Forced Convection in Micropolar Fluid Flow through a Wavy-Wall Channel

ABSTRACT

Forced convection of micropolar fluids through a periodic array of wavy-wall channels has been analyzed by using a simple coordinate transformation method and the spline alternating- direction implicit method. The effects of the wavy amplitude, the micropolar parameter, and the Reynolds number on skin friction coefficient and Nusselt number have been examined in detail. Results show that the flow through a sinusoidally curved converging-diverging channel forms a strong forward flow and a reticular vortex within each wave for larger Reynolds number and larger wavy amplitudes. For the micropolar fluids, increasing the vortex viscosity causes an increase in the total viscosity of the fluid, thus the skin friction coefficient increases while the Nusselt number decreases. Also, the influence of vortex viscosity on the minimum cross section of the wavy-wall channel and on a tiny change of the maximum cross section is manifest. Moreover, both Reynolds number and wavy amplitude tend to enhance the total heat transfer rate, regardless of whether the fluids are Newtonian or micropolar fluids.     

Fully Developed Free Convection Heat and Mass Transfer of a Micropolar Fluid Between Porous Vertical Plates

In this article, we consider the problem of fully developed natural convection heat and mass transfer of a micropolar fluid between porous vertical plates with asymmetric wall temperatures and concentrations. The resulting boundary-value problem is solved analytically by the homotopy analysis method (HAM). Profiles for velocity and microrotation are presented for a range of values of the Reynolds number and the micropolar parameter.     

Marangoni Convection Heat and Mass Transport of Power-Law Fluid in Porous Medium with Heat Generation and Chemical Reaction

This article presents a study for Marangoni convection of power-law fluid in a porous medium driven by a power-law temperature and a power-law concentration with heat generation and first-order chemical reaction. It is assumed that the surface tension varies linearly with both the temperature and the concentration. The effects of power-law viscosity on temperature and concentration fields are taken into account bya modified Fourier law and Darcy's Law for power-law fluid. An approximate analytical solution is obtained using a homotopy analytical method, which is verified by numerical ones with good agreement. The transport characteristics of velocity, temperature, and concentration fields are analyzed in detail.     

Natural Convection Heat Transfer and Entropy Generation in a Porous Trapezoidal Enclosure Saturated with Power-Law Non-Newtonian Fluids

Abstract

In the present study, natural convection heat transfer and its associated entropy generation in a porous trapezoidal enclosure saturated with a power-law non-Newtonian fluid has been numerically investigated. Horizontal walls of the enclosure are assumed to be adiabatic while the side walls are considered to be kept at a constant temperature. A continuum-based approach is adapted here to model the fluid flow through porous media and the Darcy’s law is modified to account for non-Newtonian rheological behavior of the fluid. The obtained governing equations are discretized using the finite volume method and a detailed parametric study is undertaken to account for the effects of various relevant parameters of the problem on the heat transfer and entropy generation rates. It was shown that the impact of the power-law index on both entropy generation and heat transfer significantly intensifies in a convection-dominated flow regime inside the enclosure, especially for a shear thinning liquid. Moreover, heat transfer rate and entropy generation increase as the sidewall angle is elevated.     

Entropy Generation due to Combined Natural Convection and Thermal Radiation within a Rectangular Enclosure

ABSTRACT

The present work investigates entropy production due to coupled natural convection/radiation heat transfer phenomenon in an inclined rectangular enclosure, isothermally heated from the bottom side and isothermally cooled from the other sides. The discrete-ordinate method is used in modeling the radiative transport equation while the statistical narrow band correlated-k model is adopted to deduce the radiative properties of the medium. The influence of pertinent parameters such as aspect ratio, inclination angle and walls emissivities on entropy generation is studied. It is found that the volumetric entropy generation is reduced when increasing the inclination angle of the enclosure. Moreover, it is shown that the minimum entropy production due to radiation heat transfer in participating media occurs at aspect ratio equal to unity.     

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.     

Effects of Thermal Boundary Conditions on Entropy Generation during Natural Convection

A comprehensive numerical study on entropy generation during natural convection is studied in a square cavity subjected to a wide variety of thermal boundary conditions. Entropy generation terms involving thermal and velocity gradients are evaluated accurately based on the elemental basis set via the Galerkin finite element method. The thermal and fluid irreversibilities during the conduction and convection dominant regimes are analyzed in detail for various fluids (Pr = 0.026,988.24) within Ra = 10³–10⁵. Further, the effect of Ra on the total entropy generation and average Bejan number is discussed. It is observed that thermal boundary conditions significantly affect the thermal mixing, temperature uniformity, and the entropy generation in the cavity. A case where the bottom wall is hot isothermal with linearly cooled side walls and adiabatic top wall is found to result in high thermal mixing and a higher degree of temperature uniformity with minimum total entropy generation.     

Entropy Generation During Natural Convection in a Porous Cavity: Effect of Thermal Boundary Conditions

Entropy generation plays a significant role in the overall efficiency of a given system, and a judicious choice of optimal boundary conditions can be made based on a knowledge of entropy generation. Five different boundary conditions are considered and their effect of the permeability of the porous medium, heat transfer regime (conduction and convection) on entropy generation due to heat transfer, and fluid friction irreversibilities are investigated in detail for molten metals (Pr = 0.026) and aqueous solutions (Pr = 10), with Darcy numbers (Da) between 10^?5–10^?3 and at a representative high Rayleigh number, Ra = 5 × 10⁵. It is observed that the entropy generation rates are reduced in sinusoidal heating (case 2) when compared to that for uniform heating (case 1), with a penalty on thermal mixing. Finally, the analysis of total entropy generation due to variation in Da and thermal mixing and temperature uniformity indicates that, there exists an intermediate Da for optimal values of entropy generation, thermal mixing, and temperature uniformity.     

Entropy Generation Due to Natural Convection in a Partially Open Cavity with a Thin Heat Source Subjected to a Nanofluid

This article presents a numerical study of natural convection cooling of a heat source mounted inside the cavity, with special attention being paid to entropy generation. The right vertical wall is partially open and is subjected to copper–water nanofluid at a constant low temperature and pressure, while the other boundaries are assumed to be adiabatic. The governing equations have been solved using the finite volume approach, using SIMPLE algorithm on the collocated arrangement. The study has been carried out for a Rayleigh number in the range 10³ < Ra < 10⁶, and for solid volume fraction 0 <? <0.05. In order to investigate the effect of the heat source and open boundary location, six different configurations are considered. The effects of Rayleigh numbers, heat source and open boundary locations on the streamlines, isotherms, local entropy generation, Nusselt number, and total entropy generation are investigated. The results indicate that when open boundary is located up, the fluid flow augments and hence the heat transfer and Nusselt number increase and total entropy generation decreases.     

Hydromagnetic Double-Diffusive Laminar Natural Convection in a Radiatively Participating Fluid

ABSTRACT

Two-dimensional hydromagnetic double-diffusive convection of a radiatively participating fluid confined in a rectangular enclosure is studied numerically for fixed Prandtl, Rayleigh, and Lewis numbers, Pr = 13.6, Ra = 10⁵, Le = 2. Uniform temperatures and concentrations are imposed along the vertical walls, while the horizontal walls are assumed to be adiabatic and impermeable. The damping and stabilization effects of an external horizontal magnetic field are studied for three different optical thicknesses of the semitransparent fluid as well as for an opaque medium. For moderate optical thickness, a steady compositionally dominated flow is observed for all values of Hartmann number considered, and the magnetic damping is remarkably lower than in the opaque medium, for which the flow is always thermally dominated. For optically thin and optically thick media, the thermally dominated flow is stabilized and becomes compositionally dominated as soon as the Hartmann number is increased.     

Numerical Study of Natural Convection in an Enclosure with an Internal Heat Source at Higher Rayleigh Numbers

Natural convection is extensively used in cooling of large scale electrical and electronic equipments. This work involves study of flow and heat transfer characteristics in enclosures with partial openings having an internal heat source at higher Rayleigh number (Ra_h > 10⁶). It involves the numerical simulation of 2D steady state natural convection in enclosures of different aspect ratios (H/W = 2 and 3) for five Rayleigh numbers (Ra_h = 10⁷, 10⁸, 10⁹, 10¹⁰, and 10¹¹). Two different configurations have been considered based on the number and position of vents—diagonal side (DS) and two inlets one outlet (2I1O). The time dependent nature of the flow is characterized by performing a Fast Fourier Transform (FFT) analysis of temperature and velocity at a characteristic location in the enclosure. The global parameters considered are the mass flow rate driven through the cavity by the heater and the average Nu defined over the heater surface. It is seen that with increase in Ra_h, flow becomes more fluctuating and moves towards chaotic regime and this transition is quicker at lower H/W. For the given configuration both the global parameters increases with increase in Ra_h and decrease in H/W.     

Thermal Modelling of a Natural Convection Solar Water Heating System with a Thermal Trap Collector

A mathematical model has been developed to study the performance of a solar water heating system with a thermal trap flat plate collector and in which the flow of water between the collector and the storage tank is maintained by natural convection. An expression has also been developed for the mass flow rate in terms of known parameters. The model yields exact expressions for the temperature of water in the storage tank as a function of time in terms of collector's parameters and the solar insolation. Numerical calculations have been performed to compare the performance of the hot water heating system with a thermal trap collector with the one with an ordinary flat plate collector.     

Anisotropy Effects on Heat and Fluid Flow by Unsteady Natural Convection and Radiation in Saturated Porous Media

ABSTRACT

This article deals with a numerical study of fluid flow and heat transfer by unsteady natural convection and thermal radiation in a vertical channel opened at both ends and filled with anisotropic, in both thermal conductivity and permeability, fluid-saturated porous medium. The bounding walls of the channel are gray and kept at a constant hot temperature.

In the present study we suppose the validity of the Darcy law for motion and of the local thermal equilibrium assumption. The radiative transfer equation (RTE) is solved by the finite-volume method (FVM). The numerical results allow us to represent the time–space variations of the different state variables. The sensitivity of the fluid flow and the heat transfer to different controlling parameters, namely, the single scattering albedo ω, the temperature ratio R, the anisotropic thermal conductivity ratio R_c, and the anisotropic permeability ratio R_k, are addressed. Numerical results indicate that the controlling parameters of the problem, namely, ω, R, R_c, and R_k, have significant effects on the flow and thermal field behavior and also on the transient process of heating or cooling of the medium. Effects of such parameters on time variations of the volumetric flow rate q_v and the convected heat flux Q at the channel's outlet are also studied.     

Natural Convection of a Binary Fluid in a Slightly Inclined Shallow Cavity

ABSTRACT

This article reports an analytical and numerical study of the natural convection in an inclined shallow cavity filled with a binary fluid. Newmann boundary conditions for temperature are applied to the long side walls of the enclosure, while the two short ones are assumed to be impermeable and insulated. The solutal buoyancy force are induced either by the imposition of constant fluxes of solute on the walls (double-diffusive convection, a = 0) or by temperature gradients (Soret effects, a = 1). The governing parameters for the problem are the thermal Rayleigh number,Ra_T, the Lewis number Le, the buoyancy ratio ?, the inclination of the cavity Θ, the Prandtl numberPr, the aspect ratio of the cavity A, and the constant a. For convection in an infinite layer (A > > 1), an analytical solution of the steady form of the governing equations is obtained on the basis of the parallel flow approximation. The critical Rayleigh numbers for the onset of supercritical and subcritical convection are predicted by the present model. Also, it is demonstrated that, for small enough inclinations around the horizontal plane, multiple steady states exist, some of which are unstable. Numerical solutions of the full governing equations are obtained for a wide range of the governing parameters. Good agreement is observed between the analytical prediction and the numerical simulations.     

Role of Entropy Generation On Thermal Management During Natural Convection in a Tilted Square Cavity with Isothermal and Non-Isothermal Hot Walls

Entropy generation during natural convection within tilted square cavity inclined with different angles (? = 30°and 75°) for various thermal boundary conditions (case 1: isothermal heating and case 2: non-isothermal heating) has been studied. Simulations are carried out over a range of parameters: Rayleigh number (10³ ≤ Ra ≤ 10⁵) and Prandtl numbers (Pr = 0.025 and 998.24). The numerical results are presented in terms of isotherms (θ), streamlines (ψ), entropy generation due to heat transfer (S _θ ) and fluid friction (S _ψ ). Heating strategy is energy efficient for case 2 (non-isothermal heating) due to its less total entropy generation with reasonable heat transfer rate, irrespective of Pr.     

Nonhomogeneous Heat Conduction Problem and Its Thermal Deflection Due to Internal Heat Generation in a Thin Hollow Circular Disk

This article is concerned with the determination of temperature and thermal deflection in a thin hollow circular disk under an unsteady-state temperature field due to internal heat generation within it. Initially, the disk is kept at an arbitrary temperature F(r, z). For times t > 0 heat is generated within the thin hollow circular disk at a rate of g(r, z, t) Btu/hr ft³, while the boundary surfaces at (r = a), (r = b), (z = 0) and (z = h) are kept at temperatures f ₁(z, t) and f ₂(z, t), f ₃(r, t) and f ₄(r, t), respectively. The governing heat conduction equation has been solved by using a finite Hankel transform and the generalized finite Fourier transform. The results are obtained in series form in terms of Bessel's functions. As a special case, different metallic disks have been considered. The results for temperature change and the thermal deflection have been computed numerically and illustrated graphically.     

Natural Convection Heat Transfer in an Inclined Enclosure Filled with a Water-Cuo Nanofluid

This article presents the results of a numerical study on natural convection heat transfer in an inclined enclosure filled with a water-CuO nanofluid. Two opposite walls of the enclosure are insulated and the other two walls are kept at different temperatures. The transport equations for a Newtonian fluid are solved numerically with a finite volume approach using the SIMPLE algorithm. The influence of pertinent parameters such as Rayleigh number, inclination angle, and solid volume fraction on the heat transfer characteristics of natural convection is studied. The results indicate that adding nanoparticles into pure water improves its heat transfer performance; however, there is an optimum solid volume fraction which maximises the heat transfer rate. The results also show that the inclination angle has a significant impact on the flow and temperature fields and the heat transfer performance at high Rayleigh numbers. In fact, the heat transfer rate is maximised at a specific inclination angle depending on Rayleigh number and solid volume fraction.     

Effect of Undulations on the Natural Convection Heat Transfer and Entropy Generation Inside a Porous Right-Angled Triangular Enclosure

In the present study, natural convection in a two-dimensional porous right-angled triangular enclosure with one wavy wall is studied numerically. Three cases with one, two, and three undulations on the left wall are studied in this analysis. The stream function-vorticity equations are solved using finite-difference technique and a structured nonorthogonal body-fitted mesh is used for computations. The effect of Rayleigh number (Ra = 10³–10⁶), Darcy number (Da = 10^?4–10^?2) and undulations on the heat transfer, fluid flow, and entropy generation is investigated. It is found that average Nusselt number increases with Darcy number and number of undulations present on the left wall at fixed Darcy number.     

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.     

Study on Laminar Natural Convection Heat Transfer from a Hemisphere with Uniform Heat Flux Surface

By employing the modified model based on Bejan et al., laminar natural convection heat transfer from a hemisphere with uniform heat flux surface has been numerically investigated. Extensive results of two different surface boundary conditions are obtained for a wide range of Grashof numbers(10 ≤ Gr ≤ 10~7) and Prandlt number of 0.72. The characteristics of heat transfer and fluid flow are analyzed in terms of isotherm contours and streamline patterns, radial and tangential velocities, dimensionless temperature profiles, local friction and pressure drag coefficients, as well as local and average Nusselt numbers. Meanwhile, the effects of Grashof number and adiabatic surface on flow motion and heat transfer have been studied. No recirculation zone or flow separation generates over the top of the hemisphere compared to the isothermal sphere. Owing to the curvature effect, the maximum values of local friction and pressure drag coefficients appear at the corner point B. Comparisons with the previous results are also reported in detail. All the results are in good agreement with the numerical data. Moreover, both local and average Nusselt numbers show a positive dependence on Grashof number. The values of the non-adiabatic case are smaller than that of the adiabatic case due to the preheating effect. Finally, two precise and general correlations of average Nusselt number varying with Grashof numbers have been presented, which can provide an effective prediction for the heat transfer rate in engineering applications, and offer academic values for the future research.