REWETTING OF AN INFINITE SLAB WITH BOUNDARY HEAT FLUX

This paper deals with a numerical solution of the two-dimensional quasi-static conduction equation, governing conduction controlled rewetting of an infinitely long slab with one side flooded and the other side subjected to a constant heat flux. The solution gives the quench front temperature as a function of various model parameters such as Peclet number, Biot number, and dimensionless boundary heat flux. Also, the critical boundary heat flux is obtained by setting the Peclet number equal to zero, which gives the minimum heat flux required to prevent the hot surface being rewetted.     

Transient solution of temperature field of conjugate laminar forced convection heat transfer in functionally graded hollow cylinder

In this study, the numerical analysis of conjugate heat transfer of laminar flow in a functionally graded hollow cylinder (FGHC) made of metal/ceramic for a two‐dimensional fluid and wall conduction subject to Newton boundary condition is considered. The fluid and FGHC energy equations are coupled through the continuity of temperature and heat flux at the inner wall‐fluid interface while the outer surface is subject to convective heat transfer. The continuity, momentum, and energy equations of the fluid are discretized using the finite volume approach. The effects of fluid and functionally graded material parameters, such as volume fraction index, volume composition, time history, wall‐to‐fluid thermal diffusivity ratio, wall‐to‐fluid thermal conductivity ratio, Biot number, Peclet number, and Prandtl number are investigated on the temperature field in the FGHC. The result shows that on account of the inhomogeneity of the material property, the volume fraction index has a significant effect on the other parameters and the temperature variation along the thickness. The lower the volume fraction index, the higher the inner wall (metal side) temperature, and the temperature gradient along the thickness. However, except for the variation in the wall‐to‐fluid thermal conductivity ratio, the lower the volumetric fraction, the lower the outer wall (ceramic side) temperature distribution.     

A three-region conduction-controlled rewetting analysis by the Heat Balance Integral Method

Conduction-controlled rewetting of two-dimensional objects is analyzed by the Heat Balance Integral Method (HBIM) considering three distinct regions: a dry region ahead of wet front, the sputtering region immediately behind the wet front and a continuous film region further upstream. The HBIM yields solutions for wet front velocity, sputtering length and temperature field with respect to wet front. Employing this method, it is seen that heat transfer mechanism is dependent upon two temperature parameters. One of them characterizes the initial wall temperature while the other specifies the range of temperature for sputtering region. Additionally, the mechanism of heat transfer is found to be dependent on two Biot numbers comprising a convective heat transfer in the wet region and a boiling heat transfer in the sputtering region. The present solution exactly matches with the one-dimensional analysis of K.H. Sun, G.E. Dix, C.L. Tien [Cooling of a very hot vertical surface by falling liquid film, ASME J. Heat Transf. 96 (1974) 126–131] for low Biot numbers. Good agreement with experimental results is also observed.     

Analysis of rewetting of an infinite tube by numerical fourier inversion

A semi—analytical model for the two—dimensional quasi—steady conduction equation, governing conduction controlled rewetting of an infinite tube, has been suggested. The solution yields the temperature field as a function of various input model parameters such as Peclet number, Biot number and radius ratio of the tube. Unlike earlier investigations, the present semi-analytical model predicts the temperature field for the entire domain of a tube, employing the Wiener—Hopf technique and by inverse discrete Fourier transform (IDFT) algorithm.     

A comprehensive analysis of conduction-controlled rewetting by the Heat Balance Integral Method

A two region conduction-controlled rewetting model of hot vertical surfaces with a constant wet side heat transfer coefficient and negligible heat transfer from dry side is solved by the Heat Balance Integral Method (HBIM). The HBIM yields a simple closed form solution for rewetting velocity and temperature distribution in both dry and wet regions for given Biot numbers. Using this method it has been possible to derive a unified relationship for one-dimensional object and two-dimensional slab and rod. The effect of convection is expressed by an effective Biot number whose exact value depends on the geometry and process parameters. The solutions are found to be exactly the same as reported by Duffey and Porthouse [R.B. Duffey, D.T.C Porthouse, The physics of rewetting in water reactor emergency core cooling, Nucl. Eng. Des. 25 (1973) 379–394], Thompson [T.S. Thompson, An analysis of the wet-side heat transfer coefficient during rewetting of a hot dry patch, Nucl. Eng. Des. 22 (1972) 212–224] and Sun et al. [K.H. Sun, G.E. Dix, C.L. Tien, Cooling of a very hot vertical surface by falling liquid film, ASME J. Heat Transfer 96 (1974) 126–131; K.H. Sun, G.E. Dix, C.L. Tien, Effect of precursory cooling on falling-film rewetting, ASME J. Heat Transfer 97 (1974) 360–365]. Good agreement with experimental results is also observed.     

Physical mechanisms of heat transfer during single bubble nucleate boiling of FC-72 under saturation conditions. II: Theoretical analysis

This paper is the second part of a two-part study concerning the dynamics of heat transfer during the nucleation process of FC-72 liquid. The experimental findings on the nature of different heat transfer mechanisms involved in the nucleation process were discussed in part I. In this paper, the experimental results are compared with the existing boiling models. The boiling models based on dominance of a single mechanism of heat transfer did not match the experimental results. However, the Rohsenow model was found to closely predict the heat transfer through the microconvection mechanism that is primarily active outside the bubble/surface contact area. An existing transient conduction model was modified to predict the surface heat transfer during the rewetting process (i.e. transient conduction mechanism). This model takes into account the gradual rewetting of the surface during the transient conduction process rather than a simple sudden surface coverage assumption commonly used in the boiling literature. The initial superheat energy of the microlayer (i.e. microlayer sensible energy) was accurately calculated and found to significantly contribute in microlayer evaporation. This even exceeded the direct wall heat transfer to microlayer at high surface superheat temperatures. A composite model was introduced that closely matches our experimental results. It incorporates models for three mechanisms of heat transfer including microlayer evaporation, transient conduction, microconvection, as well as their influence area and activation time. The significance of this development is that, for the first time, all submodels of the composite correlation were independently verified using experimental results.     

Transient conjugated heat transfer in thick walled pipes with convective boundary conditions

Transient conjugated heat transfer for laminar flow in the thermal entrance region of pipes is investigated by considering two dimensional wall and axial fluid conduction. The problem is handled for an initially isothermal, infinitely long, thick-walled and two-regional pipe for which the upstream region is insulated and solved numerically by a finite difference method for hydrodynamically developed flow with a step change in the ambient fluid temperature in the heated downstream region. A parametric study is done to analyse the effects of five defining parameters namely, wall thickness ratio, wall-to-fluid conductivity ratio, wall-to-fluid thermal diffusivity ratio, the Peclet number and the Biot number.     

One‐dimensional transient heat conduction in a bilayer finite slab: A case study in the printing process

In this work, a typical case of heat distribution is examined during a paper printing process, based on one‐dimensional transient heat conduction in two‐layer finite slabs with an insulated free surface, and a constant temperature free surface. Analytical solutions were obtained in non‐dimensional form. Various examples of applying these solutions are presented. The accuracy of the solutions, with respect to time, is analyzed considering the eigenvalues of their infinite solutions. It is observed that the larger the number of eigenvalues in consideration, the better the accuracy of the solutions. The model related to a two‐layer slab describes the simplified case in which all heat transfer occurs only by conduction. The solutions obtained are finally compared with the solutions for heat conduction in two semi‐infinite solids. The comparison between the two solutions shows that results are in good agreement only during short time scales. The heat distribution study is expected to be helpful in knowing the effectiveness of various mediums to be used as the reciever during the printing process; however, there is scope for development of more robust models.     

环形炉内管坯加热温度均匀性计算与分析

在考虑炽热炉底的辐射加热和导热加热的基础上,建立了环形炉内管坯二维加热模型。计算结果表明,管坯表面热流密度沿周向分布的不均匀性造成了管坯温度沿周向分布不均。炽热炉管对管坯下部表面的导热及辐射加热对其加热至关重要。     

Development of a simplified heat pipe numerical model and case study/experimental validation using a long ‘wicked’ heat pipe

This paper describes existing numerical techniques used for simulating heat pipe operation, and the development of a simplified numerical model for normal wicked/wickless heat pipes based on the analysis of current modelling methods. Vapour flow was treated as a two‐dimensional flow. Heat transfers through the liquid–wick region and wall region were computed by solving a one‐dimensional heat conduction equation. Flow in the liquid–wick region was treated as a one‐dimensional problem. The liquid and vapour flows were coupled using a set of governing equations, incorporating thermal compressibility, hydro‐dynamical and capillary relationship, as well as geometrical correlation. The finite‐difference method was employed to carry out the numerical analysis, and FORTRAN language was used to develop a computer program. The model was used to investigate the operating characteristics of a long ‘wicked’ heat pipe, including variation of cross‐sectional area, axial/radial velocity, pressure and temperature of liquid/vapour flows with height position above the liquid level. To validate the modelling predictions, a test rig was constructed to carry out experimental testing. This included measurement of surface temperatures and heat flow associated with heat‐pipe heat transfer. The results from tests were found to be in general agreement with the numerical predictions when the test conditions were close to the simulation assumptions. Copyright © 2004 John Wiley & Sons, Ltd.     

Influence of wall oscillation modes on heat transfer enhancement

We numerically investigated the influence of the wall oscillation mode on the heat transfer characteristics of a two‐dimensional channel. In the present study, two channels with different wall oscillation modes were considered: a two‐dimensional channel bounded by a fixed wall and a transversely oscillating wall (channel A) and a two‐dimensional channel in which the upper and lower walls oscillate transversely in the same manner (channel B). The fully implicit finite difference method was used for the analysis of the conservation equations and the time‐dependent coordinate transformations were applied to solve the moving boundary problem. The calculated results are summarized as follows. (1) The wall oscillation has a significant effect on the heat transfer enhancement in the low‐Reynolds‐number region for each channel. (2) If increased pressure loss must be avoided, then channel B is more suitable than channel A. © 2009 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20250     

Free surface heat loss effect on oscillatory thermocapillary flow in liquid bridges of high Prandtl number fluids

The effect of free surface heat loss on oscillatory thermocapillary flow is investigated in liquid bridges of high Prandtl number fluids. It is shown experimentally that the critical temperature difference changes by a factor of two to three by changing the air temperature relative to the cold wall temperature. In order to understand the nature and extent of the interaction between the liquid flow and the surrounding air, the heat transfer from the liquid free surface is investigated numerically for the conditions of the present experimental work. The airflow analysis shows that even when the heat loss is relatively weak (the Biot number is unity or smaller), the critical temperature difference is affected appreciably. It is shown that the heat loss effect is significant in widely conducted tests near room temperature and that the critical temperature difference is much larger than the room temperature value when the heat loss is minimized. The analysis suggests that an interaction between the surface heat loss and dynamic free surface deformation near the hot wall is responsible for the observed heat loss effect.     

Effect of the plate thermal resistance on the heat transfer performance of a corrugated thin plate heat exchanger

Two‐dimensional conjugate conduction/convection numerical simulations were carried out for flow and thermal fields in a unit model of a counter‐flow‐type corrugated thin plate heat exchanger core. The effects of the thermal resistance of the solid plate, namely the variation of the plate thickness and the difference of the plate material, on the heat exchanger performance were examined in the Reynolds number range of 100<Re<400. Higher temperature effectiveness was obtained for a thicker plate at any Reynolds number, which was a unique feature of corrugated thin plate geometry. Detailed discussions on the thermal fields revealed that restricting the heat conduction along the plate by making the plate thinner or choosing a low thermal conductivity material causes a larger plate temperature variation along the plate, and, consequently, a smaller amount of thermal energy exchanged between two fluids. © 2006 Wiley Periodicals, Inc. Heat Trans Asian Res, 35(3): 209–223, 2006; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20110     

A 3-dimensional,coupled, DNS,heat transfer model and solution for multi-hole cooling

A 3-dimensional, coupled, heat transfer model and solution for multi-hole cooling is described in this paper. It couples DNS calculations of the primary turbulent flow, the backside flow and the flow in the injection holes by solving the 3-D heat conduction equation for the wall with a mixed boundary condition, which leads to an iteration process to obtain a converged solution for the mean temperature in the wall and in the flow. The model is tested for both a laminar and a turbulent primary flow and the results show that the convergence to the solution is very efficient. The results obtained with this 3-D model are presented and compared with an adiabatic and a 1-D, conducting-wall, model. A non-dimensional parameter (Biot number) representing the relative importance of in-plane heat conduction in the wall is discussed. The cooling effectiveness predicted by the 3-D model is compared with experimental results at the same Reynolds number and satisfactory agreement is achieved.     

A spatially advancing turbulent flow and heat transfer in a curved channel

Direct numerical simulation was performed for a spatially advancing turbulent flow and heat transfer in a two‐dimensional curved channel, where one wall was heated to a constant temperature and the other wall was cooled to a different constant temperature. In the simulation, fully developed flow and temperature from the straight‐channel driver was passed through the inlet of the curved‐channel domain. The frictional Reynolds number was assigned 150, and the Prandtl number was given 0.71. Since the flow field was examined in the previous paper, the thermal features are mainly targeted in this paper. The turbulent heat flux showed trends consistent with a growing process of large‐scale vortices. In the curved part, the wall‐normal component of the turbulent heat flux was twice as large as the counterpart in the straight part, suggesting active heat transport of large‐scale vortices. In the inner side of the same section, temperature fluctuation was abnormally large compared with the modest fluctuation of the wall‐normal velocity. This was caused by the combined effect of the large‐scale motion of the vortices and the wide variation of the mean temperature; in such a temperature distribution, large‐scale ejection of the hot fluid near the outer wall, which is transported into the near inner‐wall region, should have a large impact on the thermal boundary layer near the inner wall. Wave number decomposition was conducted for various statistics, which showed that the contribution of the large‐scale vortex to the total turbulent heat flux normal to the wall reached roughly 80% inside the channel 135^° downstream from the curved‐channel inlet. © 2009 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20275     

Inverse shape design for heat conduction problems via the ball spine algorithm

ABSTRACT

In this article, a novel iterative physical-based method is introduced for solving inverse heat conduction problems. The method extends the ball spine algorithm concept, originally developed for inverse fluid flow problems, to inverse heat conduction problems by employing a subtle physical-sense rule. The inverse problem is described as a heat source embedded within a solid medium with known temperature distribution. The object is to find a body configuration satisfying a prescribed heat flux originated from a heat source along the outer surface. Performance of the proposed method is evaluated by solving many 2-D inverse heat conduction problems in which known heat flux distribution along the unknown surface is directly related to the Biot number and surface temperature distribution arbitrarily determined by the user. Results show that the proposed method has a truly low computational cost accompanied with a high convergence rate.     

Analytical method of two‐dimensional inverse heat conduction problem using Laplace transformation: Effect of number of measurement points

An analytical method has been developed for the inverse problem of two‐dimensional heat conduction using the Laplace transform technique. The inverse problem is solved for only two unknown surface conditions and the other surfaces are insulated in a finite rectangular body. In actual temperature measurement, the number of points in a solid is usually limited so that the number of temperature measurements required to approximate the temperature change in the solid becomes too small to obtain an approximate function using a half polynomial power series of time and the Fourier series of the eigenfunction. In order to compensate for this lack of measurement points, the third‐order Spline method is recommended for interpolating unknown temperatures at locations between measurement points. Eight points are recommended as the minimum number of temperature measurement points. The calculated results for a number of representative cases indicate that the surface temperature and the surface heat flux can be predicted well, as revealed by comparison with the given surface condition. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(7): 618–629, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10116     

Optimal homotopy asymptotic method for heat transfer in hollow sphere with robin boundary conditions

In this article, we have investigated heat transfer from a hollow sphere using a powerful and relatively new semi‐analytic technique known as the optimal homotopy asymptotic method (OHAM). Robin boundary conditions are applied on both the inner and outer surfaces. The effects of Biot numbers, uniform heat generation, temperature‐ dependent thermal conductivity, and temperature parameters on the dimensionless temperature and heat transfer are investigated. The results of OHAM are compared with a numerical method and are found to be in good agreement. It is shown that the dimensionless temperature increases with an increase in Biot number at the inner surface and temperature and heat generation parameters, whereas it decreases with an increase in the Biot number at the outer surface and the dimensionless thermal conductivity and radial distance parameters. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res 43(2): 124‐133, 2014; Published online 20 June 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21067     

An experimental and theoretical investigation into the heat transfer of a finned water wall tube in a circulating fluidized bed boiler

Heat transfer improvement in a water wall tube with fins was investigated in a circulating fluidized bed (CFB) boiler. Experiments were first conducted in a 6 MWth CFB boiler then a model was developed to analyse and interpolate the results. Temperatures at some discrete points within the wall cross‐section of the tube were measured by burying 0.8 mm thermocouples within a tube. Experimental data showed an increase in heat absorption up to 45 per cent. A good agreement between measured and predicted values was noted. The distribution of temperature in the metal wall and of heat flux around the outer wall of a tube with longitudinal and lateral fins was analysed by numerical solution of a two‐dimensional heat conduction equation. Effects of bed‐to‐wall heat transfer coefficient, water‐to‐tube inside heat transfer coefficient, bed temperature, water temperature and thermal conductivity of the tube material on the heat flux around the water tube are discussed. The present work also examines the influence of the length of the longitudinal fin and the water tube thickness. Heat flux was highest at the tip of the longitudinal fin. It dropped, but increased again near the root of the lateral fin. Copyright © 2000 John Wiley & Sons, Ltd.     

Numerical Solution of Periodic Heat Transfer in an Anisotropic Cylinder Subject to Asymmetric Heat Flux

Abstract

The problem of heat conduction in a two-dimensional anisotropic cylinder subject to asymmetric and periodic heat flux distribution on the outer wall is solved numerically. The dimensional analysis of the problem reveals that the heat conduction is a function of five nondimensional parameters: nondimensional frequency (α), cylinder outer to inner radius ratio (R₂), Biot number (Bi), orthotropicity factor (K₁), and anisotropicity factor (K_r1). A systematic study of the effect of each parameter is carried out over the influential range for each parameter. The results show that, depending on the combination of these parameters, the magnitude and/or phase of heat conduction in an anisotropic cylinder can be significantly different from those of an orthotropic and isotropic cylinder when subjected to the same externally imposed heat flux distribution.