Modelling of heat flux received by a bubble pump of absorption-diffusion refrigeration cycles

In the present study, the heat flux received by a bubble pump, which was simulated to a vertical tube 1 m long and with a variable diameter, was optimized. A numerical study was carried out in order to solve balance equations concerning the water-ammonia mixture in the up flow. The two-fluid model was used to derive the equations. A numerical study was carried out on a heat flux between 1 and 70 kW m⁻² and the liquid velocity was determined. The optimum flux was determined for a tube diameter equal to 4, 6, 8 and 10 mm and a mass flow rate ranging from 10 to 90 kg m⁻² s⁻¹. The optimum heat flux was correlated as a function of the tube diameter and mass flow rate, while the minimum heat flux required for pumping was correlated as a function of the tube diameter.     

Comparison of experimental data with results of some drying models for regularly shaped products

This paper presents an experimental and theoretical investigation of drying of moist slab, cylinder and spherical products to study dimensionless moisture content distributions and their comparisons. Experimental study includes the measurement of the moisture content distributions of slab and cylindrical carrot, slab and cylindrical pumpkin and spherical blueberry during drying at various temperatures (e.g., 30, 40, 50 and 60°C) at specific constant velocity (U = 1 m/s) and the relative humidity φ = 30%. In theoretical analysis, two moisture transfer models are used to determine drying process parameters (e.g., drying coefficient and lag factor) and moisture transfer parameters (e.g., moisture diffusivity and moisture transfer coefficient), and to calculate the dimensionless moisture content distributions. The calculated results are then compared with the experimental moisture data. A considerably high agreement is obtained between the calculations and experimental measurements for the cases considered. The effective diffusivity values were evaluated between 0.741 × 10⁻⁵ and 5.981 × 10⁻⁵ m²/h for slab products, 0.818 × 10⁻⁵ and 6.287 × 10⁻⁵ m²/h for cylindrical products and 1.213 × 10⁻⁷ and 7.589 × 10⁻⁷ m²/h spherical products using the Model-I and 0.316 × 10⁻⁵–5.072 × 10⁻⁵ m²/h for slab products, 0.580 × 10⁻⁵–9.587 × 10⁻⁵ m²/h for cylindrical products and 1.408 × 10⁻⁷–13.913 × 10⁻⁷ m²/h spherical products using the Model-II.     

Control of Flow and Heat Transfer in a Porous Enclosure due to an Adiabatic Thin fin on the Hot Wall

Natural convection flow in a differentially heated square enclosure filled with porous matrix with a solid adiabatic thin fin attached at the hot left wall is studied numerically. The Brinkman–Forchheimer-extended Darcy model is used to solve the momentum equations, in the porous medium. The numerical investigation is done through streamlines, isotherms, and heat transfer rates. A parametric study is carried out using the following parameters: Darcy number (Da) from 10⁻⁴ to 10⁻², dimensionless thin fin lengths (L _p) 0.3, 0.5, and 0.7, dimensionless positions (S _p) 0.25, 0.5, and 0.75 with Prandtl numbers (Pr) 0.7 and 100 for Ra = 10⁶. For Da = 10⁻³ and Pr = 0.7, it is observed that there is a counter clock-wise secondary flow formation around the tip of the fin for S _p = 0.5 for all lengths of L _p. Moreover when Da = 10⁻² the secondary circulation behavior has been observed for S _p = 0.25 and 0.75 and there is another circulation between the top wall and the fin that is separated from the primary circulation. However, these secondary circulations features are not observed for Pr = 100. It is also found that the average Nusselt number decreases as the length of the fin increases for all locations. However, the rate of decrease of average Nusselt number becomes slower as the location of fin moves from the bottom wall to the top wall. The overall heat transfer rate can be controlled with a suitable selection of the fin location and length.     

Convection in a Lid-Driven Heat-Generating Porous Cavity with Alternative Thermal Boundary Conditions

Mixed convection flow in a two-sided lid-driven cavity filled with heat-generating porous medium is numerically investigated. The top and bottom walls are moving in opposite directions at different temperatures, while the side vertical walls are considered adiabatic. The governing equations are solved using the finite-volume method with the SIMPLE algorithm. The numerical procedure adopted in this study yields a consistent performance over a wide range of parameters that were 10⁻⁴ ≤ Da ≤ 10⁻¹ and 0 ≤ Ra _I ≤ 10⁴. The effects of the parameters involved on the heat transfer characteristics are studied in detail. It is found that the variation of the average Nusselt number is non-linear for increasing values of the Darcy number with uniform or non-uniform heating condition.     

Non-Darcy buoyancy driven flows in a fluid saturated porous medium: the use of asymptotic computational fluid dynamics (ACFD) approach

Natural convection in a fluid saturated porous medium has been numerically investigated using a generalized non-Darcy approach. The governing equations are solved by using Finite Volume approach. First order upwind scheme is employed for convective formulation and SIMPLE algorithm for pressure velocity coupling. Numerical results are presented to study the influence of parameters such as Rayleigh number (10⁶ ≤Ra ≤10⁸), Darcy number (10⁻⁵ ≤ Da ≤ 10⁻²), porosity (0.4 ≤ ɛ ≤ 0.9) and Prandtl number (0.01 ≤ Pr ≤ 10) on the flow behavior and heat transfer. By combining the method of matched asymptotic expansions with computational fluid dynamics (CFD), so called asymptotic computational fluid dynamics (ACFD) technique has been employed to generate correlation for average Nusselt number. The technique is found to be an attractive option for generating correlation and also in the analysis of natural convection in porous medium over a fairly wide range of parameters with fewer simulations for numerical solutions.     

Flow boiling heat transfer of R134a and R404A in a microfin tube at low mass fluxes and low heat fluxes

An experimental investigation of flow boiling heat transfer in a commercially available microfin tube with 9.52 mm outer diameter has been carried out. The microfin tube is made of copper with a total fin number of 55 and a helix angle of 15°. The fin height is 0.24 mm and the inner tube diameter at fin root is 8.95 mm. The test tube is 1 m long and is electrically heated. The experiments have been performed at saturation temperatures between 0 and −20°C. The mass flux was varied between 25 and 150 kg/m²s, the heat flux from 15,000 W/m² down to 1,000 W/m². All measurements have been performed at constant inlet vapour quality ranging from 0.1 to 0.7. The measured heat transfer coefficients range from 1,300 to 15,700 W/m²K for R134a and from 912 to 11,451 W/m²K for R404A. The mean heat transfer coefficient of R134a is in average 1.5 times higher than for R404A. The mean heat transfer coefficient has been compared with the correlations by Koyama et al. and by Kandlikar. The deviations are within ±30% and ±15%, respectively. The influence of the mass flux on the heat transfer is most significant between 25 and 62.5 kg/m²s, where the flow pattern changes from stratified wavy flow to almost annular flow. This flow pattern transition is shifted to lower mass fluxes for the microfin tube compared to the smooth tube.     

Natural Convection in a Cavity Filled with Porous Layers on the Top and Bottom Walls

Natural convection in a partially filled porous square cavity is numerically investigated using SIMPLEC method. The Brinkman-Forchheimer extended model was used to govern the flow in the porous medium region. At the porous-fluid interface, the flow boundary condition imposed is a shear stress jump, which includes both the viscous and inertial effects, together with a continuity of normal stress. The thermal boundary condition is continuity of temperature and heat flux. The results are presented with flow configurations and isotherms, local and average Nusselt number along the cold wall for different Darcy numbers from 10⁻¹ to 10⁻⁶, porosity values from 0.2 to 0.8, Rayleigh numbers from 10³ to 10⁷, and the ratio of porous layer thickness to cavity height from 0 to 0.50. The flow pattern inside the cavity is affected with these parameters and hence the local and global heat transfer. A modified Darcy–Rayleigh number is proposed for the heat convection intensity in porous/fluid filled domains. When its value is less than unit, global heat transfer keeps unchanged. The interfacial stress jump coefficients β ₁ and β ₂ were varied from  −1 to +1, and their effects on the local and average Nusselt numbers, velocity and temperature profiles in the mid-width of the cavity are investigated.     

The influence of oil on nucleate pool boiling heat transfer

The influence of various oil contents in R134a is investigated for nucleate pool boiling on copper tubes either sandblasted or with enhanced heating surfaces (GEWA-B tube). Polyolester oils (POE) (Reniso Triton) with medium viscosity 55 cSt (SE55) and high viscosity 170 cSt (SE170) were used. Heat transfer coefficients were obtained for boiling temperatures between −28.6 and +20.1°C. The oil content varied from 0 to 5% mass fraction. For the sandblasted tube and the SE55 oil the heat transfer coefficients for the refrigerant/oil-mixture can be higher or lower than those for the pure refrigerant, depending on oil mass fraction, boiling temperature and heat flux. In some cases the highest heat transfer coefficients were obtained at a mass fraction of 3%. For the 170 cSt oil there is a clear decrease in heat transfer for all variations except for a heat flux 4,000 W/m² and −10.1°C at 0.5% oil content. The heat transfer coefficients are compared to those in the literature for a smooth stainless steel tube and a platinum wire. For the enhanced tube and 55 cSt oil the heat transfer coefficients are clearly below those for pure refrigerant in all cases. The experimental results for the sandblasted tube are compared with the correlation by Jensen and Jackman. The calculated values are within +20 and −40% for the medium viscosity oil and between +50% and −40% for the high viscosity oil. A correlation for predicting oil-degradation effects on enhanced surfaces does not exist.     

Interactive effect of oxygen diffusion and volatiles advection on transient thermal degradation of poly methyl methacrylate (PMMA)

A transient, one-dimensional model has been presented to formulate the substantial role of polymer gasification in the early stages of fire growth. The present model comprises the interaction between the oxygen diffusion and the released volatiles on the rate of polymer gasification, when the polymeric sample is subjected to an external radiative source. The model also includes different mechanisms affecting the degradation process such as in-depth thermal and oxidative decomposition, in-depth absorption of radiation and heat and mass transfer in the both gas and solid phases. The results for two different radiative heat sources (17 and 40 kW m⁻²) are reported and yielded realistic results, comparing to the published experimental data. It was found that an increase in the oxygen concentration will lead to a considerable decrease in the surface temperature as well as significant increase of gasification rate at 17 kW m⁻²; nevertheless this effect is less apparent at 40 kW m⁻².     

Steady mixed convection boundary-layer flow over a vertical flat surface in a porous medium filled with water at 4°C: variable surface heat flux

The steady mixed convection boundary-layer flow over a vertical impermeable surface in a porous medium saturated with water at 4°C (maximum density) when the surface heat flux varies as x ^m and the velocity outside the boundary layer varies as x ^(1+2m)/2, where x measures the distance from the leading edge, is discussed. Assisting and opposing flows are considered with numerical solutions of the governing equations being obtained for general values of the flow parameters. For opposing flows, there are dual solutions when the mixed convection parameter λ is greater than some critical value λ _c (dependent on the power-law index m). For assisting flows, solutions are possible for all values of λ. A lower bound on m is found, m > −1 being required for solutions. The nature of the critical point λ _c is considered as well as various limiting forms; the forced convection limit (λ = 0), the free convection limit (λ → ∞) and the limits as m → ∞ and as m → −1.     

Investigation of the different base fluid effects on the nanofluids heat transfer and pressure drop

A numerical study of laminar forced convective flows of three different nanofluids through a horizontal circular tube with a constant heat flux condition has been performed. The effect of Al₂O₃ volume concentration 0 ≤ φ ≤ 0.09 in the pure water, water-ethylene glycol mixture and pure ethylene glycol as base fluids, and Reynolds number of 100 ≤ Re ≤ 2,000 for different power inputs in the range of 10 ≤ Q(W) ≤ 400 have been investigated. In this study, all of the nanofluid properties are temperature and nanoparticle volume concentration dependent. The governing equations have been solved using finite volume approach with the SIMPLER algorithm. The results indicate an increase in the averaged heat transfer coefficient with increasing the mass of ethylene glycol in the water base fluid, solid concentration and Reynolds number. From the investigations it can be inferred that, the pressure drop and pumping power in the nanofluids at low solid volumetric concentration (φ < 3%) is approximately the same as in the pure base fluid in the various Reynolds numbers, but the higher solid nanoparticle volume concentration causes a penalty drop in the pressure. Moreover, this study shows it is possible to achieve a higher heat transfer rate with lower wall shear stress with the use of proper nanofluids.     

Numerical simulation of fluid flow and heat transfer characteristics in channel with V corrugated plates

A detailed numerical study is carried out to investigate fluid flow and heat transfer characteristics in a channel with heated V corrugated upper and lower plates. The parameters studied include the Reynolds number (Re = 2,000–5,500), angles of V corrugated plates (θ = 20°, 40°, 60°), and constant heat fluxs (q″ = 580, 830, 1,090 W/m²). Numerical results have been validated using the experimented data reported by Naphon, and a good agreement has been found. The angles of V corrugated plates (θ) and the Reynolds number are demonstrated to significantly affect the fluid flow and the heat transfer rate. Increasing the angles of V corrugated plates can make the heat transfer performance become better. The increasing Reynolds number leads to a more complex fluid flow and heat transfer rate. The numerical calculations with a non-equilibrium wall function have a better accuracy than with a standard wall function for solving high Reynolds numbers or complex flow problems.     

Unsteady flow and heat transfer analysis of an impinging synthetic jet

The present paper focuses on the analysis of unsteady flow and heat transfer regarding an axisymmetric impinging synthetic jet on a constant heat flux disc. Synthetic jet is a zero net mass flux jet that provides an unsteady flow without any external source of fluid. Present results are validated against the available experimental data showing that the SST/k − ω turbulence model is more accurate and reliable than the standard and low-Re k − ε models for predicting heat transfer from an impinging synthetic jet. It is found that the time-averaged Nusselt number enhances as the nozzle-to-plate distance is increased. As the oscillation frequency in the range of 16–400 Hz is increased, the heat transfer is enhanced. It is shown that the instantaneous Nu distribution along the wall is influenced mainly by the interaction of produced vortex ring and wall boundary layer. Also, the fluctuation level of Nu decreases as the frequency is raised.     

Heat transfer,pressure drop and flow patterns during flow boiling of R407C in a horizontal microfin tube

The heat transfer, pressure drop and flow patterns during flow boiling of R407C in a horizontal microfin tube have been investigated. The microfin tube is made of copper with a total fin number of 55 and a helix angle of 15°. The fin height is 0.24 mm and the inner tube diameter at fin root is 8.95 mm. The test tube is 1 m long. It is heated electrically. The experiments have been performed at saturation temperatures between −30°C and +10°C. The mass flux was varied between 25 and 300 kg/m²/s, the heat flux from 20,000 W/m² down to 1,000 W/m². The vapour quality was kept constant at 0.1, 0.3, 0.5, 0.7 at the inlet and 0.8, 1.0 at the outlet, respectively. The measured heat transfer coefficient is compared with the correlations of Cavallini et al., Shah as well as Zhang et al. Cavallini’s correlation contains seven experimental constants. After fitting these constants to our measured values, the correlation achieves good agreement. The measured pressure drop is compared to the correlations of Pierre, Kuo and Wang as well as Müller-Steinhagen and Heck. The best agreement is achieved with the correlation of Kuo and Wang. Almost all values are calculated within an accuracy of ±30%. The flow regimes were observed. It is shown, that changes in the flow regime affect the heat transfer coefficient significantly.     

Convective drying analysis of three-dimensional porous solid by mass lumping finite element technique

A numerical analysis of convective drying of a 3D porous solid of brick material is carried out using the finite element method and mass lumping technique. The energy equation and moisture transport equations for the porous solid are derived based on continuum approach following Whitaker’s theory of drying. The governing equations are solved using the Galerkin’s weighted residual method, which convert the governing equations into discretized form of matrix equations. The resulting capacitance matrices are made diagonal matrices by following the classical row-sum mass lumping technique. Hence with the use of the Eulerian time marching scheme, the final equations are reduced to simple algebraic equations, which can be solved directly without using an equation solver. The proposed numerical scheme is initially validated with experimental results for 1D drying problem and then tested by application to convective drying of 3D porous solid of brick material for four different aspect ratios obtained by varying the cross section of the solid. The mass lumping technique could correctly predict the wet bulb temperature of the solid under evaporative drying conditions. A parametric study carried out for three different values of convective heat transfer coefficients, 15, 30 and 45 W/m² K shows an increased drying rate with increase in area of cross section and convective heat transfer coefficient. The proposed numerical scheme could correctly predict the drying behavior shown in the form of temperature and moisture evolutions.     

Augmentation of heat transfer in a bubble agitated vertical rectangular channel

This paper presents the results of an experimental study of convective heat transfer between three parallel vertical plates symmetrically spaced with and without bubble agitation to ascertain the degree of augmentation of the heat transfer coefficients due to agitation. The centre plate was electrically heated, while the other side plates were water-cooled forming two successive parallel vertical rectangular channels of dimensions 20 cm × 3.5 cm × 35 cm (length W, gap L, height H) each. At the bottom of the hot and cold plates air spargers were fitted. Water/ethylene glycol (100%) was used to fill the channels. The superficial gas velocity ranged from 0.0016 to 0.01 m/s. Top, bottom and sides of the channels were open to the water/ethylene glycol in the chamber which is the novel aspect of this study. Experimental data have been correlated as under: Natural convective heat transfer: Nu = 0.60 Gr ^0.29, r = 0.96, σ = 0.186, 1.17 E6 < Gr < 1.48 E7; Bubble agitated heat transfer: St = 0.11(ReFrPr ²)^−0.23, r = 0.82, σ = 0.002, 1.20 E−2 < (ReFrPr ²) < 1.36 E2.     

Thin-layer drying of tomato (<Emphasis Type="Italic">Lycopersicum esculentum Mill. cv. Rio Grande</Emphasis>) slices in a convective hot air dryer

The effects of different drying temperatures on the drying kinetics of tomato slices were investigated using a cabinet-type dryer. The experimental drying data were fitted best to the to the Page and Modified Page models apart from other theoretical models to predict the drying kinetics. The effective moisture diffusivities varied from 1.015 × 10⁻⁹ to 2.650 × 10⁻⁹ m² s⁻¹over the temperature range studied, and activation energy was 22.981 kJ mol⁻¹.     

Analysis of heat and fluid flow in partially divided fluid saturated porous cavities

Fluid flow and heat transfer phenomena in partially divided cavities filled with porous media have been numerically studied in this research. A non-Darcy generalized formulation is applied to describe the behavior of fluid flow in porous media. A splitting semi-implicit finite element method is adopted to solve the governing equations. The range of Ra involved in this study is between 10⁴ and 10⁶. Three different locations of dividers are investigated to probe the geometrical effect on heat and fluid flow. The results of Da = 10⁻² display a trend similar to the non-porous medium, but those of Da = 10⁻⁴ show dramatic decrease in flow strength, as well as heat transfer rate. A different location of divider may change the local and average Nusselt numbers. Received on 10 August 1999     

Numerical and experimental studies of natural convective heat transfer from vertical and inclined narrow isothermal flat plates

Natural convective heat transfer from an isothermal narrow flat plate embedded in a plane adiabatic surface and inclined at moderate positive and negative angles to the vertical has been numerically and experimentally studied. The solution has the Rayleigh number, the dimensionless plate width, the angle of inclination, and the Prandtl number as parameters. Attention was restricted to a Prandtl number of 0.7. The numerical results have been obtained for Rayleigh numbers between 10³ and 10⁷ for dimensionless plate widths of between 0.3 and 1.2 and for angles of inclination between +45° and −45°. In the experimental study, results have been obtained for Rayleigh numbers between 4 × 10² and 10⁵ for dimensionless plate widths of 0.4 and 2.5 and for angles of inclination between +45° and −45° to the vertical. Empirical equations for the heat transfer rate have been derived.     

Modeling of water transport in roof tiles by removal of moisture at isothermal conditions

The main objective of this article is to describe the drying process of ceramic roof tiles, shaped from red clay, using diffusion models. Samples of the product with initial moisture content of 0.24 (db) were placed inside an oven in the temperatures of 55.6, 69.7, 82.7 and 98.6°C; and the data of the drying kinetics were obtained. The analytical solutions of the diffusion equation for the parallelepiped with boundary conditions of the first and third kinds were used to describe the drying processes. The process parameters were determined using an optimization algorithm based on inverse method coupled to the analytical solutions. The analysis of the results makes it possible to affirm that the boundary condition of the third kind satisfactorily describes the drying processes. The values obtained for the convective mass transfer coefficient were between 8.25 × 10⁻⁷ and 1.64 × 10⁻⁶ m s⁻¹, and for the effective water diffusivity were between 9.21 × 10⁻⁹ and 1.80 × 10⁻⁸ m² s⁻¹.