Effect of eccentricity and radius ratio on fluid flow and heat transfer inside an eccentric semicircular enclosure

latroductionNatural convechon heat transfer has gainedconsiderable attention because of itS' numerousaPPlications in the areas of energy conservation, coolingo f electrical and electronic components, design of solarcoil~, bed exchangers, and many others. Heattransfer inside annular space, air-filled cavity or annularsector has wide aPPlication in many engineeringProblems. In our earlier work["n, we have shown theeffeCt of eccentricity on heat transfer and flow field forradius ratio R'=2.0 f…     

Effect of corrugation frequencies on natural convective heat transfer and flow characteristics in a square enclosure of vee-corrugated vertical walls

A numerical investigation has been carried out on natural convective heat transfer and fluid flow in a square cavity with vee-corrugated vertical surfaces. This study covers the range of corrugation frequency from 1 to 3 and Grashof number from 10³ to 10⁵. The corrugation amplitude has been fixed at 5% of the enclosure height. The vorticity stream function formulation with the control volume based finite element method has been used to analyse the effects of corrugation frequency and Grashof number. The investigation shows that the overall heat transfer through the enclosure increases with the increase of corrugation for low Grashof number; but the trend is reversed for high Grashof number.     

Free Convective Flow of Electrically Conducting and Viscous Immiscible Fluid Flow in a Vertical Channel in the Presence of First‐Order Chemical Reaction

In this paper, the effects of chemical reaction on free convective flow of electrically conducting and viscous incompressible immiscible fluids are analyzed. The coupled nonlinear equations governing the heat and mass transfer are solved analytically and numerically with appropriate boundary conditions for each fluid and the solutions have been matched at the interface. The analytical solutions are solved by using regular perturbation method valid for small values of perturbation parameter and numerically by using finite difference method. The numerical results for various values of thermal Grashof number, mass Grashof number, Hartman number, viscosity ratio, width ratio, conductivity ratio, and chemical reaction parameter have been presented graphically in the presence and in the absence of electric field load parameter. In addition, the closed form expression for volumetric flow rate, Nusselt number, species concentration, and total heat rate added to the flow is also analyzed. The solutions obtained by finite difference method and perturbation method agree very well to the order of 10^?4 for small values of perturbation parameter.     

Finite element simulation of magnetoconvection inside a sinusoidal corrugated enclosure with discrete isoflux heating from below

A numerical investigation of the steady magnetoconvection in a sinusoidal corrugated enclosure has been performed. In this analysis, two vertical sinusoidal corrugated walls are maintained at a constant low temperature whereas a constant heat flux source whose length is varied from 20 to 80% of the reference length of the enclosure is discretely embedded at the bottom wall. The Penalty finite element method has been used to solve the governing Navier–Stokes and energy conservation equation of the fluid medium in the enclosure in order to investigate the effect of discrete heat source sizes on heat transfer for different values of Grashof number and Hartmann number. The values of the governing parameters are the Grashof number Gr (10³ to 10⁶), Hartmann number Ha (0 to 100) and Prandtl number Pr (0.71). The present numerical approach is found to be consistent and the solution is obtained in terms of stream functions and isotherm contours.     

Unsteady natural convection in a water-filled isosceles triangular enclosure heated from below

This study is concerned with transient natural convection in a water-filled isosceles triangular enclosure subject to cooling at the inclined surfaces and simultaneous heating at the base. The unsteady flows over a range of Grashof numbers are visualized using a shadowgraph technique, and corresponding numerical simulations are carried out using a Finite Volume Method. Both the experiments and numerical simulations have revealed that the transient flow development in the enclosure due to abrupt heating and cooling through the boundaries can be classified into three distinct stages, that is, an early stage, a transitional stage, and a steady/quasi-steady stage. The major flow features at each of the three stages are described and the Grashof number effects on the flow development and heat transfer are discussed. It is found that, for a fixed aspect ratio of 0.5, a transition of the unsteady flow from symmetric to asymmetric structures occurs for Grashof numbers above 2.95 × 10⁴. Moreover, the present heat transfer calculations indicate that the average Nusselt number over the inclined and horizontal surfaces approximately scales with Gr^0.2.     

Study of conjugate natural convection between vertical coaxial rectangular cylinders

Laminar natural convection between two coaxial vertical rectangular cylinders is numerically studied in this work. The outer cylinder is connected with vertical rectangular inlet and outlet pipes. The inner cylinder dissipates volumetric heat. The fluid flow and heat transfer characteristics between the cylinders are analyzed in detail for various Grashof numbers. The heat transfer rates on the individual faces of the inner cylinder are reported. The bottom face of the inner cylinder is found to associate with much higher heat rates than those of the other faces. The average Nusselt number on bottom face is more than 2.5 times of the Nusselt number averaged on all the faces. At a given elevation, local Nusselt number on the inner cylinder faces increases towards cylinder edges. The effect of thermal condition of the walls of outer cylinder, inlet and outlet on the natural convection is analyzed. The thermal condition shows strong qualitative and quantitative impact on the fluid flow and heat transfer. The variation of induced flow rate, dimensionless maximum temperature and average Nusselt numbers with Grashof number is studied. Correlations for dimensionless buoyancy-induced mass flow rate and temperature maximum are presented.     

Thermo-Solutal Buoyancy Induced Mixed Convection in a Backward Facing Step Channel using Velocity-Vorticity Formulation

Double diffusive mixed convection in a horizontal channel with backward facing step is analyzed using velocity-vorticity formulation with a focus on the effect of recirculatory flow pattern on convective heat and mass transfer. The governing equations consist of vorticity transport equation with thermal and solutal buoyancy force terms, velocity Poisson equations, energy equation, and solutal concentration equation. Galerkin's weighted residual finite-element method has been employed to solve the equations for vorticity, velocity, temperature, and concentration fields in the computational domain. Test results are obtained to study the effect of thermal Grashof number (Gr _T ), solutal Grashof number (Gr _S ), and expansion ratio on the average Nusselt and Sherwood numbers. Results indicate that the convective heat transfer increased with increase in Gr _T only when the Gr _S number is in the aiding mode. The maximum local Nusselt number is always observed to be located adjacent to the downstream of the fluid reattachment point. Using the matched method of asymptotic expansions, correlations have also been developed for average Nusselt and Sherwood numbers for both cases of aiding and opposing buoyancy forces.     

A dimensionless analysis of heat and mass transport in an adsorber with thin fins; uniform pressure approach

A numerical study on heat and mass transfer in an annular adsorbent bed assisted with radial fins for an isobaric adsorption process is performed. A uniform pressure approach is employed to determine the changes of temperature and adsorbate concentration profiles in the adsorbent bed. The governing equations which are heat transfer equation for the adsorbent bed, mass balance equation for the adsorbent particle, and conduction heat transfer equation for the thin fin are non-dimensionalized in order to reduce number of governing parameters. The number of governing parameters is reduced to four as Kutateladze number, thermal diffusivity ratio, dimensionless fin coefficient and dimensionless parameter of Γ which compares mass diffusion in the adsorbent particle to heat transfer through the adsorbent bed. Temperature and adsorbate concentration contours are plotted for different values of defined dimensionless parameters to discuss heat and mass transfer rate in the bed. The average dimensionless temperature and average adsorbate concentration throughout the adsorption process are also presented to compare heat and mass transfer rate of different cases. The values of dimensionless fin coefficient, Γ number and thermal diffusivity ratio are changed from 0.01 to 100, 1 to 10^− 5 and 0.01 to 100, respectively; while the values of Kutateladze number are 1 and 100. The obtained results revealed that heat transfer rate in an adsorbent bed can be enhanced by the fin when the values of thermal diffusivity ratio and fin coefficient are low (i.e., α^? = 0.01, Λ = 0.01). Furthermore, the use of fin in an adsorbent bed with low values of Γ number (i.e. Γ = 10^− 5) does not increase heat transfer rate, significantly.     

Natural convection in a rectangular cavity with partially active side walls

A numerical study is performed to investigate the effect of aspect ratio on the natural convection of a fluid contained in a rectangular cavity with partially thermally active side walls. The active part of the left side wall is at a higher temperature than that of the right side wall. The top and bottom of the cavity and inactive part of the side walls are thermally insulated. Nine different relative positions of the active zones are considered. The equations are discretized by the control volume method with power law scheme and are solved numerically by iterative method together with a successive over relaxation (SOR) technique. The results are obtained for Grashof numbers between 10³ and 10⁵ and the effects of the aspect ratio on the flow and temperature fields and the rate of heat transfer from the walls of the enclosure are presented. The heat transfer rate is high for the bottom–top thermally active location while the heat transfer rate is poor in the top–bottom thermally active location. The heat transfer rate is found to increase with an increase in the aspect ratio.     

Free Convection in Confined Power-Law Fluids From Two Side-by-Side Cylinders in a Square Enclosure

Laminar free convection heat transfer in power-law fluids from two side-by-side cylinders (one hot and one cold) confined in a square duct has been studied numerically in the two-dimensional flow regime. For a fixed value of the ratio of cylinder radius to size of the enclosure, the effect of geometrical placement of the cylinders is studied on the resulting velocity and temperature fields in the laminar free convection regime by considering six asymmetric locations of the two cylinders. In particular, extensive results reported herein span the range of conditions of Grashof number, 10 to 10⁵; Prandtl number, 0.7 to 100, thereby yielding the range of the Rayleigh number as 7 to 10⁷; power-law index, 0.3 to 1.8; and the relative positions (dimensionless) of the cylinders with respect to the centerline, –0.25 to 0.25. The heat transfer characteristics are analyzed in terms of the local Nusselt number along the surfaces of the two cylinders and the enclosure walls. Overall, the average Nusselt number shows a positive dependence on both the Grashof number and the Prandtl number irrespective of the values of power-law index and relative positioning of the cylinders. Also, all else being equal, shear-thinning fluid behavior promotes heat transfer with reference to that in Newtonian fluids. When the two cylinders are situated close to the bottom wall, the rate of heat transfer is augmented with reference to that for the symmetric positioning of the cylinders along the horizontal mid-plane of the enclosure. Conversely, heat transfer deteriorates as the cylinders are located above the centerline of the enclosure. The present numerical results have been consolidated via the use of a modified Rayleigh number, thereby enabling the estimation of the average Nusselt number in a new application.     

Effect of Prandtl Number on Free Convection from Two Cylinders in a Square Enclosure

This study explores the effect of Prandtl number on the laminar natural convection heat transfer to Newtonian fluids in a square enclosure consisting of one hot circular cylinder and one cold circular cylinder. The walls of the square enclosure are maintained isothermal and at the same temperature as the cold cylinder and the fluid medium. The governing partial differential equations have been solved numerically over the following ranges of conditions: Grashof number, 10 to 10⁵; Prandtl number, 0.7 to 100 (or the range of Rayleigh numbers as 7 to 10⁷); and relative positioning of the cylinders, ?0.25 to 0.25. However, the ratio of the radius of the cylinder to the side of the enclosure is held fixed at 0.2. Extensive results on the streamline and isotherm contours, the local Nusselt number distribution, and the average Nusselt number are discussed to delineate the influence of Grashof and Prandtl numbers on them for a given location with respect to the horizontal center line. The surface-averaged Nusselt number shows a positive dependence on Grashof and Prandtl numbers for a fixed location of the two cylinders. The heat transfer results have been correlated as a function of the Rayleigh number and geometric parameters, thereby enabling its prediction in a new application.     

Laminar Free Convection in Power-law Fluids in a Right Angle Triangular Duct with Heated Base

ABSTRACT

Laminar free convection in power-law fluids in a triangular duct is studied numerically to delineate the effects of the height-to-base ratio of the enclosure (0.2 to 2), power-law index (0.2 to 1.8), Grashof number (10 to 10⁴) and Prandtl number (0.7 to 100). The heat transfer is analyzed for the heated base with the other two walls being cold. Detailed kinematics is characterized by the formation of multiple recirculating zones ranging from two to four cells. Shear rate contours provide additional insights about the variation of the local viscosity in the fluid. Heatlines and the values of the Bejan number over the range of conditions are calculated to delineate the contributions of the entropy generation due to thermal effects and viscous dissipation. At low Grashof and/or Prandtl numbers, conduction dominates the overall heat transfer and this transition between the conduction and convection-dominated regimes is captured in terms of a modified Rayleigh number. The effect of aspect ratio on the Nusselt number is modulated by the values of Grashof and Prandtl numbers and power-law index. The present results have been consolidated via the use of a modified Rayleigh number for estimating the value of average Nusselt number in a new application.     

MIXED CONVECTION HEAT TRANSFER IN A TEE BRANCH

The heat transfer characteristics of a Newtonian fluid in a two-dimensional, planar, right-angled tee branch are studied over a range of inlet Reynolds numbers and Grashof numbers. The flow and heat transfer equations, subject to the Boussinesq approximation, are solved using a finite-element discretization. The effects of the branch length and the grid size on the interior flow field are examined to assess the accuracy of the solutions. Results are presented for two types of experimentally realizable boundary conditions—equal exit pressure at the outlet of each branch and specified flow split between the branches. The thermal boundary condition of uniform wall temperature is examined. The effect of increasing Reynolds number is to increase the size and strength of the recirculation zones in both the main and side branches, while that of increasing Grashof number is to decrease such an effect. For the case of equal exit pressures there is a significant flow reversal in the side branch and the exit flow rate from the main branch increases linearly with increasing Gr/Re². For the case of specified flow split, an increasing back pressure is required to be maintained at the exit of the main branch to regulate the flow split at the desired level.     

Heat Transfer in a Lid-Driven Enclosure Filled with Water-Saturated Aluminum Foams

Mixed convection in a lid-driven square enclosure filled with water-saturated aluminum foams is investigated numerically. The driving forces of fluid flow in such a system include the buoyancy force due to temperature gradient and the shear force due to lid movement, while the interaction of these forces results in various heat transfer modes. This work uses the Brinkman-Forchheimer model for fluid flow and the two-equation model for heat transfer. The top moving wall and the bottom heated wall are maintained at different constant temperatures, while the other walls are thermally insulated. The relevant parameters are the porosity of aluminum foams (ε = 0.91, 0.97), the Grashof number (Gr = 10⁴–3 × 10⁶) and the Reynolds number (Re = 10^?2–10⁴). The fluid flow and heat transfer characteristics of the present porous system are identified. Parametric study indicates that the average Nusselt number (Nu) generally increases with Gr and Re. The higher porosity promotes much more enhancement of convective heat transfer, but the lower porosity is desired for higher total heat transfer due to the higher value of effective thermal conductivity. Finally, the Nu correlation is established based on the numerical results.     

Numerical investigation of laminar forced convection of water upwards in a narrow annulus at supercritical pressure

In the present work, convection heat transfer of water at supercritical pressure in a narrow annulus at low Reynolds numbers (less than 1500) has been investigated numerically. The continuity, momentum and energy equations have been solved simultaneously using computational fluid dynamics techniques with the inlet Reynolds number ranging from 250 to 1000, Grashof number from 2.5 × 10⁵ to 1 × 10⁶ and the inlet fluid temperature from 360 °C to 380 °C. In all of the case studies, a sub-cooled water flow at supercritical pressure (25 MPa) and a temperature close to the pseudo-critical point enters the annular channel with constant heat flux at inner wall surface and insulated at outer wall. To calculate the velocity and temperature distributions of the flow, discretized form of the governing equations in the cylindrical coordinate system are obtained by the finite volume method and solved by the SIMPLE algorithm. It has been shown that the effect of buoyancy is strong and causes extensive increase in velocity near the inner wall, and consequently an increase in the convective heat transfer, which is desirable. Besides, the effects of inlet Reynolds number, Grashof number and inlet temperature on the velocity distribution and also on the heat transfer have been investigated.     

Second law analysis of an array of vertical plate-finned heat sink undergoing mixed convection

Second law analysis of an array of vertical plate-finned heat sink undergoing mixed convective heat transfer is investigated. The fluid flow and temperature fields are evaluated numerically solving the mass, momentum and energy conservation equations. The effects of Grashof number, inlet velocity, clearances, and fin spacing on entropy generation, Nusselt number, pumping power ratio and by-pass factor are presented. Total dimensionless entropy generation continuously decreases with clearances for all fin spacing, while Nusselt number shows an optimum value, especially at higher inlet velocities. There exists an optimum range of fin spacing at which Nusselt number is maximum for all Grashof numbers. The pumping power ratio shows significantly higher value for smaller fin spacing and at optimum fin spacing it decreases approximately by an order of magnitude. At optimum clearance, flow by-pass is significantly low.     

Mixed convection from an isolated spherical particle

A numerical study on mixed convection around a hot spherical particle moving vertically downwards in a still fluid medium has been made. The flow field is considered to be axisymmetric for the range of Reynolds number (based on the diameter and the settling velocity of the particle) considered. A third-order accurate upwind scheme is employed to compute the flow field and the temperature distribution. The form of the wake and the thermal field is analyzed for several values of Grashof number and the Reynolds number. The influence of buoyancy on drag and the rate of heat transfer are studied. At moderate Reynolds number, recirculating eddy develops in the downstream of the sphere. With the rise of surface temperature this eddy collapses and the fluid adjacent to the heated surface develops into a buoyant plume above the sphere. The increase in surface temperature of the sphere delays the flow separation. Our results show that the drag force and the rate of heat transfer strongly depend on Grashof number for the moderate values of Reynolds number. The conjugate heat transfer from the moving sphere is also addressed in the present paper. We have compared our computed solution with several empirical and asymptotic expressions available in the literature and found them in good agreement.     

Magnetohydrodynamic Natural Convection Flow in an Enclosure with a Finite Length Heater Using the Differential Quadrature (DQ) Method

Analysis of heat and fluid flow transport due to natural convection and magnetohydrodynamic (MHD) flows in a square enclosure with a finite length heater has been performed using the differential quadrature (DQ) technique. The heater with constant heat flux is located on the bottom wall of the enclosure and isothermal boundary conditions are applied to the right vertical wall while the remaining walls are adiabatic. The effects of heater length (0.2 ≤ ? ≤ 0.8), heater location (0.1 ≤ c/L ≤ 0.9), and direction of magnetic force (0° ≤ φ ≤ 90°) for different values of Grashof (10³ ≤ Gr ≤ 10⁶) and Hartmann numbers (0 ≤ Ha ≤ 100) on the heat and fluid flow in the enclosure are studied. According to the results obtained, heat transfer reduces when increasing the Hartmann number. The rate of reduction is higher for high values of Grashof number. The heat transfer rate for the heater closer to the cold wall is considerably higher than the heaters far from the right wall.     

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

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

An experimental study on convection heat transfer from an array of discrete heat sources

Convection heat transfer from an array of discrete heat sources inside a rectangular channel has been investigated experimentally for air. The lower surface of the channel was equipped with 8×4 flush-mounted heat sources subjected to uniform heat flux; the sidewalls and the upper wall were insulated and adiabatic. The experimental parametric study was made for an aspect ratio of AR=2, Reynolds numbers 864≤Re_Dh≤7955, and modified Grashof numbers Gr*=1.72×10⁸ to 2.76×10⁹. From the experimental measurements, surface temperature distributions of the discrete heat sources were obtained and effects of Reynolds and Grashof numbers on these temperatures were investigated. Furthermore, Nusselt number distributions were calculated for different Reynolds and Grashof numbers. Results show that surface temperatures increase with increasing Grashof number and decrease with increasing Reynolds number. However, with the increase in the buoyancy affected secondary flow and the onset of instability, temperatures level off and even drop as a result of heat transfer enhancement. This outcome can also be observed from the variation of the row-averaged Nusselt number showing an increase towards the exit.