Numerical study of radiation‐convection heat transfer

In this study, the authors attempted to introduce a simulation technique for radiation‐convection heat transfer in the high‐temperature fields of industrial furnaces, boilers, and gas turbine combustors. The convection effect was analyzed by a differential equation, but the radiation effect was analyzed by an integral equation. Thus, it was not easy to arrange both effects using the same type of equations. Then, the authors introduced the zone method and Monte Carlo method for the integral equation of the radiation effect and the finite difference method for the differential equation of the convection effect. A three‐dimensional analysis of the high‐temperature furnace was performed by this simulation technique to obtain its temperature distribution. Furthermore, another radiation‐convection heat transfer analysis in the low‐temperature living room was performed by the same technique. Finally, the authors tried to develop a computer software for radiation‐convection heat transfer and described their idea of software construction for the above. © 2002 Wiley Periodicals, Inc. Heat Trans Asian Res, 31(5): 391–407, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10042     

Coupled radiation‐convection heat transfer of high‐temperature participating medium in heated/cooled tubes

The coupled radiation‐convection heat transfer of high‐temperature participating medium in heated/cooled tubes is investigated numerically. The medium flows in a laminar and fully developed state with a Poiseuille velocity distribution, but the thermal status is developing. By the discrete ordinate method, the nonlinear integrodifferential radiative transfer equation in a cylindrical coordinate form is solved to give the radiative source term in the energy equation of coupled heat transfer. The energy equation is solved by the control volume method. The local Nusselt number and wall heat flux of convection as well as the total wall heat flux are employed to evaluate the influence of radiation heat transfer on convection. The analysis shows that the radiation heat transfer weakens the convection effect, promotes the temperature development, and significantly shortens the tube length with obvious heated/cooled effect. There is an obvious difference between the coupled heat transfer in a heated tube and that in a cooled tube, even though the medium properties are kept constant. The wall emissivity, the medium thermal conductivity and scattering albedo have significant influences on the coupled heat transfer, but the effect of medium scattering phase function is small. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 33(1): 64–72, 2004; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10137     

Thermal radiation effects of a high‐temperature developing laminar flow in a tube

The thermal radiation effects of a high‐temperature developing laminar flow in a tube are investigated numerically. The two‐dimensional steady flow and heat transfer are considered for an absorbing‐emitting gray medium, whose density is dependent on the temperature. The governing equations of the coupled process are simultaneously solved by the discrete ordinate method combined with the control volume method. For a moderate optical thickness, the velocity distribution, the temperature distribution, and the radial heat flux distribution in the medium as well as the heat flux distribution on the tube wall are presented and discussed. The results show that the thermal radiation effects of a high‐temperature medium are significant under a moderate optical thickness. The flow and convective heat transfer are weakened, and the development of temperature distribution is accelerated noticeably. © 2004 Wiley Periodicals, Inc. Heat Trans Asian Res, 33(5): 299–306, 2004; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20018     

Characteristics of combined heat transfer of superheated steam drying: Numerical study on coupled convection and gas radiation heat transfer

A numerical study on a combined radiation and forced convection heat transfer of superheated steam, which is a radiation participating real gas, in thermally developing laminar flow through a parallel‐plate channel has been conducted to investigate characteristics of superheated steam drying. The integrodifferential energy equation was solved using an implicit finite‐difference technique with a marching solution procedure and an exponential wide‐band model for the treatment of the radiative transfer part. Comparison of results with and without gas radiation in various conditions shows that fluid radiation decreases the temperature of the main stream, but increases the total heat flux at a heat transfer surface. Furthermore, the results show that the fluid radiation decreases the inversion point temperature approximately to 150 to 240 °C with the increase of optical thickness. This numerical result agrees in an order of magnitude with the previous experimental studies, but is about 100 K lower than that of former theoretical predictions without considering fluid radiation. © 2000 Scripta Technica, Heat Trans Asian Res, 29(5): 385–399, 2000     

液态金属浇注过程中流动与传热耦合数值模拟

浇注系统的设计是铸造工艺设计的主要内容。利用数值模拟技术,可对浇注系统进行优化设计。建立了液态金属流动和传热的数学模型,讨论了边界条件、初始条件的选择,对液态金属浇注过程中的流动与传热耦合问题进行了数值模拟,并对模拟结果进行了讨论。所得结论对于浇注系统和过程的优化设计具有重要的实用价值。     

A theoretical study of evaporative heat transfer in high‐velocity two‐phase flow of air–water in a small vertical tube

A theoretical study was performed to investigate the evaporative heat transfer of high‐velocity two‐phase flow of air–water in a small vertical tube under both heating conditions of constant wall temperature and constant heat flux. A simplified two‐phase flow boundary layer model was used to evaluate the evaporative heat transfer characteristics of the annular two‐phase flow. The analytical results show that the gravitational force, the gas–liquid surface tension force, and the inertial force are much smaller than the frictional force and hence can be neglected for a small tube. The evaporative heat transfer characteristics of the small tube with constant wall temperature are quite close to those of the small tube with constant heat flux. The mechanism of the heat transfer enhancement is the forced convective evaporation on the surface of the thin liquid film. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(5): 430–444, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10110     

平行流热管管内流动与传热的数值模拟研究

为研究平行流热管的工作机理,本文基于Fluent软件中的VOF模型编写了蒸发冷凝相变的UDF程序,对不同功率下平行流热管管内两相流动和传热过程进行了数值模拟研究。模拟结果显示了初始阶段平行流热管管内的气液分布,启动阶段管内包括泡状流、弹状流、环状流等复杂流型的转变过程,稳定工作阶段工质在各并联管路中互激振荡流动。在高加热功率下,管内工质的互激振荡流动更为剧烈,热量输送距离更远。研究结果为平行流热管换热器的优化设计提供了参考依据。     

Fluid‐to‐fluid scaling of heat transfer to mixed convection flow of supercritical pressure fluids

Fluid‐to‐fluid scaling for supercritical heat transfer can effectively reduce the difficulty and cost of heat transfer experiments in supercritical boilers and supercritical water reactors and can reduce the number of experiments by converting experimental data of the model fluid to the prototype fluid in organic Rankine cycles. Currently, most existing scaling methods are only suitable for forced convection, while few are developed for mixed convection where buoyancy significantly affects the heat transfer. This paper attempts to extend the applicability of scaling method to mixed convection with the aid of computational fluid dynamic simulations. The scaling parameters were analyzed first and then the shear‐stress transport k‐ω model was used to analyze the supercritical heat transfer characteristics of water and R134a to provide further information for developing a dimensionless number. The results show that significant variations of properties and flow parameters occur in the layer of y⁺ = 5 to 100 and the axial velocity gradient in this layer changes in quite a similar manner to the wall temperature. Based on numerical results, the axial velocity gradient was used with a thermal resistance analogy to derive a new dimensionless number, Re^?0.9π_A , to scale the mass flux. Then, a set of fluid‐to‐fluid scaling laws were developed to predict the heat transfer to supercritical fluids. To validate the newly proposed scaling laws, well‐developed correlations were used for forced convection flow and a direct validation method was developed for buoyancy‐influenced flow. Results show that this new scaling method exhibits reasonable accuracy for both forced and mixed convection heat transfer with supercritical fluids.     

Numerical simulation of steady natural convection heat transfer in a 3-dimensional single-ended tube subjected to a nanofluid

In this paper, 3-dimensional numerical simulation of steady natural convective flow and heat transfer are studied in a single-ended tube with non-uniform heat input. Apart from some other applications, it serves as a simplified model of the single-ended evacuated solar tube of a water-in-glass evacuated tube solar water heater. It is assumed that the sealed end of tube to be adiabatic and also the tube opening to be subjected to copper–water nanofluid. Governing equations are derived based on the conceptual model in the cylindrical coordinate system. The governing equations have been then approximated by means of a fully implicit finite volume control method (FVM), using SIMPLE algorithm on the collocated arrangement. The study has been carried out for solid volume fraction 0 ≤ φ ≤ 0.05 and maximum heat flux 100 ≤ q_m ≤ 700. Considering that the driven flow in the tube is influenced by the dimensions and the inclination angle of the solar tube, the flow patterns and temperature distributions are presented on different cross sectional planes and longitudinal sections, when the tube is positioned at different orientations.     

Transient heat transfer in a heat‐generating fin with radiation and convection with temperature‐dependent heat transfer coefficient

The transient heat transfer in a heat‐generating fin with simultaneous surface convection and radiation is studied numerically for a step change in base temperature. The convection heat transfer coefficient is assumed to be a power law function of the local temperature difference between the fin and its surrounding fluid. The values of the power exponent n are chosen to include simulation of natural convection (laminar and turbulent) and nucleate boiling among other convective heat transfer modes. The fin is assumed to have uniform internal heat generation. The transient response of the fin depends on the convection‐conduction parameter, radiation‐conduction parameter, heat generation parameter, power exponent, and the dimensionless sink temperature. The instantaneous heat transfer characteristics such as the base heat transfer, surface heat loss, and energy stored are reported for a range of values of these parameters. When the internal heat generation exceeds a threshold the fin acts as a heat sink instead of a heat source. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21012     

Fluid flow and heat transfer of natural convection adjacent to upward‐facing inclined heated plates

Turbulent transition mechanism and local heat transfer characteristics of the natural convective flows over upward‐facing inclined plates were investigated experimentally. The experiments were performed in the range of modified local Rayleigh numbers from 10⁴ to 8 × 10¹⁴ and of inclination angles θ from 0 to 90°. The flow fields over the plate and the surface temperatures of the plate were visualized with dye and liquid crystal thermometry. The results showed that longitudinal vortices play a main role in the turbulent transition over the plate of θ < 72°. These vortices appear first in the laminar boundary layer, then detach from the plate and, finally become distorted. It is found that the heat transfer is enhanced markedly by the detachment and the distortion of these vortices. The local heat transfer coefficients were measured in the laminar, transitional, and turbulent regions. The results show that the coefficients in the turbulent region become identical and independent of inclination angles. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(3): 278–291, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10091     

Numerical study on coupled fluid flow and heat transfer process in parabolic trough solar collector tube

A unified two-dimensional numerical model was developed for the coupled heat transfer process in parabolic solar collector tube, which includes nature convection, forced convection, heat conduction and fluid-solid conjugate problem. The effects of Rayleigh number (Ra), tube diameter ratio and thermal conductivity of the tube wall on the heat transfer and fluid flow performance were numerically analyzed. The distributions of flow field, temperature field, local Nu and local temperature gradient were examined. The results show that when Ra is larger than 10⁵, the effects of nature convection must be taken into account. With the increase of tube diameter ratio, the Nusselt number in inner tube (Nu₁) increases and the Nusselt number in annuli space (Nu₂) decreases. With the increase of tube wall thermal conductivity, Nu₁ decreases and Nu₂ increases. When thermal conductivity is larger than 200 W/(m K), it would have little effects on Nu and average temperatures. Due to the effect of the nature convection, along the circumferential direction (from top to down), the temperature in the cross-section decreases and the temperature gradient on inner tube surface increases at first. Then, the temperature and temperature gradients would present a converse variation at θ near π. The local Nu on inner tube outer surface increases along circumferential direction until it reaches a maximum value then it decreases again.     

Heat transfer from a vertical fin array by laminar natural convection and radiation—A quasi‐3D approach

A quasi‐3D numerical model is developed to study the problem of laminar natural convection and radiation heat transfer from a vertical fin array. An enclosure is formed by two adjacent vertical fins and vertical base in the fin array. Results obtained from this enclosure are used to predict heat transfer rate from a vertical fin array. All the governing equations related to fluid in the enclosure, together with the heat conduction equation in both fins are solved by using the Alternating Direction Implicit (ADI) method for getting the temperatures along the height of the fin and the temperature of the fluid in the enclosure. Separate analysis is carried out to calculate the heat transfer rates from the end fins in the fin array. A numerical study has been carried out for the effect of fin height, fin spacing, fin array base temperature, and fin emissivity on total heat transfer rates and effectiveness of the fin array. The numerical results obtained for an eight‐fin array show good agreement with the available experimental data. Results show that the fin spacing is the most significant parameter and there exists an optimum value for the fin spacing for which the heat transfer rate from the fin array is maximum. Correlations are presented for predicting the total heat transfer rate, average Nusselt number, and effectiveness of the fin array. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20360     

Numerical simulation of separated flow transition and heat transfer around a two‐dimensional rib

Numerical simulations of separated flow transition and heat transfer around a two‐dimensional rib mounted in a laminar boundary layer were performed. The separated shear layer becomes unstable due to the Kelvin–Helmholtz instability and generates a two‐dimensional vortex. This vortex becomes three‐dimensional and collapses in the downstream part of the separation bubble. As a result, transition from laminar to turbulent flow occurs in the separated shear layer. Streamwise vortices exist downstream of the reattachment flow region. The low‐frequency flapping motion and transition of the separated shear layer are influenced by three‐dimensional dynamics upstream of the separation bubble. Large‐scale vortices around the reattachment flow region have substantial effects on heat transfer. Downstream of the reattachment point, the surface friction coefficient and Nusselt number are different from their profiles in the laminar boundary layer and approach the distributions seen in the turbulent boundary layer. © 2007 Wiley Periodicals, Inc. Heat Trans Asian Res, 36(8): 513–528, 2007; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20177     

Effect of fins on forced convection heat transfer around a tube in an aligned‐arranged tube bundle

The effect of fins on heat transfer around a tube in an aligned‐arranged tube bundle was investigated experimentally, and the obtained results were compared for three arrangements, i.e., single tube, single tube row, and staggered‐arrangement. It was found from the experiment that the effect of fins begins to appear in an aligned‐arrangement with larger fin spacing than in a staggered‐arrangement. The degradation in the local heat transfer coefficient due to fins can be recognized not only on the rear region of the tube, as observed in other arrangements, but also on the frontal region. As a result of this phenomenon, the degradation in the average heat transfer coefficient in an aligned‐arrangement becomes larger than in other arrangements with the same fin spacing. © 2005 Wiley Periodicals, Inc. Heat Trans Asian Res, 34(8): 555–563, 2005; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20091     

Fluid flow and heat transfer of opposing mixed convection adjacent to upward‐facing,inclined heated plates

Opposing mixed convective flows of air induced over uniformly heated, upward‐facing, inclined plates were investigated experimentally. The experiments covered the ranges of the Reynolds and modified Rayleigh numbers, Re_L=7.2×10² to 1×10⁴ and Ra_L^*=5×10⁶ to 8×10⁸, and the inclination angles from θ=15 to 75^° from horizontal. The flow fields over plates were visualized with smoke. The results showed that a separation of forced boundary layer flow occurs first at the trailing edge, and then the separation point shifts toward upstream with increasing the wall heat flux, and finally, reaches to the leading edge of the plates. It was also found that the separations at the trailing and leading edges are correlated well with the non‐dimensional parameter as (Gr_θ^*/Re_L^2.5)=0.35 and 1.0, respectively. The local heat transfer coefficients of the inclined plates were also measured and the results showed that the above separation retards the heat transfer significantly from that of the forced convection. It was also revealed that the heat transfer by forced, natural, and combined convections can be classified with the above parameter as (Gr_θ^*/Re_L^2.5)<0.2,(Gr_θ^*)/Re_L^2.5)>3, and 0.2<(Gr_θ^*/Re_L^2.5)<3, respectively. © 2007 Wiley Periodicals, Inc. Heat Trans Asian Res, 36(3): 127– 142, 2007; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20151     

Numerical study of convective heat transfer in T‐bifurcating channel

A numerical study of a three‐dimensional turbulent flow in a rectangular T‐bifurcating duct was performed. It focused on the analysis of heat transfer in the branching duct at 90 to the main flow. Including separation and reattachment phenomena, the flow seemed to be anisotropic. The closure system of the full set of Navier–Stokes equations governing the flow was based on the on one point statistical modeling using a low Reynolds number second‐order full stress transport model. For several aspect ratios, results show that in addition to the recirculation zone in the branching duct close to the upstream side; pairs of streamwise vortices were generated downstream of the junction zone with their centers moving towards the symmetry plane. The effect of the aspect ratio of the branching section in enhancing this phenomenon and flow rate effect on the heat transfer were particularly analyzed in this paper.     

Fluid flow and heat transfer of opposing mixed convection adjacent to downward‐facing,inclined heated plates

Experimental investigations were carried out for opposing mixed convective flows of air adjacent to downward‐facing, inclined heated plates. The experiments covered the ranges of the Reynolds and modified Rayleigh numbers from Re_L=400 to 4600 and Ra_L^*=1.0×10⁷ to 5.4×10⁸, and the inclination angles from θ=15 to 75^° from horizontal. The flow fields over the plates were visualized with smoke. The results showed that a separation of forced boundary layer flow occurs first at the bottom edge of the plate, and then the separation point shifts toward upstream with increasing wall heat flux, and finally, reaches the top edge of the plates. It was found that the separations at the bottom and top edges are predicted with a non‐dimensional parameter (Gr_Lθ^*/Re_L^2.5)=0.35 and 1.0, respectively. The local heat transfer coefficients of the inclined plates were also measured and the results showed that the minimum coefficients appear in the separation region. Moreover, it was revealed that forced, natural, and combined convective flows can be classified by the non‐dimensional parameter (Gr_Lθ^*/Re_L^2.5). © 2008 Wiley Periodicals, Inc. Heat Trans Asian Res; Pub‐ lished online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20233     

Fluid flow and heat transfer of natural convection at a slightly inclined,upward‐facing,heated plate

Natural convective flows over upward‐facing, inclined plates were investigated experimentally, with an emphasis on the role of opposing flows that appear over the plates inclined slightly from the horizontal line. The flow fields over the plates and the surface temperatures of the heated plates were visualized with both dye and a liquid‐crystal thermometry. The results showed that both the descending and ascending flows appeared over the plates when the inclination angles of the plates were less than 15°. The two flows collided with each other at a certain distance from the plate edge, and then detached from the plate to become a thermal plume. It was found that the above distance was determined solely by the inclination angles and was independent of sizes and heat fluxes of the plates. The local heat transfer coefficients of the plates were also measured. The results showed that the heat transfer from the plate was enhanced by the occurrence of the descending flows. © 2002 Wiley Periodicals, Inc. Heat Trans Asian Res, 31(5): 362–375, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10036     

Heat transfer for flow boiling of water and critical heat flux in a half‐heated round tube under low‐pressure conditions

Heat transfer for flow boiling of water and critical heat flux (CHF) experiments in a half‐circumferentially heated round tube under low‐pressure conditions were carried out. To clarify the flow patterns in the heated section, experiments in the round tube under the same conditions were also carried out, and their results were compared. The experiments were conducted with atmospheric‐pressure water in test sections with inner diameter D = 6 mm, heated length L = 360 mm, inlet water subcooling ΔT_in = 80 K, and mass velocity G from 0 to 2000 kg/(m²·s) for the half‐circumferentially heated round tube and from 0 to 7000 kg/(m²·s) for the full‐circumferentially heated tube. The experimental data demonstrated that the wall temperature near the outlet of the half‐circumferentially heated tube remained almost the same until CHF. It was found that burnout occurred when the flow regime changed from churn flow to annular flow, and the liquid film on the heated wall dried out although liquid film on the unheated wall remained. © 2002 Wiley Periodicals, Inc. Heat Trans Asian Res, 31(3): 149–164, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10022