Numerical modeling of heat and mass transfer characteristics during the forced convection drying of a square cylinder under strong blockage

Two-dimensional analysis of heat and mass transfer during drying of a square cylinder (SC) for confined flow with a strong blockage ratio (β?=?0.8) was performed using the alternating direction implicit (ADI)-based software. The influence of Reynolds number (Re?=?10–50) and moisture diffusivity number (D?=?1?×?10^?5???1?×?10^?8?m²/s) on the heat and mass transfer mechanisms was investigated. The convective heat transfer coefficients on SC surfaces were obtained using a commercial software package. The moisture content distributions inside a SC under transient conditions were calculated using the ADI method. The calculations showed that a higher Reynolds number enhances the overall mean Nusselt number and heat transfer coefficient value. The largest mean Nusselt number and heat transfer coefficient values were obtained at the front face of the SC, which makes the greatest contribution to the overall mean Nusselt number and heat transfer coefficient values for all surfaces of the SC. The effect of Reynolds number on the overall drying time was also investigated. Low Reynolds number and moisture diffusivity values lead to an increase in the overall drying time (Δt_od). For Re?=?10, the Δt_od values are 502.19?→?220288?s and for Re?=?50, the Δt_od values are 126.14?→?70353.21?s for a moisture diffusivity range of D?=?1?×?10^?5???1?×?10^?8?m²/s. Δt_od-Re?=?10/Δt_od-Re?=?50 ratios are 3.98–3.89 and 3.13 for a moisture diffusivity range of D?=?1?×?10^?5???1?×?10^?8?m²/s. Δt_od-D2/Δt_od-D1 is 7.47 for Re?=?10, and Δt_od-D3/Δt_od-D2 is 7.63 for Re?=?50, whereas Δt_od-D3/Δt_od-D1 is 438.66 for Re?=?10, and Δt_od-D3/Δt_od-D1 is 557.74 for Re?=?50. Additionally, iso-moisture contours of SC were presented and relations for Nusselt number and mass transfer coefficient values were derived.     

Laminar natural convection heat and mass transfer in vertical rectangular ducts

The present work investigates numerically the laminar natural convection heat and mass transfer in open vertical rectangular ducts with uniform wall temperature/uniform wall concentration (UWT/UWC) or uniform heat flux/uniform mass flux (UHF/UMF) boundary conditions. The vorticity–velocity formulation is applied to solve for the coupled momentum, energy and concentration equations. Results of dimensionless induced volume rate Q, average Nusselt number Nu and Sherwood number Sh are presented in terms of channel length L, buoyancy ratio N, Grashof number Gr, Schmidt number Sc and aspect ratio γ. Analytical solutions for Q, Nu and Sh for the UWT/UWC case are derived under fully developed condition. In addition, the correlation equations of Q, Nu and Sh for both boundary conditions are also presented.     

Experimental investigation of forced and mixed convection heat transfer in a foam-filled horizontal rectangular channel

An experimental study was performed to investigate the heat transfer characteristics of the mixed convection flow through a horizontal rectangular channel where open-cell metal foams of different pore densities (10, 20 and 30 PPI) were situated. A uniform heat flux was applied at all of the bounding walls of the channel. For each of three values of the uniform heat flux, temperatures were measured on the entire surfaces of the walls. Results for the average and local Nusselt numbers are presented as functions of the Reynolds and Richardson numbers. The Reynolds number based on the channel height of the rectangular channel was varied from 600 to 33000, while the Richardson number ranged from 0.02 to 103, extending over forced, mixed and natural convection. Second important parameter that influences the heat transfer is the aspect ratio of the foams. Three different aspect ratios (AR) as 0.25, 0.5 and 1 are tested. Based on the experimental data, new empirical correlations have been constructed to link the Nusselt number. The results of all cases were compared to that of the empty channel and the literature. We found that our results were in agreement with those that are mentioned in the literature.     

Numerical simulation of conjugate heat and mass transfer during multi-dimensional freeze drying of slab-shaped food products

The freeze drying characteristics of planar and slab-shaped food products were numerically studied using a simulation program that considered the conjugate heat and mass transfer, sublimation of ice, and motion of sublimation interface. The fixed grid method, which was adopted in the numerical simulation, was able to handle the complex sublimation interface during the multi-dimensional freeze drying of slab-shaped products appropriately. The results showed that the lateral permeable surface of the slab-shaped products significantly altered the freeze drying characteristics by reducing the diffusion length for the water vapor transport as well as by increasing the interfacial area for sublimation. These two effects were found to cooperatively enhance the freeze drying rate while decreasing the average sublimation temperature.     

Natural convection heat transfer between concentric rectangular parallelepipeds

Natural convection heat transfer between concentric rectangular parallelpipeds was studied numerically for low Rayleigh numbers Ra(≦ 3500) with aspect ratios of the inner parallelepiped of 2.0, 4.0, 6.0, and 8.0. It has been found that the flow patterns for the higher Rayleigh numbers in the space over the inner parallelpiped are ring or rectangular rolls. The number of rolls increases with the aspect ratio. The flow pattern in the side space is an oblong circulation, which extends into the bottom space. The local Nusselt number distribution on the top surface of the inner parallelpiped has peaks at the stagnation points. The relation between the Nusselt and Rayleigh numbers on the top surface is similar to that of the Rayleigh–Bénard convection obtained by Silveston (Chandrasekhar S.Hydrodynamic and Hydromagnetic Stability, 1961, p 68, Oxford University Press), while on the side and bottom surfaces the Nusselt number increases proportionately with the power of the Rayleigh number. © 2001 Scripta Technica, Heat Trans Asian Res, 30(2): 152–163, 2001     

Development of new correlations for forced convection heat transfer during cooling of products

This paper presents the new, simple but powerful effective Nusselt–Reynolds correlations for estimating the effective convective heat transfer coefficients of spherical and cylindrical products cooled in water and air flows. In this respect, both experimental and theoretical works were obtained. In the experimental case, several spherical and cylindrical products, namely, tomatoes, pears and cucumbers were cooled in water and air flow and their centre temperature variations were measured. In the theoretical case, the effective convective heat transfer coefficients for the individual spherical and cylindrical products were determined using the centre temperature data in the present approach including Dincer's models. Therefore, the new Nusselt–Reynolds correlations were developed using the effective convective heat transfer coefficient values and a general diagram of Nu/Pr^1/3 against Reynolds number was drawn. This study indicates that the present effective Nu–Re correlations are capable of estimating the effective convective heat transfer coefficients of any spherical and cylindrical shaped products exposed to water and air cooling in practical applications in a simple and accurate manner.     

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     

Evaluating the performance of forced convection heat transfer enhancement

Two methods for assessing thermal performance were evaluated for four kinds of forced convective heat transfer augmentations. On method uses the first law of thermodynamics, i.e., the heat transfer improvement at (1) constant Reynolds number, (2) constant pressure loss, and (3) constant pumping power. The other method uses the second law of thermodynamics, i.e., the entropy generation. The first method restricts the effective region and the second method supplies the condition for achieving the minimum entropy generation rate. © 1998 Scripta Technica, Heat Trans Jpn Res, 27(2): 142–154, 1998     

Thermal boundary condition effects on forced convection heat transfer

We propose a numerical solution of an adjoint problem of forced convection heat transfer to evaluate the mean heat transfer characteristics under arbitrary thermal boundary conditions. Using the numerical solution of the adjoint problem under the Dirichlet condition, which can be computed by slightly modifying a conventional heat transfer code, we obtain an influence function of local surface temperature on total heat transfer. As a result, the total heat transfer for arbitrary surface temperature distributions can be calculated by the influence function. Similarly, using the numerical solution of the adjoint problem under the Neumann condition, we can also obtain an influence function of the local heat flux on the mean surface temperature. The influence functions for a circular cylinder and for an in-line square rod array are presented to illustrate the capability of this method. © 1999 Scripta Technica, Heat Trans Asian Res, 28(3): 227–238, 1999     

Evaporative mass transfer in turbulent forced convection duct flows

Experiments were performed to determine the mass transfer characteristics for evaporation from partially filled pans of distilled water recessed in the floor of a flat rectangular duct through which turbulent air flow was passed. During the course of the experiments, parametric variations were made of the Reynolds number of the air flow, the streamwise length of the pan, and the distance between the top of the pan and the water surface (hereafter referred to as the step height). For all of the operating conditions of the experiments, the measured Sherwood numbers were well correlated with the Reynolds number provided that the step height was used as the characteristic dimension. Guided by analytical considerations, a second correlation was constructed which provides Sherwood number predictions for operating conditions corresponding to pans longer than those used in the present experiments. By making use of the analogy between heat and mass transfer, it was shown how Nusselt numbers can be obtained from the Sherwood number correlations.     

Three dimensional numerical modeling of simultaneous heat and moisture transfer in a moist object subjected to convective drying

The drying behavior of a moist object subjected to convective drying is analyzed numerically by solving heat and moisture transfer equations. A 3-D numerical model is developed for the prediction of transient temperature and moisture distribution in a rectangular shaped moist object during the convective drying process. The heat transfer coefficients at the surfaces of the moist object are calculated with an in-house computational fluid dynamics (CFD) code. The mass transfer coefficients are then obtained from the analogy between the thermal and concentration boundary layer. Both these transfer coefficients are used for the convective boundary conditions while solving the simultaneous heat and mass transfer governing equations for the moist object. The finite volume method (FVM) with fully implicit scheme is used for discretization of the transient heat and moisture transfer governing equations. The coupling between the CFD and simultaneous heat and moisture transfer model is assumed to be one way. The effect of velocity and temperature of the drying air on the moist object are analyzed. The optimized drying time is predicted for different air inlet velocity, temperature and moisture content. The drying rate can be increased by increasing the air flow velocity. Approximately, 40% of drying time is saved while increasing the air temperature from 313 to 353 K. The importance of the inclusion of variable surface transfer coefficients with the heat and mass transfer model is justified.     

Natural convection heat transfer between horizontal concentric rectangular pipes

Natural convection heat transfer between concentric rectangular pipes was studied numerically. It has been found that rolls of even numbers form in the region on the top surface of the inner pipe. The number of rolls depends on both the Rayleigh number and the aspect ratio. An oblong circulation of flow forms in the region between the side surface of the inner pipe and the surface of the outer pipe. The aspect ratio does not have much effect on the average Nusselt number at the side surface of the inner pipe. The relation between the Nusselt and Rayleigh numbers at the top surface resembles that of the Rayleigh-Bénard convection obtained by Silveston (Chandrasekhar, S. 1961. Hydrodynamic and Hydromagnetic Stability, Oxford University Press, 68). The average Nusselt number at the bottom surface of the inner pipe decreases with increasing aspect ratio because the region where heat transfer is affected significantly by convection is limited. © 1998 Scripta Technica, Heat Trans Jpn Res, 27(4): 271–283, 1998     

Laminar mixed convection heat and mass transfer in vertical rectangular ducts with film evaporation and condensation

The investigation of mixed convection heat and mass transfer in vertical ducts with film evaporation and condensation has been numerically examined in detail. This work is primarily focused on the effect of film evaporation and condensation along the wetted wall with constant temperature and concentration on the heat and mass transfer in rectangular vertical ducts. The numerical results, including the distributions of dimensionless axial velocity, temperature and concentration distributions, Nusselt number as well as Sherwood number are presented for moist air mixture system with different wall temperatures and aspect ratios of the rectangular ducts. The results show that the latent heat transport with film evaporation and condensation augments tremendously the heat transfer rate. Better heat transfer enhancement related with film evaporation is found for a system with a higher wall temperature.     

褐煤干燥过程对流传热特性的数值模拟

以干燥器内对流传热问题为研究对象,建立了褐煤干燥过程气-固对流传热模型。通过流-固界面传热耦合,利用CFD仿真技术进行模拟,对褐煤在不同粒径、风速及温度下的干燥过程进行了数值模拟,得到不同工况下的温度场分布及对流传热系数。根据模拟结果拟合得到气-固传热关联式,结果表明该关联式与褐煤干燥过程较吻合,可为工程实践提供理论指导。     

3d-Transient modeling of heat and mass transfer during heat treatment of wood

In the current work, three-dimensional Navier-Stokes equations along with the energy and concentration equations for the fluid coupled with the energy and mass conservation equations for the solid (wood) are solved to study the transient heat and mass transfer during high thermal treatment of wood. The model for wood is based on Luikov's approach and solves a set of coupled heat and mass transfer equations. The model equations are solved numerically by the commercial package FEMLAB for the temperature and moisture content histories under different treatment conditions. The simulation of the proposed conjugate problem allows the assessment of the effect of the heat and mass transfer within wood on the transfer in the adjacent gas, providing good insight on the complexity of the transfer mechanisms.     

Analysis of two‐dimensional heat and moisture transfer during drying of spherical objects

This paper deals with the numerical and analytical modelling of two‐dimensional heat and moisture transfer during drying of a spherical object. Drying is considered to be a process of simultaneous heat and moisture transfer whereby moisture is vapourized by means of a drying fluid (e.g. air), as it passes over a moist object. Numerical modelling of two‐dimensional heat and moisture transfer during drying of a spherical object is carried out using an explicit finite‐difference approach. Temperature and moisture distributions inside the object are determined by using the developed computer code. Moreover, the results predicted from the present model are compared with the experimental data available in the literature and a considerably high agreement is found. Copyright © 2003 John Wiley & Sons, Ltd.     

Unsteady conjugate forced convection heat/mass transfer in ensembles of spherical particles with cell models

Numerical methods are used to investigate the transient, conjugate, forced convection heat/mass transfer in multiparticle systems at low to moderate Reynolds numbers. The interparticle interactions have been accounted for by using the simple cell models. The momentum and heat/mass balance equations were solved numerically in spherical coordinates system by a finite difference method. The values considered for the sphere Reynolds number are Re < 100. The computations were focused on the influence of the voidage and physical properties ratios on the heat/mass transfer rate for sphere Peclet number, 10 ? Pe ? 1000.     

Laminar forced convection heat transfer with phase change material emulsions

Results of an experimental study of laminar forced convection heat transfer in a circular duct with a phase change material emulsion (n-octadecane in water) are presented in this paper. The bulk Stefan numbers considered in this study range up to 3.0 and the concentration of phase change material range up to 30% by volume. The results show that the heat transfer characteristics for phase change material emulsions are similar to those of microencapsulated phase change material suspensions, thus confirming that the microcapsule walls do not affect the heat transfer process significantly.     

Laminar forced convection heat transfer with phase change material suspensions

This paper presents results related to laminar forced convection heat transfer to a phase change material suspension in a circular duct with constant wall heat flux. An effective specific heat approach has been used to model the heat transfer process for a flow with a fully developed velocity profile. The model has been verified by comparing its numerical predictions with previous theoretical results as well as well as experimental data. A simple correlation for wall temperature rise as a function of the tube length that can be used for future design has been developed based on a parametric study.