Decrease In Heat Transfer Rate Research Articles

Modeling of In-Tube Condensation of Zeotropic Mixtures

Studies in the literature have shown that zeotropic mixture condensation rates are lower than those predicted using a pure-fluid approach. This has been attributed to the decrease in fluid temperature that occurs with zeotropic mixtures and to the development of concentration gradients in the vapor-phase that limit the condensation heat transfer. The decrease in the apparent heat transfer coefficient is not consistent across mass fluxes, tube diameters, fluid combinations, saturation pressures, and concentrations. Several modeling techniques exist, which allow engineers to model the decrease in heat transfer rates. This study provides guidelines on when the mass transfer effects can be neglected and when it is appropriate to apply established models in the literature. A condensation database containing fluid combinations of pairs of hydrocarbons, ammonia and water, and synthetic refrigerants across large changes in operating conditions, tube diameters, and concentrations is used to validate the approach. The proposed framework predicts that the Bell and Ghaly (1973, “An Approximate Generalized Design Method for Multicomponent/Partial Condensers,” AIChE Symp. Ser., 69, pp. 72–79) approach is valid for mid- and high-reduced pressures, i.e., above 0.40, while explicitly accounting for mass transfer is necessary at lower reduced pressures, i.e., below 0.40, where the influence of the temperature glide in the Bell and Ghaly method is weighted too strongly.

Thermal transport to droplets on heated superhydrophobic substrates

This paper reports on measurements of thermal transport to solitary sessile water droplets placed on heated superhydrophobic substrates maintained at constant temperature. A single water droplet of nominally 3mm diameter is placed on a preheated substrate and allowed to evaporate completely while being imaged from two angles with video cameras and an infrared camera. Substrate temperatures are varied from 60°C to 230°C and total evaporation time and heat transfer rate are determined. Three different rib-patterned superhydrophobic substrates are investigated of 0.5, 0.8, and 0.95 cavity fraction (relative projected cavity area of substrate to total projected surface area). The rib features range in width from 2 to 30μm and in height from 15 to 20μm. Results are also obtained for a smooth hydrophobic substrate for comparison. Droplet evaporation times increase with substrate cavity fraction while overall heat transfer rates decrease. At subcritical substrate temperatures the Nusselt number is larger for lower cavity fraction substrates. For supercritical substrate temperatures, as the cavity fraction increases nucleate boiling is delayed to higher substrate temperatures and the Leidenfrost point occurs at lower temperature. At the highest cavity fraction explored nucleate boiling does not occur at any substrate temperature. At temperatures above the Leidenfrost point the influence of cavity fraction is negligible.

Energy and exergy efficiency of heat pipe evacuated tube solar collectors

In this paper, a heat pipe evacuated tube solar collector has been investigated both theoretically and experimentally. A detailed theoretical method for energy and exergy analysis of the collector is provided. The method is also evaluated by experiments. The results showed a good agreement between the experiment and theory. Using the theoretical model, the effect of different parameters on the collector?s energy and exergy efficiency has been investigated. It is concluded that inlet water temperature, inlet water mass flow rate, the transmittance of tubes and absorptance of the absorber surface have a direct effect on the energy and exergy efficiency of the heat pipe evacuated tube solar collector. Increasing water inlet temperature in heat pipe evacuated solar collectors leads to a decrease in heat transfer rate between the heat pipe?s condenser and water.

Characteristics of instantaneous heat transfer rates in three heat-transfer-coefficient regimes

Instantaneous heat transfer coefficients (h) for flows of various fluids (mercury, air, water, and motor oil) over plates inclined at various angles have been fundamentally examined. We have discovered three distinctive regimes, in which fluids behave interestingly. In regime I, as h increases, instantaneous heat transfer rates (q) decrease, defying our physical intuition. Regime II exhibits maxima in q-versus-h curves. In regime III, h becomes a strong function of time especially for t∈[0,1s], revealing the possible deficiency of traditional lumped-capacitance models. Results of computational simulations are obtained using COMSOL commercial package whose algorithm is based on the Galerkin finite element method, and exhibit qualitatively-correct trends when compared with classical solutions for steady-state cases.

Optimization analysis of convective–radiative longitudinal fins with temperature-dependent properties and different section shapes and materials

The main aim of this study is to obtain an optimum design point for fin geometry, so that heat transfer rate reaches to a maximum value in a constant fin volume. Effect of fin thicknesses ratio (τ), convection coefficient power index (m), profile power parameter (n), base thickness (δ) and fin material are evaluated in the fin optimization point for heat transfer rate, effectiveness and efficiency. It’s assumed that the thickness of longitudinal fins varies with length in a special profile, so four different shapes (rectangular, convex, triangular and concave) are considered. In present study, temperature-dependent heat generation, convection and radiation are considered and an analytical technique based on the least square method is proposed for the solution methodology. Results show that by increasing the fin thicknesses ratio, maximum heat transfer rate decreases and Copper among the other materials has the most heat transfer rate in a constant volume.

Effect of Prandtl Number on Laminar Natural Convective Heat Transfer inside Cavity

A numerical investigation of laminar natural convective heat transfer inside cavity filled with air having left heated wall and cold left wall. The top and bottom walls of the cavity are kept to be adiabatic. The finite volume approach for the Prandlt Number pr=0.7, 3,6,10 and Ra 104 are used to solve the governing equations, in which buoyancy is modeled via the Boussinesq approximation in FLUENT. The visualization of flow patterns and temperature fields are shown by means of streamlines and isotherms, respectively. The influence of Prandlt numbers on the hot wall of the cavity are analyzed. Variations of the maximum value of the dimensionless stream function and Nusselt Number were also presented. The computed result indicated that Nusselt number increases along the length of the hot wall and then gradually decreases near the end of the wall. Also as Prandlt number increases heat transfer rate decreases.

Performance of Vertical Tube Passive Condenser with the Effects of Noncondensable and Secondary Cooling Water

An experimental work was carried out on a passive containment cooling system (PCCS) test facility where the effects of change in secondary cooling pool water level and the presence of a noncondensable on the PCCS heat transfer characteristics were investigated. Two condensation flow regimes, complete condensation and flow-through condensation relevant to initial and late stages of PCCS operation, were investigated where secondary cooling pool water level decreases with time. A single tube and a tube bundle test section were used. Steady-state tests with half full and half secondary pool levels were performed using single and four-tube bundle test sections. Transient tests were carried out on the tube bundle test section where the secondary pool water decreases continuously due to boil-off. Transient tests carried out with secondary pool water level change showed that the system pressure for complete condensation mode increases with decrease in water level; however, rate of condensation is almost constant. If the PCCS is operated in through-flow mode the system pressure (primary side pressure) is constant; however, the condensate rate decreases, indicating that some of the steam does not condense. A decrease in pool water level to the top header initially decreases the inlet steam pressure, indicating slight heat transfer enhancement due to efficient cooling of PCCS tubes due to two-phase mixture. When the water level is below three-fourths of the tube height the inlet steam pressure increases with decrease in the water level, indicating decrease in PCCS heat transfer rate. The presence of a noncondensable also reduced PCCS condensation heat transfer.

Non-similar solutions for mixed convection along a wedge embedded in a porous medium saturated by a non-Newtonian nanofluid

Purpose – The purpose of this paper is to present a boundary layer analysis for the mixed convection past a vertical wedge in a porous medium saturated with a power law type non-Newtonian nanofluid. Numerical results for friction factor, surface heat transfer rate and mass transfer rate have been presented for parametric variations of the buoyancy ratio parameter Nr, Brownian motion parameter Nb, thermophoresis parameter Nt, Lewis number Le and the power law exponent n. The dependency of the friction factor, surface heat transfer rate (Nusselt number) and mass transfer rate on these parameters has been discussed. Design/methodology/approach – This general non-linear problem cannot be solved in closed form and, therefore, a numerical solution is necessary to describe the physics of the problem. An implicit, tri-diagonal finite-difference method has proven to be adequate and sufficiently accurate for the solution of this kind of problems. Therefore, it is adopted in the present study. Variable step sizes were used. The convergence criterion employed in this study is based on the difference between the current and the previous iterations. When this difference reached 10−5 for all the points in the η directions, the solution was assumed to be converged, and the iteration process was terminated. Findings – The results indicate that as the buoyancy ratio parameter (Nr) and thermophoresis parameter (Nt) increase, the friction factor increases whereas the heat transfer rate (Nusselt number) and mass transfer rate (Sherwood number) decrease. As the Brownian motion parameter (Nb) increases, the friction factor and surface mass transfer rates increase whereas the surface heat transfer rate decreases. As Le increases, mass transfer rates increase. As the power law exponent n increases, the heat and mass transfer rates increase. Research limitations/implications – The analysis is valid for natural convection dominated regime. The combined forced and natural convection dominated regimes will be reported in a future work. Practical implications – The approach used is useful in optimizing the porous media heat transfer problems in geothermal energy recovery, crude oil extraction, ground water pollution, thermal energy storage and flow through filtering media. Originality/value – The results of the study may be of some interest to the researchers of the field of porous media heat transfer. Porous foam and microchannel heat sinks used for electronic cooling are optimized utilizing the porous medium. The utilization of nanofluids for cooling of microchannel heat sinks requires understanding of fundamentals of nanofluid convection in porous media.

Experimental investigation of heat transfer from inclined flat surface to aqueous foam

Paper presents the results of the experimental investigation of heat transfer process between the inclined flat surface and the longitudinal upward macrofoam (foam) flow. Investigation was performed on the special laboratory stand using macrofoam, which was generated inside the channel on the perforated plate. Foaming solution was made from the 0.5% concentration of the washing powder (TIDE Absolute) solution in water and gas (air). Macrofoam parameters: velocity 0.10÷0.30m/s; volumetric void fraction 0.996÷0.998; bubble dimensions 0.005÷0.015m. Inclination angle of the flat surface 45°. Experimental surface was heated using electric current; surface temperature varied from 16.8 to 36.2°C; foam flow temperature varied from 14.6 to 19.5°C.Investigation showed that the heat transfer rate depends on the foam flow characteristics (velocity and volumetric void fraction) and on the drained liquid film parameters (film thickness, film flow velocity and direction). It was stated that the heat transfer rate increases with the increase of the foam flow velocity up to the critical value. When the foam flow velocity exceeds the critical value, the thickness of the drained liquid film begins to grow and heat transfer rate decreases. Further augmentation of the foam flow velocity forms a concurrent drained liquid flow and heat transfer intensity increases again.The experimental results were compared with the results obtained for the vertical flat surface and for the different types of the tube bundles as well.

Mixed convective boundary layer flow over a vertical cylinder embedded in a porous medium saturated with a nanofluid

Purpose – The purpose of this work is to study the mixed convection boundary layer flow past a vertical cylinder in a porous medium saturated with a nanofluid. Numerical results for friction factor, surface heat transfer rate and mass transfer rate have been presented for parametric variations of the buoyancy ratio parameter Nr, Brownian motion parameter Nb, thermophoresis parameter Nt and Lewis number Le. The dependency of the surface heat transfer rate (Nusselt number) and mass transfer rate on these parameters has been discussed. Design/methodology/approach – Solutions of the set of non-similarity equations are obtained by employing the implicit finite difference method together with Keller box elimination method. Findings – It was found that the heat transfer rate decreases and mass transfer rates increase as Lewis number increases. The heat and mass transfer rates increase as the buoyancy ration parameter increases. As the thermophoresis parameter Nt increases, the heat transfer rate decreases where as the mass transfer rate increases. As the Brownian parameter Nb increases, the heat transfer rate decreases. Brownian motion decelerates the flow in the nanofluid boundary layer. Brownian diffusion promotes heat conduction. The heat and mass transfer rates increase as the buoyancy ratio number Nr increases. The Brownian motion and thermophoresis of nanoparticles increases the effective thermal conductivity of the nanofluid. Both Brownian diffusion and thermophoresis give rise to cross diffusion terms that are similar to the familiar Soret and Dufour cross-diffusion terms that arise with a binary fluid. Research limitations/implications – The analysis is valid for steady, mixed convection two-dimensional boundary layer flow in a nanofluid-saturated Darcy porous medium. An extension to non-Darcy porous medium is left as a part of future study. Practical implications – The research is applicable for enhancing heat exchanger effectiveness by employing nanofluids. Originality/value – The study is useful to engineers interested in designing heat exchangers, water and atmospheric pollution.

Numerical simulation of natural convection of nanofluids in a square cavity with several pairs of heaters and coolers (HACs) inside

In this study, natural convection inside a square cavity filled with nanofluids with several pairs of heaters and coolers (HACs) inside is investigated numerically in the range of Rayleigh numbers between 104 and 107. Walls of the cavity are insulated and heaters and coolers walls are isothermal with temperatures of Th and Tc (Th>Tc). Two-dimensional Navier–Stokes and energy equations are solved using finite volume discretization method. Effects of various design parameters on the heat transfer rate are investigated. Design parameters considered in this study are: position, surface area, shape and orientation of HACs, volume fraction and types of nanoparticles. The results show that the highest and the lowest impacts of design parameters, on the enhancement of heat transfer rate are caused by changing the HAC position and types of nanoparticles, respectively. Moreover, it is found that for a constant surface area of the HAC at the entire range of Rayleigh number, rate of the heat transfer increases with changing orientation of the HAC from horizontal to vertical. Our simulations indicate that the heat transfer rate at all Rayleigh numbers can be enhanced more efficiently by increasing number of HACs than increasing the HAC size. The optimum value of volume fraction of nanoparticles which result in the highest rate of heat transfer in most cases found to be equal to 1%, and beyond that the heat transfer rate decreases.

Heatline visualization for conjugate heat transfer of a couple stress fluid from a vertical slender hollow cylinder

The flow visualization has been made using the heat function concept for the conjugate heat transfer effects on the transient free convective couple stress fluid flow over a vertical slender hollow circular cylinder with the inner surface kept at a constant temperature. The governing non-linear equations are solved numerically by using an unconditionally stable implicit method. Numerical results show that the deviations of flow variables of couple stress fluid from those of the Newtonian fluid turn out to be considerable. Boundary layer flow visualization indicates that the streamlines exist starting from the leading edge to the far downstream, while the heatlines terminate at a finite distance from the cylinder wall. It is noticed that the steady-state values of average skin-friction and heat transfer rate decrease as the conjugate-conduction parameter increases.

Natural convection heat and mass transfer from a sphere in non-Newtonian nanofluids

A boundary layer analysis has been presented for the natural convection flow of a non-Newtonian nanofluid past a sphere. Solutions of the set of nonsimilarity equations are obtained by employing the implicit finite difference method together with Keller box elimination method. Numerical results for friction factor, surface heat transfer rate and mass transfer rate have been presented for parametric variations of the material parameters, buoyancy ratio parameter [Formula: see text], Brownian motion parameter NB, thermophoresis parameter NT and Schmidt number Sc. The dependency of the surface heat transfer rate (Nusselt number) and mass transfer rate on these parameters has been discussed. It was found that the heat transfer rate decreases and mass transfer rates increase as Schmidt number increases. The friction factor and heat transfer rates decrease as the cross viscosity parameter [Formula: see text] increases. The heat transfer rates increase and mass transfer rates decrease as the buoyancy ratio parameter N increases. As the thermophoresis parameter NT increases, the heat and mass transfer rates increase. As the Brownian parameter NB increases, the heat and mass transfer rates decrease. Brownian motion decelerates the flow in the nanofluid boundary layer. Brownian diffusion promotes heat conduction. The Brownian motion and thermophoresis of nanoparticles increase the effective thermal conductivity of the nanofluid. Both Brownian diffusion and thermophoresis give rise to cross diffusion terms that are similar to the familiar Soret and Dufour cross diffusion terms that arise with a binary fluid.

Stagnation Point Flow of a Nanofluid toward an Exponentially Stretching Sheet with Nonuniform Heat Generation/Absorption

This paper deals with the steady two-dimensional stagnation point flow of nanofluid toward an exponentially stretching sheet with nonuniform heat generation/absorption. The employed model for nanofluid includes two-component four-equation nonhomogeneous equilibrium model that incorporates the effects of Brownian diffusion and thermophoresis simultaneously. The basic partial boundary layer equations have been reduced to a two-point boundary value problem via similarity variables and solved analytically via HAM. Effects of governing parameters such as heat generation/absorption λ, stretching parameter ε, thermophoresis , Lewis number Le, Brownian motion , and Prandtl number Pr on heat transfer and concentration rates are investigated. The obtained results indicate that in contrast with heat transfer rate, concentration rate is very sensitive to the abovementioned parameters. Also, in the case of heat generation , despite concentration rate, heat transfer rate decreases. Moreover, increasing in stretching parameter leads to a gentle rise in both heat transfer and concentration rates.

Transient analysis of diffusive chemical reactive species for couple stress fluid flow over vertical cylinder

The unsteady natural convective couple stress fluid flow over a semi-infinite vertical cylinder is analyzed for the homogeneous first-order chemical reaction effect. The couple stress fluid flow model introduces the length dependent effect based on the material constant and dynamic viscosity. Also, it introduces the biharmonic operator in the Navier-Stokes equations, which is absent in the case of Newtonian fluids. The solution to the time-dependent non-linear and coupled governing equations is carried out with an unconditionally stable Crank-Nicolson type of numerical schemes. Numerical results for the transient flow variables, the average wall shear stress, the Nusselt number, and the Sherwood number are shown graphically for both generative and destructive reactions. The time to reach the temporal maximum increases as the reaction constant K increases. The average values of the wall shear stress and the heat transfer rate decrease as K increases, while increase with the increase in the Sherwood number.

Analytical investigation of oscillating flow heat transfer in pulse tubes

In the present paper, a two-dimensional compressible oscillating flow in the tube section of a pulse tube refrigerator system is modeled, based on the successive approximation method. In this respect, the variables are expanded up to second-order terms. For pulse tubes with an outer adiabatic surface, the conservation equations of mass, momentum, energy, and the equation of state for the ideal gas are applied. The effects of operating frequency and taper angle on the temperature distribution, heat transfer behavior, and time-averaged enthalpy flow during a cycle are investigated. Increasing the frequency leads to a higher heat transfer rate in the pulse tube. The enthalpy flow, as the cooling performance representative of the pulse tube, reaches maximum for an optimum convergent taper angle. The temperature distribution and heat transfer process along the axial direction, as well as the phase behavior of the heat transfer coefficient, are also studied. It is shown that, moving from the cold to the hot end of the pulse tube, the temperature variation domain and heat transfer rate decrease.

Natural convection of power-law fluid between two-square eccentric duct annuli

The present paper numerically studies two-dimensional steady-state natural convection of non-Newtonian power-law fluid between two eccentric horizontal square ducts with constant temperature. The inner and outer ducts are assumed to be held at hot and cold temperatures, respectively. The conservation equations of mass, momentum and energy are dicretized using finite volume technique based on second order upwind and finally SIMPLE algorithm is utilized to solve the resultant system of equations. The effects of power-law index (0.6⩽n⩽1.4), Rayleigh number (103⩽Ra⩽106), aspect ratio (0.25⩽AR⩽0.75), eccentricity (-0.2⩽e⩽+0.2) and Prandtl number (10⩽Pr⩽103) on heat and fluid flows are investigated. Also the Nusselt number for various values of governing parameters is obtained and discussed. The results indicate that with increasing the power-law index n from 0.6 to 1.4 the mean Nusselt number that indicates heat transfer rate decreases. It is shown that there is a minimum situation for the Nusselt number versus the eccentricity dependent on the other parameters. Also it is found that varying the Prandtl number almost does not affect heat transfer characteristics except for some cases.

Natural convection heat transfer of nanofluids along a vertical plate embedded in porous medium

The unsteady natural convection heat transfer of nanofluid along a vertical plate embedded in porous medium is investigated. The Darcy-Forchheimer model is used to formulate the problem. Thermal conductivity and viscosity models based on a wide range of experimental data of nanofluids and incorporating the velocity-slip effect of the nanoparticle with respect to the base fluid, i.e., Brownian diffusion is used. The effective thermal conductivity of nanofluid in porous media is calculated using copper powder as porous media. The nonlinear governing equations are solved using an unconditionally stable implicit finite difference scheme. In this study, six different types of nanofluids have been compared with respect to the heat transfer enhancement, and the effects of particle concentration, particle size, temperature of the plate, and porosity of the medium on the heat transfer enhancement and skin friction coefficient have been studied in detail. It is found that heat transfer rate increases with the increase in particle concentration up to an optimal level, but on the further increase in particle concentration, the heat transfer rate decreases. For a particular value of particle concentration, small-sized particles enhance the heat transfer rates. On the other hand, skin friction coefficients always increase with the increase in particle concentration and decrease in nanoparticle size.

A thermal non-equilibrium approach for 2D natural convection due to lateral heat flux: Square as well as slender enclosure

This paper reports the influence of local thermal non-equilibrium state between solid porous matrix and saturated fluid on natural convection in enclosure. The two dimensional steady flow is induced by constant heat flux on side walls of the enclosure, when both horizontal walls are insulated. The governing equations are solved numerically by ADI method and analytically by using parallel flow assumption valid for slender enclosure. A comparative study has been made between convection in square cavity and the same in slender enclosure. Numerical experiments indicate that in comparison with square cavity, where a sharp decrease of local heat transfer rate for fluid (Nuf) takes place up to a certain small value of interface heat transfer coefficient (H), in slender enclosure a smooth decrease of Nuf has been observed in the entire range of H when conductivity ratio (γ) is very small. However, for relatively high values of γ (e.g., γ=10), Nuf is almost independent of H in both geometries. For a given γ, when the value of H is relatively very high, up to a certain value of Ra the difference between both solid as well as fluid temperature rates is negligible. Corresponding temperature contours of two phases becomes almost identical in magnitude as well as patterns point of view, which indicates that equilibrium state between two phases is achieved. Finally, in equilibrium state maximum heat transfer rate used to take place at a certain value (Ao) of aspect ratio, lying in between 1 and 1.5, and is almost independent of all equilibrium parameters. In case of non-equilibrium state, Ao acts as an increasing function of γ.

Natural Convective Boundary-Layer Flow Over a Vertical Cylinder Embedded in a Porous Medium Saturated With a Nanofluid

In this paper, a boundary layer analysis is presented for the natural convection past a vertical cylinder in a porous medium saturated with a nanofluid. Numerical results for friction factor, surface heat transfer rate, and mass transfer rate have been presented for parametric variations of the buoyancy ratio parameter Nr, Brownian motion parameter Nb, thermophoresis parameter Nt, and Lewis number Le. The dependency of the friction factor, surface heat transfer rate (Nusselt number), and mass transfer rate on these parameters has been discussed. The results indicate that as Nr, Nb, and Nt increase, the friction factor and heat transfer rate (Nusselt number) decrease. The mass transfer rate (Sherwood number) increases with Le, Nb, and Nt.