Direct and inverse mixed convections in an enclosure with ventilation ports

The numerical study presented in this work describes the direct and inverse mixed convection problems in a slot-ventilated enclosure subjected to an unknown heat flux on one side. Particularly, the interaction of internal natural convection with the cold ventilated flow leads to various flow fields depending on the Richardson number, Reynolds number, and the functional form of the imposed boundary heat flux. Fluid and heat transport structures across the enclosure are visualized by the streamlines and heatlines, respectively. Subsequently, an iterative conjugate gradient method is applied such that the gradient of the cost function is introduced when the appropriate sensitivity and adjoint problems are defined for a domain of arbitrary geometries. In this approach, no a priori information is needed about the unknown boundary heat fluxes to be determined. The accuracy of the heat flux profile solutions is shown to depend strongly on the values of Reynolds number and flux functional forms. Effects of measurement errors on the accuracy of estimation are also investigated. The present work is significant for the flow control simultaneously involving the natural convection and forced convection.     

Computation of turbulent natural convection with the elliptic-blending differential and algebraic flux models

A computation of turbulent natural convection in enclosures with the elliptic-blending based differential and algebraic flux models is presented. The primary emphasis of the study is placed on an investigation of accuracy of the treatment of turbulent heat fluxes with the elliptic-blending second-moment closure for the turbulent natural convection flows. The turbulent heat fluxes are treated by the elliptic-blending based algebraic and differential flux models. The proposed models are applied to the prediction of turbulent natural convections in a 1:5 rectangular cavity and in a square cavity with conducting top and bottom walls. It is shown that both the elliptic-blending based models predict well the mean velocity and temperature, thereby the wall shear stress and Nusselt number. It is also shown that the elliptic-blending based algebraic flux model produces solutions which are as accurate as those by the differential flux model.     

Inverse design involving combined radiative and turbulent convective heat transfer

This work considers an inverse boundary design problem which involves radiation and convection heat transfer. The objective is finding the heat flux distribution required on heaters located on the top and side walls of a two-dimensional enclosure that satisfies both the temperature and heat flux distributions prescribed on the design surface of the enclosure. A turbulent air flow is generated by a fan located inside the chamber. The problem is described by a system of non-linear, ill-conditioned equations, which is solved by an iterative procedure. The solution are obtained by regularizing the system of equations by means of the TSVD method.     

Determining boundary heat flux profiles in an enclosure containing solid conducting block

A numerical implementation of estimating boundary heat fluxes in enclosures is proposed in the present work. Particularly, the flow field is dynamically coupled with the heat convection in the fluid and the heat conduction in the solid domain. An iterative conjugate gradient method is applied such that the gradient of the cost function is introduced when the appropriate sensitivity and adjoint problems are defined. In this approach, no a priori information is needed about the unknown function to be determined. Numerical solutions are obtained for the case of a square enclosure centrally-inserted with a solid block and subjected to an unknown heat flux on one side and to known conditions on the remaining sides. Fluid and heat transports are visualized by the streamlines and heatlines respectively, which are evidently affected by the thermal Rayleigh number, solid body size and thermal conductivity of solid phase, and the functional form of the imposed heat flux. The accuracy of the heat flux profile estimations is shown to depend strongly on the thermal Rayleigh number, body size and relative thermal conductivity of the solid material. Effects of functional form of the unknowns, sensors number and position, and measurement errors on the accuracy of estimation are also investigated. The present work is significant for the flow control simultaneously involving the heat conduction and convection.     

Numerical simulation of turbulent natural convection of nanofluid with thermal radiation inside a tall enclosure under the influence of magnetohydrodynamic

In the present study, the natural convective heat transfer in the turbulent flow of water/CuO nanofluid with volumetric radiation and magnetic field inside a tall enclosure has been numerically investigated. The thermophysical properties of nanofluid have been considered variable with temperature and the effects of Brownian motion of nanoparticles have been considered. The main objective of this work is an investigation of the effect of using water/CuO nanofluid and presence of magnetic field on turbulent natural convection in three types of enclosures (vertical, inclined, and horizontal) by considering the volumetric radiation. The governing equations on turbulent flow domain under the influence of the magnetic field and by considering the combination of volumetric radiation and natural convection have been solved by a coupled algorithm. For validating the present research, a comparison has been carried out with the laminar natural convection flow under the influence of the magnetic field and radiation effects and also, the natural turbulent convection flow of previous studies and a proper coincidence has been achieved. The results indicated that by increasing volume fraction and Hartmann number the average Nusselt number enhances and reduces, respectively. By adding 1% CuO nanoparticles to the base fluid, heat transfer improves from 10.59% to 17.05%. However, by increasing the volume fraction from 1% to 4%, heat transfer improves from 1.35% to 4.90%. By increasing Hartmann number from 0 to 600, heat transfer reduces from 9.29% to 22.07%. Also, the results show that the ratio of deviation angle of the enclosure to the horizontal surface has considerable effects on heat transfer performance. Therefore, in similar conditions, the inclined enclosure with a deviation angle of 45° compared to the vertical and horizontal enclosure has better thermal performance.     

Solution of the inverse steady state convection problem in a porous medium by adjoint equations

The inverse free convection problem in a porous medium is solved by adjoint equaitons and conjugate gradient. A derivation of the set of adjoint equations in the steady case is provided. Numerical solutions are obtained for the case of a rectangular enclosure subjected to an unknown heat flux on one side, and to known conditions on the remaining sides. Results are presented for different flux profiles with a Rayleigh number ranging from 0 to 10⁴ and the effect of noise in the input data is also examined.     

Periodic heat transfer in directly opposed free and forced convection flow

An experimental study of the heat transfer from small circular cylinders placed horizontal to a downward flowing air stream is reported. Based on heat-transfer measurements and flow visualization, a model for directly opposed free and forced convection was developed. Three modes of flow were observed. For very low velocities the free convection, buoyant plume dominates the heat transfer. At a “lower critical” Reynolds number, when the free and forced convections are of the same order of magnitude, a well defined periodic heat transfer was obtained. The periodic heat transfer was due to the build-up of the buoyant forces to a magnitude where they overcame the downward force of the air flow. At an “upper critical” Reynolds number the periodic heat transfer abruptly ceases. For velocities greater than the upper critical limit the forces due to the air flow dominate. A potential like, laminar sheet forms, as a shroud around the thermal layer of the hot cylinder. The average heat transfer from the cylinder decreases with increasing Reynolds number for both the case of dominant free convection and the periodic heat-transfer regime. The minimum value of the heat transfer occurred at the upper critical Reynolds number.     

Heat transfer of a non-Newtonian fluid (Carbopol aqueous solution) in transitional pipe flow

An experimental study of the forced convection heat transfer for non-Newtonian fluid flow in a pipe is presented. We focus particularly on the transitional regime. A wall boundary heating condition of heat flux is imposed. The non-Newtonian fluid used is Carbopol (polyacrylic acid) aqueous solutions. Detailed rheology as well as the variation of the rheological parameters with temperature are reported. Newtonian and shear thinning fluids are also tested for comparative purposes. The characterization of the flow and the thermal convection is made via the pressure drop and the wall temperature measurements over a range of Reynolds number from laminar to turbulent regime. Our measurements show that the non-Newtonian character stabilizes the flow, i.e., the critical Reynolds number to transitional flow increases with shear thinning and yield stress. The heat transfer coefficients are given and compared with heat transfer laws for different regime flows. Details when the heat transfer coefficient loses rapidly its local dependence on the Reynolds number are analyzed.     

Identification of wall heat flux for turbulent forced convection by inverse analysis

An inverse problem for turbulent forced convection between parallel flat plates is investigated. The space- and time-dependent heat flux at the upper wall is estimated from the temperature measurements taken inside the flow. In the present study, the conjugate gradient method is adopted for the estimation of the unknown wall heat flux. No prior information is needed for the functional form of the wall heat flux in the inverse analysis. The effects of the measurement errors, the functional form of the wall heat flux, and the location of the sensors on the accuracy of the estimation are investigated. The reconstruction of the wall heat flux is satisfactory when simulated exact or noisy data are input to the inverse analysis. The sensitivity coefficients are discussed in this paper. As expected, it is shown that the accuracy of the estimation can be improved when the sensors are located closer to the upper wall.     

Dual steady transports of heat and moisture in a vent enclosure with all round states of ambient air

Combined natural convective heat and moisture transports in a moist-air-filled enclosure with four free vent ports are numerically investigated. Four situations of ambient air states, hot and humid (I), hot and arid (II), cold and arid (III), and cold and humid (IV), are taken into consideration. Convective transports of semi-enclosed air, heat and moisture are respectively analyzed using the contours of streamfunction, heatfunction and massfunction, in addition to the isotherms and iso-concentrations. Overall convective heat transfer rate (Nu) and moisture transfer rate (Sh) of the internal concentrated heat and moisture source have been correlated with the thermal Rayleigh number respectively within the domain of the heat transfer driven flows and that of moisture transfer driven flows. When different initial convective flow conditions were imposed in the cases (I) and (IV), dual steady flow states of semi-enclosed heat and moisture convection are observed, and heat and moisture transport potentials can be enhanced or inhibited depending on the flow solution branches. These results can be adopted to guide the design of natural ventilation in the humid regions.     

Reduced-order modeling of turbulent forced convection with parametric conditions

Accurate reduced-order models of turbulent flows have been traditionally constructed with the proper orthogonal decomposition (POD), however the method has been limited to prototypical flows over a narrow parameter range. An orthogonal complement subspace method is developed here to treat inhomogeneous boundary conditions while implicitly coupling the velocity and temperature fields of turbulent convection. A new flux matching procedure is formulated as a state space residual series expansion to efficiently model parameter dependent convection, greatly extending the utility of the reduced-order modeling framework. An illustrative test case of turbulent channel flow over heated blocks shows flow and thermal models with 95% accuracy over the domain can be produced, while simultaneously reducing the number of degrees of freedom by a factor of 10³. Error bounds are formulated and provide a posteriori error estimates for the reduced-order model.     

Effects of a Thick Plate on the Excess Temperature of Iso-Heat Flux Heat Sources Cooled by Laminar Forced Convection Flow: Conjugate Analysis

A conjugate analysis via the finite volume approach is performed to study the effects of a thick plate on the excess (peak) temperature of an iso-heat flux heat source cooled by laminar forced convection flow. A thick plate of temperature-dependent thermal conductivity is placed between the heat sources and the cooling fluid. A cooling fluid flows over the thick plate and removes the heat by laminar forced convection. On account of the two-dimensional heat redistribution in the finite thick plate with one face subjected to iso-heat flux and the other face exposed to forced flow, the interface ceases to be an iso-heat flux and, consequently, reduces the excess temperature of the heat sources. In the numerical analysis, the thickness of the plate is relaxed one by one to search for the optimal thickness that minimizes the excess temperature. It is shown that the reduction in the excess temperature due to the insertion of the thick plate with optimal thickness depends upon the Reynolds number of the fluid flow and the fluid-to-solid thermal conductivity ratio.     

SIMULTANEOUS ESTIMATION OF INLET TEMPERATURE AND WALL HEAT FLUX IN TURBULENT CIRCULAR PIPE FLOW

An inverse heat convection problem is solved for simultaneous estimation of unknown inlet temperature and wall heat flux in a thermally developing, hydrodynamically developed turbulent flow in a circular pipe based on temperature measurements obtained at several different locations in the stream. The direct problem of turbulent forced convection is solved with a finite difference method with appropriate algebraic turbulence modelling. Although we seek for two unknown functions, we formulate the inverse problem as one of parameter estimation through the representation of the unknown inlet temperature profile and the wall heat flux distribution by one-dimensional finite element interpolation. Nodal values of the inlet temperature and the wall heat flux at chosen positions are determined as unknown parameters through the Levenberg–Marquardt algorithm for minimization procedure. Numerical results for several testing cases with different magnitudes of measurement errors are examined by using simulated experimental data. The effects of the number and the locations of the temperature measurement points are discussed.     

NUMERICAL EVALUATION OF WEAKLY TURBULENT FLOW PATTERNS OF NATURAL CONVECTION IN A SQUARE ENCLOSURE WITH DIFFERENTIALLY HEATED SIDE WALLS

This article presents the results of numerical evaluation of weakly turbulent natural convection of air in a rectangular enclosure with differentially heated side walls and adiabatic horizontal walls. The turbulence in the natural convection was described by k–ε equations, which were solved by Strang splitting, while average thermal and fluid flow fields were described by statistically averaged equations, which were solved by the projection method PmIII. The combined application of projection method and the Strang splitting characterizes the numerical method in this study. Numerical results for Rayleigh number 1.58 × 10⁹ have revealed reasonable agreement with the existing experimental ones, with some discrepancy attributable to the adiabatic boundary conditions on the horizontal walls. The results are also in good agreement with some published numerical results, particularly at higher Rayleigh numbers. However, comparison with the latest experimental data reveals that the turbulent heat flux model is not quite capable of giving satisfactory temperature distribution.     

Computation of a turbulent natural convection in a rectangular cavity with the elliptic-blending second-moment closure

A numerical study of a turbulent natural convection in an enclosure with the elliptic-blending second-moment closure (EBM) is presented. The primary emphasis of the study is placed on an investigation of the accuracy and numerical stability of the elliptic-blending second-moment closure for the turbulent natural convection flow. The turbulent heat fluxes in this model are treated by the general gradient diffusion hypothesis (GGDH). The model is applied to the prediction of a natural convection in a rectangular cavity and the computed results are compared with the experimental data commonly used for a validation of the turbulence models. The results are also compared with those by the two-layer model, the SST model, the V2-f model and the second-moment differential stress and flux model. It is shown that the elliptic blending model predicts as good as or better than the existing models for the mean velocity and turbulent quantities although this model employs a simpler GGDH for treating the turbulent heat fluxes.     

Acknowledgment

An experimental and numerical study has been carried out in order to investigate mixed and natural convection heat transfer in a two-dimensional enclosure. A discrete isothermal heat source is located at one of the vertical walls. Also, two ventilation ports are at the bottom and on top of the opposite wall. A forced flow condition was imposed by providing an inlet of air at the bottom port. A Mach–Zehnder interferometer was used to visualize the temperature field within the enclosure and to determine the local and average heat transfer characteristics of the heat source. Five heater positions on the vertical wall and different Rayleigh numbers (4.5 × 10⁵ to 1.15 × 10⁶) and Reynolds numbers (120 to 1600) were considered in the experiments. A finite volume code has been developed based on the SIMPLE algorithm and hybrid discretization scheme for the numerical study. It is observed that the interaction of natural convection with the forced flow leads to various flow fields depending on the Richardson number, Reynolds number and the heater position. Also, results show different trends for variation of the average Nusselt number with the heater position at low and high Reynolds numbers. An optimum position for the heat source, at which the maximum heat transfer is achieved, exists for high Reynolds numbers and has been found to be at the middle of the vertical wall.     

Conduction-combined forced and natural convection in lid-driven enclosures divided by a vertical solid partition

Numerical simulations of the conduction-combined forced and natural convection (mixed convection) heat transfer and fluid flow have been performed for 2-D lid-driven square enclosure divided by a partition with a finite thickness and finite conductivity. Left vertical wall of enclosure has two different orientations in positive or negative vertical coordinate. Buoyancy forces are taken into account in the system. Horizontal walls are adiabatic while two vertical walls are maintained isothermal temperature but the temperature of the left moving wall is higher than that of the right stationary wall. Thus, heat transfer regime between moving lid and partition is mixed convection. Conduction occurs along the partition. And, pure natural convection is formed between the partition and the right vertical wall. This investigation covers a wide range of Richardson number which is changed from 0.1 to 10, thermal conductivity ratio varies from 0.001 to 10. It is observed that higher heat transfer was formed for higher Richardson number for upward moving wall for all values of thermal conductivity ratio. When forced convection becomes effective, the orientation of moving lid becomes insignificant. Heat transfer is a decreasing function of increasing thermal conductivity ratio for all cases and Richardson numbers.     

History recovery and source identification of multiple gaseous contaminants releasing with thermal effects in an indoor environment

Thermal transport and transient dispersion of pollutants emitted from two discrete strips within the displacement ventilation enclosure have been modeled numerically. Following the full numerical simulation of turbulent air flows, the inverse determinations of multiple pollutant sources were conducted by the use of quasi reversibility methodology. Direct simulation together with the turbulent streamlines and turbulent heatlines demonstrate that the enclosure flow pattern, enclosure air thermal level and heat transfer potential will depend on the interactions of external forced flow and thermal buoyancy driven flows, i.e., Reynolds number (2 × 10³ ? Re ? 10⁴) and Grashof number (10⁶ ? Gr ? 10¹⁰). In subsequent forward time and backward time modeling of airborne pollutant transports, temporal evolutions of enclosure average concentration and pollutant exhaust are shown to depend on the supplying velocity (Re), thermal plume (Gr), pollutant diffusivity (0.1 ? Sc ? 2), and the pitch between both sources (0.2H ? d_PSL = d_PSR ? 0.7H). Reverse time modeling of airborne spread has demonstrated that increasing the spread rate and the concentration sensitivity of airborne pollutants will facilitate the identification of pollutant sources.     

Exergy transfer characteristics of forced convective heat transfer through a duct with constant wall temperature

The exergy transfer characteristics of fluid flow and heat transfer inside a circular duct under fully developed laminar and turbulent forced convection are presented. Temperature is kept constant at the duct wall. The exergy transfer Nusselt number is put forward and the analytical expressions for exergy transfer Nusselt number are obtained as functions of heat transfer Nusselt number, Reynolds number, Prandtl number, etc. The variations of the local and mean convective exergy transfer coefficient, non-dimensional exergy flux, exergy transfer rate, etc. with operating parameters are presented graphically. By reference to a smooth duct and taking air as working fluid, a numerical analysis of the influence of the Reynolds number and non-dimensional cross-sectional position on exergy transfer characteristics has been conducted. The results show that the process parameters and configuration in the fluid flow and heat transfer inside a duct should be properly selected so that the forced convection process could have the best exergy utilization. In addition, the results corresponding to the exergy transfer and energy transfer are compared.     

Component analysis of a steady inverse convection problem solution in a porous medium

A steady-state inverse free convection problem is solved by conjugate gradient and adjoint equations in a porous medium confined within a square enclosure subjected to an unknown heat flux on one side, and to isothermal and adiabatic conditions on the other sides. Numerical solutions for sinusoidal flux profiles are examined on the basis of a Fourier decomposition for Rayleigh numbers ranging from 0 to 10⁴. Analytical perturbation results for the first iteration are provided, showing the initial effects of convection on the inverse solution. It is found that the problem involves scales of different magnitudes, slowing down convergence, mainly through the step size, as convection develops.