layer changes in axial direction. Melting is not sensitive to the cavity height and the tube length, but is very responsive to the liquid inlet temperature.     

Convective Flows in a Melt During Crystal Growth under Periodic Temperature Field Conditions

The results of an analysis of thermo-gravitational convection in Czochralski single-crystal growth from a melt under periodic temperature field conditions are presented. The numerical modeling is based on solving the unsteady 3-D Navier-Stokes and heat conduction equations in the Boussinesq approximation. It is shown that using different heating regimes for the crystal medium provides additional opportunities for controlling heat and mass transfer.     

Use of experiment and an inverse method to study interface heat transfer during solidification in the investment casting process

A technique to determine the thermal boundary conditions existing during the solidification of metallic alloys in the investment casting process is presented. Quantitative information about these conditions is needed so that numerical models of heat transfer in this process produce accurate results. In particular, the variation of the boundary conditions both spatially and temporally must be known. The method used involves the application of a new inverse heat conduction method to thermal data recorded during laboratory experiments of aluminium alloy solidification in investment casting shell moulds. The resultant heat transfer coefficient for the alloy/mould interface is calculated. An experimental programme to determine requisite mould thermal properties was also undertaken. It was observed that there is significant variation of the alloy/mould heat transfer coefficient during solidification. It is found to be highly dependent on the alloy type and on the vertical position below the initial free surface of the liquid metal. The aluminium casting alloys used in this study were 413, A356, 319 (Aluminum Association designations), and commercially pure aluminium. These alloys have significantly different freezing ranges. In particular, it was found that alloys with a high freezing range solidify with rates of heat transfer to the mould which are very sensitive to metallostatic head.     

Crosslinking of a polyester resin in the heated plain sheet copper mould

The crosslinking of the unsaturated polyester was studied by using experiments and a model of the process. The kinetic parameters were calculated from the heat flux–time curves obtained by differential scanning calorimetry (DSC, Netzsch–Simultaneous Thermal Analyser DSC 200), working in DSC (dynamic) mode. The temperature–time histories were studied in plain sheet copper mould. The mathematical model was constructed by taking into account the heat transferred by conduction through the resin, as well as the kinetics of heat generated by the crosslinking reaction. The contributions to the rise in temperature from heat conduction and chemical reaction are different in different parts of the composite, and can explain the temperature-, or degree of crosslinking (DOC)–time histories. By considering temperature–time histories developed within the sample, more extensive knowledge of the process can be obtained. The effect of the heat transfer by conduction through the composite as well as the internal heat generated by the cure reaction is clearly shown, despite the complexity of the process. Finally, good agreement between experimental data and predicted mathematical model of the crosslinking process in plane sheet mould was shown.     

Controlled random search technique for estimation of convective heat transfer coefficient

This paper is concerned with a method for solving inverse heat conduction problem. The method is based on the controlled random search (CRS) technique in conjunction with modified Newton–Raphson method. The random search procedure does not need the computation of derivative of the function to be evaluated. Therefore, it is independent of the calculation of the sensitivity coefficient for nonlinear parameter estimation. The algorithm does not depend on the future-temperature information and can predict convective heat transfer coefficient with random errors in the input temperature data. The technique is first validated against an analytical solution of heat conduction equation for a typical rocket nozzle. Comparison with an earlier analysis of inverse heat conduction problem of a similar experiment shows that the present method provides solutions, which are fully consistent with the earlier results. Once validated, the technique is used to investigate another estimation of heat transfer coefficient for an experiment of short duration, high heating rate, and employing indepth temperature measurement. The CRS procedure, in conjunction with modified Newton–Raphson method, is quite useful in estimating the value of the convective heat-transfer coefficient from the measured transient temperature data on the outer surface or imbedded thermocouple inside the rocket nozzle. Some practical examples are illustrated, which demonstrate the stability and accuracy of the method to predict the surface heat flux.     

Measurement of heat transfer coefficient and axial dispersion coefficient using temperature oscillations

A periodic transient test technique based on the axial dispersion model is proposed for the determination of both heat transfer coefficients and axial dispersion coefficients in heat exchangers. The model uses a parameter called the axial dispersive Peclet number to account for the deviation of the flow pattern from ideal plug flow. It takes both axial dispersion in the fluid and axial heat conduction in the wall into account and is solved analytically by means of a complex Fourier transform. Experiments conducted on dented copper tubes show that axial dispersion has a significant effect on the dynamic temperature response of a heat exchanger.     

Heat transfer in specularly reflecting tubes

Heat exchange inside a specularly reflecting tube is analysed. Expressions are obtained for heat transfer between cross-sections, between incremental wall annuli, between finite wall annuli, and combinations of the above. The expressions are related to the angle factor for opposed discs, but are infinite summations; they are easily evaluated, requiring some 20 emissivity terms. The basic disc-to-disc expression also represents the fraction of radiation leaving a disc that is still propagating at some distance along the tube, including reflection. Special case results are obtained for the radiant loss from double and single ended holes. For the practical application considered, it was found that conduction and radiation could be treated separately, permitting evaluation of a radiation loss factor for a specularly reflecting tube between two heat reservoirs     

Conjugate forced convection and heat conduction in circular microchannels

The effects of axial heat conduction in the solid walls of microchannels of circular cross-sections are analyzed here. A systematic approach is adopted, with the aim of pointing out the influence of geometrical parameters and of solid wall thermal conductivity on microchannel heat transfer. The reliability of a commonly adopted criterium, based on the so-called axial conduction number, to assess the relevance of axial heat conduction is also discussed. Numerical simulations concern the simultaneously developing laminar flow of a constant property fluid in microchannels of different length, wall thickness and wall material, heated with a uniform heat flux at the outer surface, for different values of the Reynolds number. Moreover, since often in experimental tests the two end sections of the microchannel wall are not perfectly insulated, the effects of heat losses through these sections are also considered. A hybrid finite element procedure, which implies the step-by-step solution of the parabolized momentum equations in the fluid domain, followed by the solution of the energy equation in the entire domain, corresponding to both the solid and the fluid parts, is used for the numerical simulations.     

Rate dependence of temperature fields and energy dissipations in non-static pseudoelasticity

The temperature fields and the energy dissipations of shape memory alloys during the stress-induced martensitic transformations are studied theoretically and experimentally. The effect of the loading rate is analyzed. It was found that the temperature field inside a shape memory alloy sample varies strongly in space and time. The increase rate of the temperature is given by the difference between the rate of the latent heat release and the rate of the heat convection and conduction. The notion and the rate dependence of the energy dissipation are discussed in connection with the stress–strain hysteresis, the entropy production, and the Clausius–Duhem inequality.     

Transient heat conduction from a vertical rod buried in a semi-infinite medium with variable heating strength

In this paper, a variable heating strength model (VHS model) is developed to predict transient heat conduction from a vertical rod buried in a semi-infinite medium. Unlike past studies, the current VHS model permits a VHS along the rod. Both axial heat conduction through the rod and lateral heat conduction to the surrounding ground are modeled. A derived distribution of axial heating strength is then applied to a finite line heat source model to predict transient temperature changes in the surrounding medium. The predicted results show how the rod’s radius and ground’s thermal conductivity affect the vertical variation of heating strength and temperature response. Additional simulations predict the long-term temperature increase in the ground, due to a power transmission tower installed in a region of initially frozen ground.     

Thermodynamic optimization of contact melting of phase change material inside a horizontal cylindrical capsule

Finite time thermodynamic analysis is applied to the contact melting process of phase change material inside a horizontal cylindrical capsule. With the minimum entropy generation in given time as the objective function the quadratic nonlinear ordinary differential equation that the optimal melting process should be satisfied is derived. The dimensionless liquid height, melt liquid film thickness, Nusselt number, melting rate, optimal wall temperature and entropy generation are obtained by the numerical method. The optimal results are discussed and compared with the unoptimizable analytical results under the condition of constant wall temperature. It is found that the heat transfer and thermodynamics performance of the optimal melting process is better than that of the melting with constant wall temperature.     

Laminar heat transfer characteristics of internally finned tube with sinusoidal wavy fin

Comparative numerical study of laminar heat transfer characteristics of annular tubes with sinusoidal wavy fins has been conducted both experimentally and numerically with Re = 299–1,475. The uniform heat flux is imposed on the tube outside wall surface. Two tube materials (copper and stainless steel) are considered. It is found that the fluid temperature profile is not linear but convex along the flow direction due to the axial heat conduction in tube wall, and the effects of axial heat conduction on the heat transfer decreases with an increase in Reynolds number or decrease in tube wall thermal conductivity. The axial distributions of local Nusselt number could reach periodically fully developed after 3–5 cycles. The convectional data reduction method based on the traditional method should be improved for tube with high thermal conductivity or low Reynolds numbers, Otherwise, the heat transfer performance of internally finned tube may be underestimated.     

The extended Graetz problem with piecewise constant wall heat flux for laminar and turbulent flows inside concentric annuli

In the present paper, the heat transfer characteristics in the thermal entrance region of concentric annuli have been analysed for laminar and turbulent internal flow. Axial heat conduction effects in the fluid have been taken into account. The present paper shows an exact analytical solution for the problem of a piecewise uniform wall heat flux. The obtained analytical solution for the extended Graetz problem is as simple and efficient to compute as the related solution of the parabolic problem. The obtained results show the effect of axial heat conduction in the fluid for a semi-infinite heated section as well as for a finite length of the heated section. It is shown, that for a finite length of the heated section, axial heat conduction effects might be important even for higher Peclet number.     

Axial heat conduction effects in the entrance region of circular ducts

This paper describes the transport of thermal energy within a small distance after an abrupt wall temperature change in a circular duct. In general, the axial conduction becomes significant when the Peclet number is small. The results indicate that the inclusion of axial conduction in the fluid substantially increases the wall heat flux at near the thermal inlet location. The exact series solution leads to a modified Graetz type problem. This exact solution is augmented by an asymptotic solution describing the wall heat flux near the thermal entrance location.     

Inverse approach and sensitivity analysis for identification of ingot-mould thermal resistance in continuous casting of metals

The problem of appropriate location of the sensors for identification of ingot – mould thermal resistance during continuous casting of metals is the subject of the paper. Analysed problem belongs to the group of inverse problems. The present work shows also the method of identification of unknown thermal resistance using the temperature measurements at the number of sensors located in the wall of the mould. The influence of the location of the sensors on the results of identification is analysed. The best location of the sensors results from the sensitivity analysis for the steady-state inverse heat conduction problem. Validation of the proposed inverse method is realized by comparison of the results taken from solution of inverse and direct problems. Several numerical examples are presented and analysed.