Numerical Study of Entropy Generation for Natural Convection in Rectangular Cavity with Circular Corners

This article numerically studies entropy generation due to natural convection in a rectangular cavity with circular corners. In this work, in order to solve the governing equations, an explicit finite-volume procedure and a time-marching method are utilized. Also, instead of the conventional algorithms of SIMPLE, SIMPLEM, and SIMPLEC, an artificial compressibility technique is applied for coupling the continuity to the momentum equations. Entropy generation, as a representation of irreversibility and efficiency loss in engineering heat transfer processes, is analyzed in detail. In this work, effects of the radius of walls corner, Rayleigh number, and distribution ratio on total entropy generation, Nusselt number, and Bejan number are also evaluated. The results show that entropy generation decreases with the increase of the radius of the walls’ corner and increases with the increase of Rayleigh number, aspect ratio, and irreversibility ratio.     

A numerical investigation of the effect of heating methods on saturated nucleate pool boiling

Using a numerical model, the effect of heating methods on saturated nucleate pool boiling is investigated parametrically for smooth and rough nickel and copper heater plates. The boiling curve moved right with decreasing thickness for the smooth and rough nickel and copper heaters in the constant-heat-flux heating method. This trend was reversed in the constant-temperature heating method; the boiling curved shifted left with decreasing heater thickness. However, the later trend was not affected by the heater material and thickness and the surface roughness (mean cavity radius). The boiling curves were identical for the constant internal generation rate and the constant-heat-flux heating method. The use of ac instead of dc resistive heating caused the boiling curve generally to move left. This behavior was not linear with the heat flux, heater material, or surface conditions. No hysterisis was found when the heat flux was increased and then decreased gradually to original values.     

Effects of the Dipole Position on Thermomagnetic Convection in a Locally Heated Shallow Enclosure: Thermodynamic and Transport Analysis

Steady-state thermomagnetic convection in a shallow cavity under zero-gravity conditions is numerically investigated for different positions of the field-source. Two symmetrically placed, discrete, flush-mounted heaters of identical strengths represent power-dissipaters in electronics/MEMS applications. The sidewalls are isothermal heat sinks. Correlations between the field-source position and the flow morphology have been established. The distribution patterns of maximum heater temperatures and pertinent heat transfer parameters are explained. The local entropy generation due to heat transfer and fluid friction irreversibilities are determined. The total entropy generation is found to be almost entirely dependent on heat transfer irreversibility. The dipole position that minimizes the total entropy generation also produces the lowest average temperature on the heaters.     

Conjugate heat transfer in open cavities with a discrete heater at its optimized position

In this article, we determined optimum position of a discrete heater by maximizing the conductance and then studied heat transfer and volume flow rate with the discrete heater at its optimum position in open cavities. Continuity, Navier–Stokes and energy equations are solved by finite difference-control volume numerical method. The relevant governing parameters were: the Rayleigh numbers from 10⁶ to 10¹², the Prandtl number, Pr = 0.7, the cavity aspect ratio, A = H/L from 0.5 to 2, the wall thickness l/L from 0.05 to 0.15, the heater size h/L from 0.15 to 0.6, and the conductivity ratio k_r from 1 to 50. We found that the global conductance is an increasing function of the Rayleigh number, the conductivity ratio, and a decreasing function of the wall thickness. Best thermal performance is obtained by positioning the discrete heater at off center and slightly closer to the bottom. The Nusselt number and the volume flow rate in and out the open cavity are an increasing function of the Rayleigh number and the wall thickness, and a decreasing function of the conductivity ratio. The Nusselt number is a decreasing function of the cavity aspect ratio and the volume flow rate is an increasing function of it.     

Natural Convection in a Vertical Annuli with Discrete Heat Sources

In this article, we numerically study natural convection heat transfer in a cylindrical annular cavity with discrete heat sources on the inner wall, whereas the outer wall is isothermally cooled at a lower temperature, and the top wall, the bottom wall, and unheated portions of the inner wall are assumed to be thermally insulated. To investigate the effect of discrete heating on the natural convection heat transfer, at most two heating sources located near the top and bottom walls are considered, and the size and location of these discrete heaters are varied in the enclosure. The governing equations are solved numerically by an implicit finite difference method. The effect of heater placements, heater lengths, aspect ratio, radii ratio, and modified Rayleigh number on the flow and heat transfer in the annuli are analyzed. Our numerical results show that when the size of the heater is smaller, the heat transfer rates are higher. We also found that the heat transfer in the annular cavity increases with radii ratio and modified Rayleigh number, and can be enhanced by placing a heater with the smaller length near the bottom surface.     

Bubble nucleation on micro line heaters under steady or finite pulse of voltage input

Nucleation temperatures on micro line heaters under steady voltage input were measured precisely by obtaining the I-R (current-resistance) characteristic curves of the heaters having dimensions of 50 μm in length, 3 or 5 μm in width, and 0.583 μm in thickness. The bubble nucleation temperature on the heater with 3 μm width is higher than the superheat limit, while the temperature on the heater with broader width of 5 μm is considerably less than the superheat limit. The nucleation temperature under a finite voltage pulse input was also measured for 5-μm width heater. The nucleation temperatures were also estimated by using the molecular cluster model for bubble nucleation on the cavity free surface with effect of contact angle. The bubble nucleation process was observed by a microscope/35 mm camera unit with a flash light of μs duration.     

Analysis of entropy generation due to natural convection in square enclosures with multiple discrete heat sources

Entropy generation due to natural convection in an enclosure heated locally from below with two isoflux sources was investigated. The flow and temperature fields were determined by numerical simulation of two-dimensional laminar conservation equations for mass, momentum and energy. For heaters of equal length and strength, the effects of Rayleigh number and heater position on flow and temperature fields and local entropy generation were examined. For heaters of unequal heater length and heater strength, the effects of heater length and strength ratios were investigated. Minimum entropy generation rate was achieved for the same condition at which the minimum peak heater temperature was obtained.     

Second law optimization of a solar air heater having chamfered rib–groove roughness on absorber plate

Artificially roughened solar air heaters perform better than the plane ones under the same operating conditions. However, artificial roughness leads to even more fluid pressure thereby increasing the pumping power. The entropy generation in the duct of solar air heater having repeated transverse chamfered rib–groove roughness on one broad wall is studied numerically. Roughness parameters, viz., relative roughness pitch P/e, relative roughness height e/D_h relative groove position g/P, chamfer angle φ and flow Reynolds number Re have a combined effect on the heat transfer as well as fluid friction. The entropy generation is minimized and reasonably optimized designs of roughness are found.     

Numerical Study of Pressure Drop and Thermal Characteristics of Al2O3–Water Nanofluid Flow in Horizontal Annuli

In this paper the results of numerical study of the mixed convection heat transfer of Al₂O₃–water nanofluid in a horizontal annuli are presented. Steady, laminar flows in symmetric configurations are considered. Single-phase fluid approach is adopted for nanofluid modeling. The governing equations are discretized using the finite-volume method. A SIMPLE-like algorithm has been applied for pressure–velocity coupling on the collocated arrangement. In order to validate the code performance, the numerical results are compared with those available in the literature and good agreement is achieved. The effects of some important parameters such as nanoparticle volume fraction, aspect ratio, Grashof number, and heat flux ratio are studied and discussed in detail. In general, it is observed that the local Nusselt number increases with increase in nanoparticle concentration, Grashof number, and radius ratio. However, when increasing the nanoparticle concentration there are considerable increments in pressure drop and pumping power, which are not desirable. On the other hand, changes in the skin friction coefficient are negligible.     

Entropy generation in transpiration cooling of concentric spherical shells

The present paper deals with transpiration cooling of two concentric spherical shells. The analysis includes the calculation for the radial distribution of temperature and volumetric entropy generation, and the total rate of entropy generation in the thermal system. Standard air is considered as the cooling fluid. Results showed that the entropy generation increases with increasing temperature difference between the sphere surfaces. Variation of either mass flow rate or radius ratio affects volumetric entropy distribution and the total rate of entropy generation of the processes. The increase of mass flow rate or radius ratio increases the total rate of entropy generation. The performance of the system is analyzed by calculating irreversibility to heat transfer ratio at both inner and outer sphere surfaces. It was found that irreversibility to heat transfer ratio at the inner sphere surface increases with increasing mass flow rate, or decreasing radius ratio. The opposite is true for the outer sphere surface.     

Convective transport in rectangular cavities partially heated at the bottom and cooled at one side

Laminar natural convection heat transfer inside air-filled, rectangular enclosures partially heated from below and cooled at one side is studied numerically. A computational code based on the SIMPLE-C algorithm is used for the solution of the system of the mass, momentum, and energy transfer governing equations. Simulations are performed for a complete range of heater size, for Rayleigh numbers based on the height of the cavity ranging from 10~3to 10~6, and for height-to-width aspect ratios of the cavity spanning from 0.25 to 4. It is found that the heat transfer rate increases with increasing the heater size and the Rayleigh number, while it decreases with increasing the aspect ratio of the cavity. Dimensionless heat transfer correlations are also proposed.     

Three-dimensional numerical analysis of the natural convection and entropy generation of MWCNTs-H2O and air as two immiscible fluids in a rectangular cuboid with fillet corners

A numerical investigation has been carried out to study the natural convection and entropy generation within the three-dimensional enclosure with fillets. There are two immiscible fluids of Multi-Walled Carbon Nano-Tubes (MWCNTs)-water and air in the enclosure, which is simulated as two discrete phases. There are two heaters with constant heat flux at the sides, and the top and bottom walls are kept at cold constant temperature. The finite volume approach is applied to solve the governing equations. Moreover, a numerical method is developed based on the three-dimensional solution of Navier–Stokes equations. The fluid flow, heat transfer, and total volumetric entropy generation due to natural convection are studied carefully in a three-dimensional enclosure. The effects of the corner radius of fillets (r?=?0, 0.15, 0.2, and 0.25), Rayleigh number (10³?Ra?6), and solid volume fraction (φ?=?0.002 and 0.01) of the nanofluid have been investigated on both natural convection characteristic and volumetric entropy generation.* The results show that the curved corner can be an effective method to control fluid flow and energy consumption, and three dimensional solutions render more accurate results.     

EFFECTS OF ADAPTIVITY ON FINITE ELEMENT SCHEMES FOR TURBULENT HEAT TRANSFER AND FLOW PREDICTIONS

This article reports convection heat transfer in a short and tall annular enclosure with two discrete isoflux heat sources of different lengths. The discrete heat sources are mounted at the inner wall and the outer wall is maintained at a lower temperature, whereas the top and bottom walls and the unheated portions of the inner wall are kept at adiabatic. An implicit finite-difference method is employed to solve the vorticity–stream function formulations of the governing equations. The significant influence of the discrete heaters on the flow and heat transfer is analyzed for a wide range of modified Rayleigh numbers, aspect ratio, and length ratio (?) of heat sources. Our numerical results reveal that the average Nusselt number decreases with aspect ratio, whereas the magnitude of maximum temperature increases with the aspect ratio. For most of the parametric cases considered in the present study, the heat transfer rate is found to be higher at the bottom heater than at the top heater except for ? = 0.5. The effect of heater length ratio on the heat transfer rate is noticeable for unit aspect ratio, whereas its effect is insignificant as the aspect ratio increases. Furthermore, it was found that the maximum temperature is found generally at the top heater except for the case ? = 0.5, where the maximum temperature is found at the bottom heater.     

Effects of pressure,orientation, and heater size on pool boiling of water with nanocoated heaters

Parametric tests were experimentally conducted to observe the role of average nanoparticle size, pressure, heater orientation, and heater size during pool boiling of water using Al₂O₃ nanoparticle coated flat heaters. Results indicate that pool boiling performance is dependent on the parameters tested, except the nanoparticle size, for both uncoated and nanocoated surfaces. The nanoparticle coated heater consistently produced dramatic Critical Heat Flux enhancement relative to the uncoated surface at all tested conditions. It was postulated that the better wettability in the nanocoating, especially its ability to continuously rewet the base of the growing bubbles, was the main cause of enhancement.     

Free convection heat transfer of non Newtonian nanofluids under constant heat flux condition

Two different kinds of non-Newtonian nanofluids were prepared by dispersion of Al₂O₃ and TiO₂ nanoparticles in a 0.5 wt.% aqueous solution of carboxymethyl cellulose (CMC). Natural convection heat transfer of non-Newtonian nanofluids in a vertical cylinder uniformly heated from below and cooled from top was investigated experimentally. Results show that the heat transfer performance of nanofluids is significantly enhanced at low particle concentrations. Increasing nanoparticle concentration has a contrary effect on the heat transfer of nanofluids, so at concentrations greater than 1 vol.% of nanoparticles the heat transfer coefficient of nanofluids is less than that of the base fluid. Indeed it seems that for both nanofluids there exists an optimum nanoparticle concentration that heat transfer coefficient passes through a maximum. The optimum concentrations of Al₂O₃ and TiO₂ nanofluids are about 0.2 and 0.1 vol.%, respectively. It is also observed that the heat transfer enhancement of TiO₂ nanofluids is higher than that of the Al₂O₃ nanofluids. The effect of enclosure aspect ratio was also investigated. As expected, the heat transfer coefficient of nanofluids as well as the base fluid increases by increasing the aspect ratio.     

Surface effects of ribbon heaters on critical heat flux in nanofluid pool boiling

This paper deals with a study of enhanced critical heat flux (CHF) and burnout heat flux (BHF) in pool boiling of water with suspended silica nanoparticles using Nichrome wires and ribbons. Previously the current authors and other researchers have reported three-digit percentage increase in critical heat flux in silica nanofluids. This study investigates the effect of various heater surface dimensions, cross-sectional shapes as well as surface modifications on pool boiling heat transfer characteristics of water and water-based nanofluids. Our data suggest that the CHF and BHF decrease as heater surface area increases. For concentrations from 0.1 vol% to 2 vol%, the deposition of the particles on the wire allows high heat transfer through inter-agglomerate pores, resulting in a nearly 3-fold increase in burnout heat flux at very low concentrations. The nanoparticle deposition plays a major role through variation in porosity. The CHF enhancement is non-monotonic with respect to concentration. As the concentration is increased, the CHF and BHF decrease prior to increasing again at higher concentrations. Results show a maximum of 270% CHF enhancement for ribbon-type heaters. The surface morphology of the heater was investigated using SEM and EDS analyses, and it was inferred that the 2 vol% concentration deposition coating had higher porosity and rate of deposition compared with 0.2 vol% case.     

Effect of aspect ratio on entropy generation in a rectangular cavity with differentially heated vertical walls

In the present study, entropy generation in rectangular cavities with the same area but different aspect ratios is numerically investigated. The vertical walls of the cavities are at different constant temperatures while the horizontal walls are adiabatic. Heat transfer between vertical walls occurs by laminar natural convection. Based on the obtained dimensionless velocity and temperature values, the distributions of local entropy generation due to heat transfer and fluid friction, the local Bejan number and local entropy generation number are determined and related maps are plotted. The variation of the total entropy generation and average Bejan number for the whole cavity volume at different aspect ratios for different values of the Rayleigh number and irreversibility distribution ratio are also evaluated. It is found that for a cavity with high value of Rayleigh number (i.e., Ra = 10⁵), the total entropy generation due to fluid friction and total entropy generation number increase with increasing aspect ratio, attain a maximum and then decrease. The present results are compared with reported solutions and excellent agreement is observed. The study is performed for 10² < Ra < 10⁵, 10^− 4 < ? < 10^− 2, and Pr = 0.7.     

Numerical Investigation of the Magnetic Field Effects on the Entropy Generation and Heat Transfer in a Nanofluid Filled Cavity with Natural Convection

This paper presents a numerical investigation of the entropy generation and heat transfer in a ferrofluid (water and 4% Fe₃O₄ nanoparticles) filled cavity with natural convection using a two phase mixture model and control volume technique. The effect of applying a nonuniform magnetic field on the entropy generation and heat transfer in the cavity and also the interaction of magnetic force and the buoyancy force are investigated. Based on the obtained results, applying a magnetic field will enhance the heat transfer mechanism. Furthermore, by applying the nonuniform magnetic field on the ferrofluid filled cavity with natural convection, the total entropy generation is decreased considerably at higher Rayleigh numbers. Therefore, applying a magnetic field can be considered as a suitable method for entropy generation minimization in order to have high efficiency in the system.     

Numerical investigation of the MHD forced convection and entropy generation in a straight duct with sinusoidal walls containing water–Al2O3 nanofluid

This paper examines forced convection heat transfer and entropy generation of a nanofluid laminar flow through a horizontal channel with wavy walls in the presence of magnetic field, numerically. The Newtonian nanofluid is composed of water as base fluid and Al₂O₃ as nanoparticle which is exposed to a transverse magnetic field with uniform strength. The inlet nanofluid with higher temperature enters the cool duct and heat is exchanged along the walls of a wavy channel. The effects of the dominant parameters including Reynolds number, solid volume fraction, Hartmann number, and different states of amplitude sine waves are studied on the local and average Nusselt number, skin friction, and total entropy generation. Computations show excellent agreement of the present study with the previous literature. The computations indicate that with the increasing strength of a magnetic field, Nusselt number, skin friction, and total entropy generation are increased. It is found that increasing the solid volume fraction of nanoparticles will increase the Nusselt number and total entropy generation, but its effect on the skin friction is negligible. Also, results imply that increasing amplitude sine waves of the geometry has incremental effect on both Nusselt number and skin friction, but its effect on the total entropy generation is not so tangible.     

The Influence of Geometry on the Thermal Performance of Microchannels in Laminar Flow With Viscous Dissipation

Micro heat exchangers may achieve very high heat transfer coefficients thanks to their small dimensions and high area-to-volume ratio even in laminar flow, a highly desirable feature in many industrial applications. The main drawback of these devices is the high frictional losses—especially for liquid flows—that make viscous dissipation no longer negligible. In order to enhance heat transfer, modification of the channels’ cross-section is a viable strategy. In this work the fully developed steady laminar flow of a Newtonian liquid through a microchannel subject to uniform heat flux, uniform peripheral temperature boundary conditions in the presence of viscous dissipation is investigated. Entropy generation numbers and the constrained total heat transfer area performance evaluation criterion are employed to assess the influence of smoothing the corners of an initially rectangular cross section, with an aspect ratio ranging from 1 to 0.03 under four different types of geometrical constraints. The governing equations and the results are expressed in nondimensional form, with the intensity of viscous dissipation being exemplified by the Brinkman number, which is demonstrated to increase its maximum allowable value when corners are smoothed. The results are reported as a function of the nondimensional radius of curvature and aspect ratio and show that smoothing the corners almost invariably brings an improvement for a fixed heated perimeter.