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.     

Numerical analysis of Grashof number,Reynolds number and inclination effects on mixed convection heat transfer in rectangular channels

Mixed convection heat transfer in rectangular channels has been investigated computationally under various operating conditions. The lower surface of the channel is subjected to a uniform heat flux, sidewalls are insulated and adiabatic, and the upper surface is exposed to the surrounding fluid. Solutions were obtained for Pr=0.7, inclination angles 0° ≤ θ ≤ 90°, Reynolds numbers 50 ≤ Re ≤ 1000, and modified Grashof numbers Gr = 7.0×10⁵ to 4.0×10⁶. The three-dimensional elliptic governing equations were solved using a finite volume based computational fluid dynamics (CFD) code. From a parametric study, local Nusselt number distributions were obtained and effects of channel inclination, surface heat flux and Reynolds number on the onset of instability were investigated. Results obtained from the simulations are compared with the literature and a parallel conducted experimental study, from which a good agreement was observed. The onset of instability was found to move upstream for increasing Grashof number. On the other hand, onset of instability was delayed for increasing Reynolds number and increasing inclination angle.     

Numerical investigation of fluid flow and heat transfer under high heat flux using rectangular micro-channels

A 3D-conjugate numerical investigation was conducted to predict heat transfer characteristics in a rectangular cross-sectional micro-channel employing simultaneously developing single-phase flows. The numerical code was validated by comparison with previous experimental and numerical results for the same micro-channel dimensions and classical correlations based on conventional sized channels. High heat fluxes up to 130 W/cm² were applied to investigate micro-channel thermal characteristics. The entire computational domain was discretized using a 120 × 160 × 100 grid for the micro-channel with an aspect ratio of (α = 4.56) and examined for Reynolds numbers in the laminar range (Re 500–2000) using FLUENT. De-ionized water served as the cooling fluid while the micro-channel substrate used was made of copper. Validation results were found to be in good agreement with previous experimental and numerical data [1] with an average deviation of less than 4.2%. As the applied heat flux increased, an increase in heat transfer coefficient values was observed. Also, the Reynolds number required for transition from single-phase fluid to two-phase was found to increase. A correlation is proposed for the results of average Nusselt numbers for the heat transfer characteristics in micro-channels with simultaneously developing, single-phase flows.     

Numerical analysis of natural convection heat transfer from rectangular shrouded fin arrays on a horizontal surface

The main aim of this investigation is to discover the effects of clearance parameters on the steady-state heat transfer. In order to solve the three-dimensional elliptic governing equations, a finite volume based CFD code was used. The clearance gap between fin tips and shroud, the base and fin temperatures and the size and configuration of the finned surfaces were varied during the parametric study. The numerical results have been compared to existing experimental values from the literature and the comparison shows a good agreement. It is found that the heat transfer coefficient increases with the increase in the clearance parameter and it approaches to the value of heat transfer coefficient obtained for unshrouded fin arrays.     

Experimental investigation of mixed convection heat transfer from longitudinal fins in a horizontal rectangular channel

Mixed convection heat transfer from longitudinal fins inside a horizontal channel has been investigated for a wide range of modified Rayleigh numbers and different fin heights and spacings. An experimental parametric study was made to investigate effects of fin spacing, fin height and magnitude of heat flux on mixed convection heat transfer from rectangular fin arrays heated from below in a horizontal channel. The optimum fin spacing to obtain maximum heat transfer has also been investigated. During the experiments constant heat flux boundary condition was realized and air was used as the working fluid. The velocity of fluid entering channel was kept nearly constant (0.15 ? w_in ? 0.16 m/s) using a flow rate control valve so that Reynolds number was always about Re = 1500. Experiments were conducted for modified Rayleigh numbers 3 × 10⁷ < Ra¹ < 8 × 10⁸ and Richardson number 0.4 < Ri < 5. Dimensionless fin spacing was varied from S/H = 0.04 to S/H = 0.018 and fin height was varied from H_f/H = 0.25 to H_f/H = 0.80. For mixed convection heat transfer, the results obtained from experimental study show that the optimum fin spacing which yields the maximum heat transfer is S = 8–9 mm and optimum fin spacing depends on the value of Ra¹.     

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 periodic mixed convective heat transfer in a rectangular cavity with a vibrating lid

Periodic behavior of the mixed convective flow in a rectangular cavity with a vibrating lid is investigated numerically in this study. The periodic flow patterns and heat transfer characteristics found are discussed with attention being focused on the interaction between the frequency of the lid velocity vibration and the frequency of the natural periodic flow. Several practical cases are investigated to evaluate the effects of the frequency of vibration of lid velocity (W) at Re = 100 and Gr = 5 × 10⁵. The frequency of the natural periodic flow can be most clearly seen when the lid is moved at a constant-velocity (without vibration). As the vibration is imposed on the lid with the dimensionless frequency of the lid velocity varied between 0.1 and 0.3, the combined effects of the natural frequency and the lid vibration frequency on the transient variations in the flow and the thermal characteristics have been observed. When the dimensionless frequency of lid velocity vibration is increased to be equal to or higher than 0.4, the natural periodic flow frequency disappears, and the lid vibration frequency dominates the flow field, which means that the periodic flow field has locked-on to the lid vibration.     

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.     

Numerical simulation of conjugate,turbulent mixed convection heat transfer in a vertical channel with discrete heat sources

This paper presents the results of a comprehensive numerical study to analyze turbulent mixed convection in a vertical channel with a flush-mounted discrete heat source in each channel wall. The conjugate heat transfer problem is solved to study the effect of various parameters like the thermal conductivity of the wall material (k_s), the thermal conductivity of the flush-mounted discrete heat source (k_c), Reynolds number (Re_s), modified Richardson number (Ri⁎) and the aspect ratio of the channel (AR). The standard k–ε turbulence model, modified by including buoyancy effects, without wall functions, has been used for the analysis. The two-dimensional governing equations are discretised on a semi-staggered, non-uniform grid, using the finite volume method. The asymptotic computational fluid dynamics (ACFD) technique has been then applied to obtain a correlation for the non-dimensional maximum temperature θ¯_max, which can be used for a wide range of parameters.     

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.     

Conjugate heat transfer of mixed convection for viscoelastic fluid past a horizontal flat-plate fin

A conjugate mixed convection heat transfer problem of a second-grade viscoelastic fluid past a horizontal flat-plate fin has been studied. Governing equations include heat conduction equation of the fin, and continuity equation, momentum equation and energy equation of the fluid, have been analyzed by a combination of a series expansion method, the similarity transformation and a second-order accurate finite difference method. Solutions of a stagnation flow (β = 1.0) at the fin tip and a flat-plate flow (β = 0) on the fin surface were obtained by a generalized Falkner–Skan flow derivation. These solutions have been used to iterate with the heat conduction equation of the fin to obtain distributions of the local convective heat transfer coefficient and the fin temperature. Ranges of dimensionless parameters, the Prandtl number (Pr), the elastic number (E), the free convection parameter (G) and the conduction–convection coefficient (N_cc) are from 0.1 to 100, 0.001 to 0.01, 0 to 1.5 and 0.05 to 2.0, respectively. The elastic effect in the flow could increase the local heat transfer coefficient and enhance the heat transfer of a horizontal flat-plate fin. In addition, same as results from Newtonian fluid flow and conduction analysis of a horizontal flat-plate fin, a better heat transfer has been obtained with a larger N_cc, G and Pr.     

Experimental investigation of mixed convection heat transfer in a rectangular channel with discrete heat sources at the top and at the bottom

Mixed convection heat transfer in a top and bottom heated rectangular channel with discrete heat sources has been investigated experimentally for air. The lower and upper surfaces of the channel were equipped with 8 × 4 flush-mounted heat sources subjected to uniform heat flux. Sidewalls, the lower and upper walls were insulated and adiabatic. The experimental study was made for an aspect ratio of AR = 6, Reynolds numbers 955 ≤ Re_Dh ≤ 2220 and modified Grashof numbers Gr* = 1.7 × 10⁷ to 6.7 × 10⁷. From experimental measurements, surface temperature and Nusselt number distributions of the discrete heat sources were obtained for different Grashof numbers. Furthermore, Nusselt number distributions were calculated for different Reynolds numbers. Results show that surface temperatures increase with increasing Grashof number. The row-averaged Nusselt numbers first decrease with the row number and then, due to the increase in the buoyancy affected secondary flow and the onset of instability, they show an increase towards the exit as a result of heat transfer enhancement.     

Forced convection heat transfer to water with air injection in a rectangular duct

A study was made of forced convection heat-transfer to water and air-water mixtures in a horizontal rectangular duct with air injection through one porous heated wall. The main independent variables are the rate of air injection through the porous wall, the superficial liquid velocity in the duct, and the amount of air mixed with the water upstream of the heated test section; the method of mixing the upstream air and water is also varied. The dependent variables reported are the heat-transfer coefficient, over a range of approximately 60:1, and the flow pattern, extending from bubble flow through to annular flow.     

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.     

Numerical analysis of transient mixed convection flow in storage tank: influence of fluid properties and aspect ratios on stratification

Sensible heat storage in fluids generates thermal stratification. In order to improve thermodynamic system efficiency, stratification should be promoted much more. To this scope, this article presents a numerical study of transient mixed convection. The study investigates the use of different fluids as a heat storage medium in cylindrical cavities with different aspect ratios. The effect of the fluids is made through the variation of physical properties represented through the Prandtl number. The system consists of a cavity with fluid injection at the top and fluid discharge at the bottom. Transient, two-dimensional, mixed convection flows in a thermal storage tank have been studied using finite volume method. The governing equations are the conservation equations for laminar natural convection flow based on the Boussinesq approximation. Forced convection flow is superimposed through the use of appropriate boundary conditions (inflow and outflow conditions). The study considers three representative fluids i.e. Torada oil, ethylene glycol and water. It considers also cavities with aspect ratios varying from 3 to 1/3. Flow analysis is made through typical transient temperature distributions for the three fluids and for different configurations. The performances of thermal energy storage using these fluids are analyzed through the transient thermal storage efficiency.     

Conjugate conduction-forced convection heat transfer analysis of a rectangular nuclear fuel element with non-uniform volumetric energy generation

The main objective of this paper is to present a comparative study of uniform and non-uniform volumetric energy generation in a rectangular nuclear fuel element washed by upward moving stream of liquid sodium. Employing finite difference schemes, the boundary layer equations governing the flow and thermal fields in the fluid domain are solved simultaneously with two-dimensional energy equation in the solid domain by satisfying the continuity of temperature and heat flux at the solid–fluid interface. Numerical results are presented for a wide range of aspect ratio, A_r, conduction–convection parameter, N_cc, total energy generation parameter, Q_t, and flow Reynolds number, Re_H. It is concluded that for the same total energy generation, a somewhat realistic non-uniform volumetric energy generation puts greater restriction on the thermal power generation as compared to the idealistic uniform volumetric energy generation. Further, it is found that despite the total energy generation being the same for two cases, the non-uniform volumetric energy generation within the fuel element results in considerably higher energy dissipation rate.     

Numerical analysis of natural convection in a rectangular enclosure horizontally divided into fluid and porous regions

This paper describes an analytical study of laminar natural convection heat transfer in a rectangular enclosure horizontally divided into fluid and porous regions. The Navier-Stokes equation governs the fluid motion in the fluid region, while Brinkman's extension of Darcy's law is assumed to hold within the porous region. These equations are solved using a finite-element method in the range 10³ ⩽ Ra_f ⩽ 10⁵ and 10⁻³ ⩽ Da ⩽ 10⁵. The experiment is also performed using a rectangular enclosure filled with silicone oil and glass beads. It is shown that the flow pattern, temperature distribution and Nusselt number obtained from the numerical calculation satisfactorily predict the experimental data.     

Numerical modeling of heat and mass transfer during forced convection drying of rectangular moist objects

A two-dimensional analysis of heat and mass transfer during drying of a rectangular moist object is performed using an implicit finite difference method, with the convective boundary conditions at all surfaces of the moist object. The variable convective heat and mass transfer coefficients are considered during the drying process. The external flow and temperature fields are first numerically predicted through the Fluent CFD package. From these distributions, the local distributions of the convective heat transfer coefficients are determined, which are then used to predict local distributions of the convective mass transfer coefficients through the analogy between the thermal and concentration boundary layers. Also, the temperature and moisture distributions for different periods of time are obtained using the code developed to determine heat and mass transfer inside the moist material. Furthermore, the influence of the aspect ratio on the heat and mass transfer is studied. It is found that the convective heat transfer coefficient varies from 4.33 to 96.16 W/m² K, while the convective mass transfer coefficient ranges between 9.28 × 10⁻⁷ and 1.94 × 10⁻⁵ m/s at various aspect ratios. The results obtained from the present analysis are compared with the experimental data taken from the literature, and a good agreement is observed.