Numerical analysis of convective heat transport in a porous semi‐trapezoidal enclosure with radiation effect

A theoretical and numerical study of natural convection of two‐dimensional laminar incompressible flow in a semi‐trapezoidal porous enclosure in the presence of thermal radiation is conducted. The semi‐trapezoidal enclosure has an inclined left wall that in addition to the right vertical wall is maintained at a constant temperature, whereas the remaining (horizontal) walls are adiabatic. The Darcy‐Brinkman isotropic model is utilized. The governing partial differential equations are transformed using a vorticity stream function and nondimensional quantities and the resulting governing nonlinear dimensionless equations are solved using the finite difference method with incremental steps. The impacts of the different model parameters (Rayleigh number [Ra], Darcy number [Da], and radiation parameter [Rd]) on the thermofluid characteristics are studied in detail. The computations show that convective heat transfer is enhanced with the greater Darcy parameter (permeability). The flow is accelerated with the increasing buoyancy effect (Rayleigh number) and heat transfer is also increased with a greater radiative flux. The present numerical simulations are more relevant to hybrid porous media solar collectors.     

Numerical visualization via heatlines for natural convection in porous bodies of rhombic shapes subjected to thermal aspect ratio-based heating of walls

Visualization of heat flow and trajectories has been employed during buoyancy induced (natural) convection within porous rhombic 2D cavities of different base angles involving various intensities of the thermal state of the bottom wall via tuning thermal aspect ratios (A_r). The thermal mixing effect at the core, heat transport rates at side walls and heat supply rate by the bottom wall have been elucidated at various limits of Pr and A_r for low and high Darcy number regimes. The heatline tool has been found to be indispensable to analyze the convection heat transport at various locations and trajectories of heat propagation from the hot zone to cooler zone of walls involving various scenarios.     

Internal gravity wave resonance of thermal convection fields in a square cavity with heat‐flux vibration

In this paper, the thermal convection field and its resonance phenomena in a square cavity with sinusoidal heat‐flux vibration were numerically investigated. As the angular velocity ω is changed, the thermal convection field at Pr = 0.71,Ra = 10⁶ is found to be classified into 5 regions. In particular, the field has the local maximum relative amplitude of midplane Nusselt's number at ω_c = 350, which corresponds to the angular velocity of internal gravity wave ω_r estimated by a theoretical equation proposed by Thorpe. This shows that the local enhancement is induced by internal gravity wave resonance. Such correspondence is observed for Ra ≥ 10⁵,Ra ≥ 10⁶ for Pr = 0.71, 7.1, respectively. For these ranges of Ra we propose a correlation equation, a function of Pr and Gr only, to estimate the resonant angular velocity. © 2006 Wiley Periodicals, Inc. Heat Trans Asian Res, 35(5): 309–322, 2006; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20122     

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.     

Modeling of double diffusive buoyant flow in a solar collector with water‐CuO nanofluid

The behavior of a prism‐shaped solar collector with a right triangular cross sectional area is investigated numerically. The water‐CuO nanofluid is taken as the functioning liquid through the solar collector. The leading differential equations with boundary conditions are solved by the penalty finite element method using Galerkin's weighted residual scheme. The performance of parameters in terms of temperature, mass, velocity distributions, radiative, convective heat and mass transfer, mean temperature and concentration of nanofluid, mid height horizontal‐vertical velocities, and sub‐domain average velocity field are investigated systematically. These parameters include the Rayleigh number Ra and the solid volume fraction φ. The outcome explains that the performance of the solar collector can be enhanced with the largest Ra and φ. The code validation shows excellent concurrence with the hypothetical outcome obtainable in the literature. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21039     

Heat Transfer by Nanofluid with Different Nanoparticles in a Solar Collector

The buoyancy flow and heat transfer characteristics inside a solar collector having the flat‐plate cover and sinusoidal corrugated absorber are analyzed numerically. The water‐based nanofluid with alumina and copper nanoparticles is used as the working fluid inside the solar collector. The governing partial differential equations with proper boundary conditions are solved by the finite element method using Galerkin's weighted residual scheme. The behavior of both nanoparticles related to performance such as temperature and velocity distributions, radiative and convective heat transfers, mean temperature, and velocity of the nanofluid is investigated systematically. This performance includes the solid volume fraction, namely ?₁ and ?₂, with respect to Al ₂ O ₃ and Cu nanoparticles. The results show that the better performance of heat transfer inside the collector is found by using the highest ?₂ than ?₁. The result of this study expresses a good agreement with the theoretical result available in the literature. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(1): 61–79, 2014; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21061     

Storage Silos Self Ventilation: Interlinked Heat and Mass Transfer Phenomenon

This work is to better understand heat and mass transfer by natural convection in a vertical, open ended, and porous cylinder. The effects of buoyancy forces and chemical reaction on the natural convection are studied numerically and discussed for a large range of Rayleigh number (Ra _T ), buoyancy ratio (N), and reaction rate (Ak). A map diagram (Ra _T , A, Ak) of the two observed flow types, with and without fluid recirculation, was obtained. The analysis shows that the results strongly depend on the controlling parameters and demonstrates the effect on the recirculating possible flow. Thus, it's confirmed that the rate of heat transfer increases with increasing Rayleigh, and it is particularly sensitive to the values of dimensionless reaction rate (Ak) and aspect ratio (A).     

Numerical investigation of low Prandtl number effect on mixed convection in a horizontal channel by the lattice Boltzmann method

The main purpose of this study is to numerically investigate the Prandtl number effect on mixed convection in a horizontal channel heated from below using the thermal lattice Boltzmann method (TLBM). The double-population model with two different lattices is used, in particular, the D2Q9 for the velocity field and D2Q5 for the thermal field. The developed lattice Boltzmann method code to simulate the fluid flow and heat transfer in the channel was validated with available literature results based on classical numerical methods, especially the finite volume method for Pr = 6.4 and the finite difference method for Pr = 0.667. The results obtained with the TLBM have shown good agreement with the conventional methods cited. The dynamic and thermal characteristics of the fluid flow were examined in the field of low Prandtl number, such that 0.05 ≤ Pr ≤ 0.667, and also compared to Pr = 6.4; for Ra = 2420 and 7400, the Reynolds number was fixed at 1. The results showed that the influence is relatively significant for the dynamic structure of flow convection for Pr ≤ 0.3 and is little influential beyond this value.     

Modeling of a Solar Water Collector with Water‐Based Nanofluid Using Nanoparticles

The pressure‐velocity form of the Navier–Stokes equations, energy equation, and concentration equation are used to represent the mass, momentum, energy, and concentration conservations of the nanofluid medium in the solar collector. The governing equations and corresponding boundary conditions are converted to dimensionless form and solved numerically by the finite element method. The physical domain is discretized by triangular mesh elements with six nodes. The working fluid is water‐based nanofluid with two nanoparticles, namely, silver (Ag) and copper oxide (CuO). The study includes computations for different values of buoyancy ratio (Nr) and Schmidt number (Sc). Flow, heat, and mass transfer characteristics are presented in the forms of streamlines, isotherms, and iso‐concentrations. In addition, results for the average radiative, convective heat and mass transfer, mean temperature and concentration of nanofluid, mid‐height horizontal‐vertical velocities, and subdomain average velocity field are offered and discussed for the above‐mentioned parametric conditions. Results show that the effects of Nr and Sc on the convective‐radiative heat and mass transfer phenomenon inside the collector are significant for all values of Nr and Sc studied. Comparison and validation with the standard experimental/numerical data is given in brief. The variation of the obtained result is presented as 34% with the result of experimental data. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(3): 270–287, 2014; Published online 30 September 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21080     

Heatline analysis of heat recovery and thermal transport in materials confined within triangular cavities

Heat recovery from hot fluids in material processing industries is important for environmental and thermal management. Present work involves numerical visualization of heat flow in entrapped cavities filled with hot materials. The concept of heatline is used to visualize the heat energy trajectory. The system involves entrapped triangular cavities filled with hot fluid (Pr = 0.015, 0.026, 0.7 and 1000). At low Rayleigh number (Ra), it is found that the heatlines are smooth and perfectly normal to the isotherms indicating the dominance of conduction for both the triangles. As Ra increases, flow slowly becomes convection dominant. Multiple heat flow circulations with high intensity are formed within the lower triangular domain especially for low Pr numbers, whereas, less intense convective heat flow circulations are observed for the upper triangle. Multiple circulations are absent for both the triangular domains involving fluids with higher Pr numbers. It is observed that the heat transfer rates are monotonic for the upper triangle whereas a few local maxima in heat transfer rates occur for smaller Pr within lower triangular domain. Overall, fluid with any Pr may be useful for enhanced heat transfer within the upper triangle but fluid with high Pr may be preferred for the lower triangle.     

Theoretical approach of a flat-plate solar collector taking into account the absorption and emission within glass cover layer

A rigorous theoretical approach of a flat-plate solar collector with a black absorber considering the glass cover as an absorbing–emitting media is presented. The glass material is analyzed as a non-gray plane-parallel medium subjected to solar and thermal irradiations in one-dimensional case using the Radiation Element Method by Ray Emission Model (REM²). The optical constants of a clear glass window proposed by Rubin have been used. These optical constants, 160 values of real part n and imaginary part k of the complex refractive index of a clear glass, cover the range of interest for calculating the solar and thermal radiative transfer through the glass cover. The computational time for predicting the thermal behavior of solar collector was found to be prohibitively long for the non-gray calculation using 160 values of n and k. Therefore a suitable semi-gray model is proposed for rapid calculation. The profile of the efficiency curve obtained in the present study was found to be not linear in shape. Indeed, the heat loss from the collector is a combination of convection and radiation and highly non linear. The effect of the outside convective heat transfer on the efficiency curve is also studied. In fact, when the convection is the dominant heat transfer mode compared with the radiation one, the profile of the efficiency curve is more or less straight line. Consequently, the heat loss coefficient could be calculated using Klein model. It has been also shown that the effect of the wind speed on the glass cover mean temperature is very important. This effect increases with the increase of the mean absorber temperature.     

Numerical Analysis Of Mixed Convection In Inclined Tubes With External Longitudinal Fins

Laminar mixed convection in the entrance region of an inclined tube with longitudinal external fins (corresponding to the basic element of a flat plate solar collector) has been studied numerically. The system is subjected to a uniform solar flux and convective losses on its top surface; it is insulated on its bottom surface. The results show that the secondary flow induced by buoyancy has a very significant effect on the axial flow and on the isotherms in both the fluid and the solid. Furthermore, due to circumferential conduction in the tube wall, more heat reaches the fluid from the bottom half of the fluid–solid interface than from its top half. The circumferentially average Nusselt number shows the usual decrease with axial distance from the tube inlet towards a constant value in the fully developed region. This constant value is considerably higher for the finned tube than the corresponding value for a bare tube. Both these values are significantly higher than one for fully developed forced convection. A parametric study shows the effects of the fin and tube materials, of the solar flux and the fin’s width on the thermal performance of the collector.     

Combined non-gray radiative and conductive heat transfer in solar collector glass cover

A rigorous approach for the radiative heat transfer analysis in solar collector glazing is developed. The model allows a more accurate prediction of thermal performance of a solar collector system. The glass material is analysed as a non-gray plane-parallel medium subjected to solar and thermal irradiations in the one-dimensional case using the Radiation Element Method by Ray Emission Model (REM by REM).This method is used to analyse the combined non-gray convective, conductive and radiative heat transfer in glass medium. The boundary surfaces of the glass are specular. The spectral dependence of the relevant radiation properties of glass (i.e. specular reflectivity, refraction angle and absorption coefficient) are taken into consideration. Both collimated and diffuse incident irradiation are applied at the boundary surfaces using the spectral solar model proposed by Bird and Riordan. The optical constants of a commercial ordinary clear glass material have been used. These optical constants (100 values) of real and imaginary parts of the complex refractive index of the glass material cover the range of interest for calculating the solar and thermal radiative heat transfer through the solar collector glass cover. The model allows the calculation of the steady-state heat flux and temperature distribution within the glass layer. The effect of both conduction and radiation in the heat transfer process is examined. It has been shown that the real and imaginary parts of the complex refractive index have a substantial effect on the layer temperature distribution. The computational time for predicting the combined heat transfer in such a system is very long for the non-gray case with 100 values of n and k. Therefore, a simplified non-gray model with 10 values of n and k and two semi-gray models have been proposed for rapid computations. A comparison of the proposed models with the reference non-gray case is presented. The result shows that 10 bandwidths could be used for rapid computation with a very high level of accuracy.     

Three－Dimensional Numerical Simulation of Natural Convection Heat Transfer in an Inclined Cylindrical Annulus

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Effect of Buoyancy on the Perfomance of Solar Air Collectors with Different Structures

In order to study the effect of buoyancy on the performance of solar air collector, the theoretical analysis and experimental tests of four solar air collectors with different structures under natural convection and mixed convection are carried out. The results show that the air temperature rise of the protrusion-corrugated plate air collector is the highest in the natural convection, which is 9.17 Chigher than that of the flat plate collector, and the air outlet velocity is 0.19 m/s, increasing by 16.88% than that of the flat plate collector. Observing the effects on the heat transfer performance of mixed convection, it can be found, in addition to the protrusion-corrugated plate air collector, the buoyancy plays a positive role on the other three solar air collectors in the upward flow, while the buoyancy plays a negative role on the other three solar air collectors in the downward flow, and the enhanced degree of the buoyancy to the corrugated plate air collector is the largest, while the enhancement degree of the flat plate collector is the least.     

Internal gravity wave resonance of thermal convection fields in rectangular cavities with heat‐flux vibration (effects of aspect ratio on the fields)

In this paper the thermal convection field and its resonance phenomena in a rectangular cavity with heat‐flux vibration are numerically examined and the results are compared with those of a square cavity. As in the case of α=1, the critical angular velocity at which the relative amplitude of the midplane Nusselt number α_m has a local maximum agrees very well with the resonance angular velocity of the internal gravity wave ω_r, estimated by the theoretical equation proposed by Thorpe, even when the aspect ratio is α=5 and the Prandtl number is Pr=0.71 for a range of the Rayleigh number Ra. However, α_m has two local maxima for a larger Ra, which is peculiar to the case of larger α. The time variation of sub‐components of the fluctuating component of the midplane Nusselt number shows that the phase at the maximum value of α_m agrees well with that of the sub‐component of velocity for the first resonance angular velocity ω_r. For the other angular velocity ω_r2, the phase of α_m agrees with that of the sub‐component of temperature. Moreover, we found that the boundary angular velocity ω₀ between the first two of the five ω regions, which classify the thermal convection fields against ω, can be expressed by a function of α, Ra, and Pr and that α_m is independent of α and Ra for a relatively wide range of ω/ω₀. © 2007 Wiley Periodicals, Inc. Heat Trans Asian Res, 36(3): 158– 171, 2007; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20149     

A novel case study for thermal radiation through a nanofluid as a semitransparent medium via discrete ordinates method to consider the absorption and scattering of nanoparticles along the radiation beams coupled with natural convection

Natural convection in a volumetric radiant enclosure filled by a nanofluid is studied numerically for the first time by using discrete ordinates (DO) method to consider the absorption and scattering coefficients of nanoparticles on the radiation beams through the nanofluid as a semitransparent medium. Present nanofluid is a mixture of Al₂O₃ nanoparticles suspended in water as the base fluid. The volume concentration percentages of nanoparticles are almost small to make a semitransparent medium which means the achieved results can be used in the flat plate solar collectors. Moreover the SIMPLE algorithm of finite volume method for Navier-Stokes continuity, momentum and energy equations are solved and coupled with DO to simulate the total radiation and natural convection in a shallow inclined rectangular 2-D enclosure. This shape of enclosure is chosen due to it might represent the usual configuration of a solar collector. The enclosure inner walls are the gray diffuse emitters and reflectors. The effects of various amounts of Rayleigh number and volume concentration at different values of wavelength are investigated. The positive effect of wave length on radiation heat flux and consequently total heat flux of radiation and natural convection is observed.     

Natural Convection of a Binary Fluid in a Slightly Inclined Shallow Cavity

ABSTRACT

This article reports an analytical and numerical study of the natural convection in an inclined shallow cavity filled with a binary fluid. Newmann boundary conditions for temperature are applied to the long side walls of the enclosure, while the two short ones are assumed to be impermeable and insulated. The solutal buoyancy force are induced either by the imposition of constant fluxes of solute on the walls (double-diffusive convection, a = 0) or by temperature gradients (Soret effects, a = 1). The governing parameters for the problem are the thermal Rayleigh number,Ra_T, the Lewis number Le, the buoyancy ratio ?, the inclination of the cavity Θ, the Prandtl numberPr, the aspect ratio of the cavity A, and the constant a. For convection in an infinite layer (A > > 1), an analytical solution of the steady form of the governing equations is obtained on the basis of the parallel flow approximation. The critical Rayleigh numbers for the onset of supercritical and subcritical convection are predicted by the present model. Also, it is demonstrated that, for small enough inclinations around the horizontal plane, multiple steady states exist, some of which are unstable. Numerical solutions of the full governing equations are obtained for a wide range of the governing parameters. Good agreement is observed between the analytical prediction and the numerical simulations.     

Two phase simulation of nanofluid flow and heat transfer using heatline analysis

In this study Control Volume based Finite Element Method is applied to solve the problem of natural convection heat transfer in an enclosure filled with nanofluid. The important effect of Brownian motion and thermophoresis has been included in the model of nanofluid. The inner sinusoidal and outer circular walls are maintained at constant temperatures while the two other walls are thermally insulated. The heat transfer between cold and hot regions of the enclosure cannot be well understood by using isotherm patterns so heatline visualization technique is used to find the direction and intensity of heat transfer in a domain. Effects of thermal Rayleigh number (Ra), buoyancy ratio number (Nr) and Lewis number (Le) on streamline, isotherm, isoconcentration and heatline are examined. The results indicate that the average Nusselt number decreases as buoyancy ratio number increases until it reaches a minimum value and then starts increasing. As Lewis number increases, this minimum value occurs at higher buoyancy ratio number.