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.     

Effects of film evaporation on laminar mixed convection heat and mass transfer in a vertical channel

A numerical study of finite liquid film evaporation on laminar mixed convection heat and mass transfer in a vertical parallel plate channel is presented. The influences of the inlet liquid mass flow rate and the imposed wall heat flux on the film vaporization and the associated heat and mass transfer characteristics were examined for air-water and air-ethanol systems. Predicted results obtained by including transport in the liquid film are contrasted with those where liquid film transport is neglected, showing that the assumption of an extremely thin film made by Tsay and Yan (Wärme- und Stoffübertragung 26, 23–31 (1990)) is only valid for a system with a small liquid mass flow rate. Additionally, it is found that the heat transfer between the interface and gas stream is dominated by the transport of latent heat associated with film evaporation. The magnitude of the evaporative latent heat flux may be five times greater than that of sensible heat flux.     

Mixed convection heat transfer enhancement through film evaporation in inclined square ducts

The investigation of mixed convection heat transfer enhancement through film evaporation in inclined square ducts has been numerically examined in detail. The main parameters discussed in this work include the inclined angle, the wetted wall temperature and the relative humidity of the moist air mixture. The numerical results of the local friction factor, Nusselt number and Sherwood number are presented for moist air mixture system. Attention was particular paid to the effects of latent heat transport on the heat transfer enhancement. Results show that the latent heat transport with film evaporation augments tremendously the heat transfer rate. The heat transfer rate can be enhanced to be 10 times of that without mass transfer, especially for a system with a lower temperature. Besides, better heat and mass transfer rates related with film evaporation are found for case with a higher wetted wall temperature. The increase in the relative humidity of moist air in the ambient causes the decrease in heat transfer enhancement.     

Conjugate mixed convection heat transfer from a vertical rectangular fin

A numerical investigation of the heat transfer from a rectangular fin by combined forced and natural convection is presented. Results are given for buoyancy parameters in the range of $\text{0 ?}\text{Gr/Re}{}^2\text{? 2}$ and convection - conduction parameters in the range of $\text{0 ? √}\text{Re k}{}_{\mathrm{f}}\text{L/k}{}_{\mathrm{s}}\text{b}\text{? 10}$. The results are compared with the conventional fin theory and it is found that concerning the fin efficiency, the latter produces acceptable results although it is not strictly correct.     

Laminar film condensation heat transfer of hydrogen and nitrogen inside a vertical tube

There have been a number of experimental investigations on condensing heat transfer to cryogenic fluids. The investigations with nitrogen and oxygen have shown reasonable agreement between experimental data and those predicted by Nusselt's theory. On the other hand, in the previous investigations with much colder fluids, such as hydrogen, deuterium, and helium, the experimental condensing heat transfer coefficients are smaller than those predicted by Nusselt's theory, and these differences become much larger when the film Reynolds number or decreasing temperature difference across the condensate film is decreased. In the present investigation, hydrogen and nitrogen were condensed inside a vertical tube (d = 15 mm, L = 30 mm) under steady‐state conditions, respectively, and condensing heat transfer coefficients were precisely measured. From the experimental results, the condensing heat transfer coefficients for saturated hydrogen and nitrogen vapors agree with those predicted by Nusselt's theory within ±20%. The results of the present study suggest that deuterium and helium might also behave as predicted by Nusselt's theory. © 2001 Scripta Technica, Heat Trans Asian Res 30(7): 542–560, 2001     

Mixed convection heat transfer in horizontal rectangular ducts with radiation effects

The study of mixed convection heat transfer in horizontal ducts with radiation effects has been numerically examined in detail. This work is primarily focused on the interaction of the thermal radiation with mixed convection for a gray fluid in rectangular horizontal ducts. The vorticity–velocity method is employed to solve the three-dimensional Navier–Stokes equations and energy equation simultaneously. The integro-differential radiative transfer equation was solved by the discrete ordinates method. The attention of the results is focused on the effects of thermal buoyancy and radiative transfer on the development of temperature, the friction factor and the Nusselt number. Results reveal that radiation effects have a considerable impact on the heat transfer and would reduce the thermal buoyancy effects. Besides, the development of temperature is accelerated by the radiation effects.     

Mixed convection heat transfer in inclined rectangular ducts with radiation effects

A numerical study was carried out to investigate the radiation effect on the characteristics of the mixed convection fluid flow and heat transfer in inclined ducts. The three-dimensional Navier–Stokes equations and energy equation are solved simultaneously with the vorticity–velocity method. The integro-differential radiative transfer equation was solved by the discrete ordinates method. The effects of the thermal buoyancy and the radiative transfer on the distributions of the bulk fluid temperature, the friction factor and the Nusselt number are emphasized in detail. Results indicate that radiation effects have a considerable impact on the heat transfer and tend to reduce the thermal buoyancy effects. In addition, the development of the bulk fluid temperature is enhanced by the radiation effects.     

Combined mixed convection and radiation heat transfer in rectangular ducts rotating about a parallel axis

The study of combined heat transfer of convection and radiation in rectangular ducts rotating in a parallel mode was investigated numerically in detail. The coupled momentum and energy equations are solved by the DuFort–Frankel numerical scheme to examine the interactions of convection with radiation. The integro-differential radiative transfer equation is solved by the discrete ordinates method. Results are presented over a wide range of the governing parameters. The present results reveal that the rotational effect in a square duct is more significant than that in a rectangular one. The predictions also demonstrate that the radiation presents significant effects on the axial distributions of the total Nusselt number, Nu_t, and tends to reduce the centrifugal-buoyancy effects. The effect of rotation on the Nu_t is restricted in the entrance region, however, the radiation affects the heat transfer through out the channel. Additionally, the Nu_t increases with the decrease in the conduction-to-radiation parameter N_C.     

Developing laminar mixed convection with heat and mass transfer in horizontal and vertical tubes

The effects of the solutal and thermal Grashof numbers on the flow, temperature and concentration fields in tubes with uniform heat flux and concentration at the fluid-solid interface have been investigated numerically using a three-dimensional axially parabolic model. Results show a complex development of the flow field which is strongly influenced by the values of the two Grashof numbers and by the tube inclination. For vertical tubes the flow field is also influenced by the relative direction of the flow and the buoyancy forces. In general, very close to the tube inlet forced convection boundary layer development dominates. Further downstream, the effects of solutal buoyancy predominate while those of thermal origin determine the flow field far downstream and, in particular, the fully developed conditions. The axial evolution of the wall shear stress τ_z, the Nusselt number Nu_z and the Sherwood number Sh_z in both horizontal and vertical tubes are presented for different combinations of the two Grashof numbers. For horizontal tubes and vertical tubes with upward flow these three variables are greater than the corresponding ones for forced convection. The opposite is true for downward flow in vertical tubes.     

Laminar conjugate mixed convection in a vertical channel with heat generating components

Conjugate mixed convection arising from protruding heat generating ribs attached to substrates (printed circuit boards) forming channel walls is numerically studied. The substrates with ribs form a series of vertical parallel plate channels. Assuming identical disposition and heat generation of the ribs on each board, a channel with periodic boundary conditions in the transverse direction is considered for analysis. The governing equations are discretised using a control volume approach on a staggered mesh and a pressure correction method is employed for the pressure–velocity coupling. The solid regions are considered as fluid regions with infinite viscosity and the thermal coupling between the solid and fluid regions is taken into account by the harmonic thermal conductivity method. Parametric studies are performed by varying the heat generation based Grashof number in the range 10⁴–10⁷ and the fan velocity based Reynolds number in the range 0–1500, with air as the working medium. Results are obtained for the velocity and temperature distributions, natural convection induced mass flow rate through the channel, the maximum temperatures in the heat sources and the local Nusselt numbers. The natural convection induced mass flow rate in mixed convection is correlated in terms of the Grashof and Reynolds numbers. In pure natural convection the induced mass flow rate varies as 0.44 power of Grashof number. The maximum dimensionless temperature is correlated in terms of pure natural convection and forced convection inlet velocity asymptotes. For the parameter values considered, the heat transferred to the working fluid via substrate heat conduction is found to account for 41–47% of the heat removal from the ribs.     

Simultaneous mass and heat transfer under mixed convection along a vertical cone

Steady laminar binary mixed convection flow along a vertical circular cone under the combined buoyancy effects of thermal and species diffusion is studied analytically. The analysis is confined to mass diffusion processes with low concentration levels. In the analysis the surface of the cone is assumed to be at a uniform temperature and uniform concentration. Numerical results for the local Sherwood number, local Nusselt number and local friction factor are presented. Representative temperature, concentration and velocity profiles are also shown. The analysis covers the diffusion of common gases and vapours into air. Considerations are given to the situations where the buoyancy forces assist and oppose the forced convection flow for various possible combinations of the thermal and species diffusion processes.     

Cocurrent turbulent mixed convection heat and mass transfer in falling film of water inside a vertical heated tube

A detailed numerical study has been conducted in order to analyse the combined buoyancy effects of thermal and mass diffusion on the turbulent mixed convection tube flows. Numerical results for air-water system are presented under different conditions. A low Reynolds number k-ε turbulent model is used with combined heat and mass transfer analysis in a vertical heated tube. The local heat fluxes, Nusselt and Sherwood numbers are reported to obtain an understanding of the physical phenomena. Predicted results show that a better heat transfer results for a higher gas flow Reynolds number Re, a higher heat flux q_w or a lower inlet water flow Γ₀. Additionally, the results indicate that the convection of heat by the flowing water film becomes the main mechanism for heat removal from the wall.     

Upflow turbulent mixed convection heat transfer in vertical pipes

The present work deals with the results of an experimental investigation on heat transfer in water cooled vertical pipes, for thermal–hydraulic conditions ranging from forced convective flow to mixed convective flow. The flow of water in the pipe is upwards.Experimental data confirm the reduction in the heat transfer rate for mixed convection in upward heat flow, mainly due to the laminarization effect in the near-wall region (buoyancy effect) . They are in a very good agreement with numerical methods, such as the k–-model.A new method for the calculation of the heat transfer coefficient in upward mixed convection heated flow is proposed. It is based on the well-known superposition method (heated downflow) modified accounting for the phenomenology of the upward heated flow in comparison with downflow heated conditions.     

Laminar flow of viscoelastic fluids in rectangular ducts with heat transfer: A finite element analysis

A numerical study on the laminar flow and heat transfer behavior of viscoelastic fluids in rectangular ducts is conducted using the finite element approach. A Criminale-Ericksen-Fibley relation is applied to describe the viscoelastic character of the fluid, and a hydrodynamically and thermally fully developed flow with the H1 thermal boundary condition is considered. The finite element procedure employed yields essentially mesh-independent predictions with a fairly moderate computational effort. Computed results are presented and discussed in terms of the secondary flow field, the temperature field, the friction factor and the Nusselt number. In particular it is shown that the presence of a secondary flow markedly alters the temperature field and results in a substantial heat transfer enhancement with all duct aspect ratios considered.     

Convection heat and mass transfer along a vertical heated plate with film evaporation in a non-Darcian porous medium

A numerical analysis has been carried about to study the heat and mass transfer of forced convection flow with liquid film evaporation in a saturated non-Darcian porous medium. Parametric analyses were conducted concerning the effects of the porosity ε, inlet liquid Reynolds number Re_l, inlet air Reynolds number Re_a on the heat and mass transfer performance. The results conclude that better heat and mass transfer performances are noticed for the system having a higher Re_a, a lower Re_l, and a higher ε. Re_l plays a more important role on the heat and mass transfer performance than Re_a and ε. For the case of ε = 0.4 and Re_a = 10,000, the increases of Nu and Sh for Re_l = 50 are about by 33.9% and 35.3% relative to the values for Re_l = 250.     

Effect of transpiration on combined heat and mass transfer in mixed convection along a vertical plate

The effect of transpiration velocity on the heat and mass transfer characteristics of mixed convection flow along a permeable vertical flat plate under the combined effects of thermal and mass diffusion is analysed. The diffusion-thermo and thermo-diffusion effects as well as the interfacial velocities due to mass diffusion are negligibly small. The plate is maintained at a uniform temperature and species concentration. Numerical results for the local skin-friction, the local Nusselt number and the local Sherwood number, as well as for the velocity, the temperature and the concentration profiles, are presented for diffusion of common species into air only. In general, it has been found for thermally assisted flow that the local surface shear-, heat-, and mass-transfer rates decrease owing to suction of fluid. This trend reversed for blowing of fluid. In addition this trend is higher for species of larger Schmidt number as well as for increasing buoyancy force.     

G-jitter fully developed combined heat and mass transfer by mixed convection flow in a vertical channel

The effect of g-jitter induced combined heat and mass transfer by mixed convection flow in microgravity for a simple system consisting of two heated vertical parallel infinite flat plates held at constant but different temperatures and concentrations. The governing equations are solved analytically for the induced velocity, temperature and concentration distributions. Graphical results for the velocity profile of the oscillating flow in the channel are presented and discussed for various parametric physical conditions. Despite the simplicity of the problem, it does display some features, which have also been observed in real mixed convection flows, such as flow reversal and flow dependence on the buoyancy parameter ratio.     

Laminar natural convection in differentially heated rectangular enclosures with vertical diffusive walls

Real enclosures have diffusive walls. A procedure is developed to evaluate the natural convection effective global Nusselt number for rectangular enclosures with vertical diffusive walls. The effective Nusselt number is evaluated using the temperature difference imposed over the exterior faces of the enclosure, the usual correlations for rectangular enclosures without diffusive walls, and the diffusive properties of the solid vertical walls, which are concentrated on a single dimensionless parameter. The proposed procedure is tested by comparing the obtained results with those achieved from the complete two-dimensional numerical simulation of the conjugated heat transfer problem occurring in the complete enclosure, with diffusive walls. The result is a helpful tool that promptly helps the thermal engineer when dealing with enclosures with diffusive walls.     

Laminar film condensation driven latent thermal energy storage in rectangular containers

This paper focuses on numerically analyzing the thermal transport phenomena in the transient conjugate problem of melting and laminar film condensation. The key focus is to identify an optimum container aspect ratio/shape and conditions for which the heat storage time and the storage capacity are minimum and maximum respectively. Since most solid–liquid phase change materials (PCMs) suffer from poor thermal conductivities, the major resistance to heat transfer comes from PCM. Hence, high thermal conductivity, low-cost metal foam is suggested for use along with PCM to minimize this resistance. The conjugate transient problem of film condensation driven solid–liquid phase change of PCM impregnated inside porous metal foam is numerically analyzed. An effective heat capacity formulation is employed for modeling the transient PCM phase change in porous foam and is solved using finite element method. It is coupled with laminar film condensation on the outside of the storage container. The model is then used for selecting the best aspect ratio for thermal energy storage (TES) containers that enables to store comparatively the maximum heat. The results of the developed model showed that the major resistance to heat transfer and hence efficient thermal energy storage depends strongly on the aspect ratio of the PCM storage containers.