Muneer A. Ismael

Natural Convection in Differentially Heated Partially Porous Layered Cavities Filled with a Nanofluid

Natural convection heat transfer in a differentially heated and vertically partially layered porous cavity filled with a nanofluid is studied numerically based on double–domain formulation. The left wall, which is adjacent to the porous layer, is isothermally heated, while the right wall is isothermally cooled. The top and bottom walls of the cavity are thermally insulated. Impermeable cavity walls are considered except the interface between the porous layer and the nanofluid layer. The Darcy–Brinkman model is invoked for the porous layer which is saturated with the same nanofluid. Equations govern the conservation of mass, momentum, and energy with the entity of nanoparticles in the fluid filling the cavity and that are saturated in the porous layer are modeled and solved numerically using under successive relaxation upwind finite difference scheme. The contribution of five parameters are studied, these are; nanoparticle volume fraction ϕ (0–0.1), porous layer thickness Xp(0–0.9), Darcy number Da (10−7–1), aspect ratio A (1, 2, 4), and Rayleigh number Ra (103–106). The nanofluid is considered to be composed of copper nanoparticles and water as a base fluid. The results have shown that with the aid of a nanofluid, the convective heat transfer can be enhanced even at a low permeable porous medium. It is found that when Ra ≤ 105, there is a critical porous layer thickness Xp at which the Nusselt number is maximum. Otherwise, the Nusselt number Nu decreases rapidly with Xp. Correlations of Nu with the other parameters are established and tested for A = 2.

Entropy Generation and Natural Convection of CuO-Water Nanofluid in C-Shaped Cavity under Magnetic Field

This paper investigates the entropy generation and natural convection inside a C-shaped cavity filled with CuO-water nanofluid and subjected to a uniform magnetic field. The Brownian motion effect is considered in predicting the nanofluid properties. The governing equations are solved using the finite volume method with the SIMPLE (Semi-Implicit Method for Pressure Linked Equations) algorithm. The studied parameters are the Rayleigh number (1000 ≤ Ra ≤ 15,000), Hartman number (0 ≤ Ha ≤ 45), nanofluid volume fraction (0 ≤ φ ≤ 0.06), and the cavity aspect ratio (0.1 ≤ AR ≤ 0.7). The results have shown that the nanoparticles volume fraction enhances the natural convection but undesirably increases the entropy generation rate. It is also found that the applied magnetic field can suppress both the natural convection and the entropy generation rate, where for Ra = 1000 and φ = 0.04, the percentage reductions in total entropy generation decreases from 96.27% to 48.17% for Ha = 45 compared to zero magnetic field when the aspect ratio is increased from 0.1 to 0.7. The results of performance criterion have shown that the nanoparticles addition can be useful if a compromised magnetic field value represented by a Hartman number of 30 is applied.

Conjugate Heat Transfer in a Porous Cavity Heated by a Triangular Thick Wall

The conjugate natural convection-conduction heat transfer in a square domain composed of a cavity heated by a triangular solid wall is studied under steady state condition. The vertical and horizontal walls of the triangular solid are kept isothermal and at the same hot temperature T h . The other boundaries surrounding the porous cavity are kept adiabatic except the right vertical wall, where it is kept isothermally at the lower temperature T c . Equations governing the heat transfer in the triangular wall and heat and fluid flow, based on the Darcy model, in the fluid-saturated porous medium together with the derived relation of the interface temperature are solved numerically using the second order central differences finite difference scheme with the successive over relaxation (SOR) method. The investigated parameters are the Rayleigh number Ra (100-1000), solid to fluid saturated porous medium thermal conductivity ratio Kr (0.1–10), and the triangular wall thickness D (0.05-1). The results are presented in the conventional form; contours of streamlines and isotherms and the local and average Nusselt numbers. An uncommon behavior of the heat transfer in the porous medium with the triangular wall thickness D is observed and accounted.

Magnetic Field Effect on Mixed Convection in Lid-Driven Trapezoidal Cavities Filled With a Cu–Water Nanofluid With an Aiding or Opposing Side Wall

The present study investigates mixed convection inside a Cu–water nanofluid filled trapezoidal cavity under the effect of a constant magnetic field. The mixed convection is achieved by the action of lid-driving of the right hot inclined side wall in the aiding or the opposing direction. The left inclined side wall is fixed and kept isothermal at a cold temperature. The horizontal top and bottom walls are fixed and thermally insulated. The magnetic field is imposed horizontally. The problem is formulated using the stream function-vorticity procedure and solved numerically using an efficient upwind finitedifference method. The studied parameters are: the Richardson number Ri1⁄4 (0.01–10), the Hartman number Ha1⁄4 (0–100), the volume fraction of Cu nanoparticles u1⁄4 (0–0.05), and the inclination angle of side walls U1⁄4 (66 deg, 70 deg, 80 deg). The results have shown that the suppression effect of the magnetic field for the aiding case is greater than that for the opposing case. Meanwhile, the enhancement of the Nusselt number due to the presence of the Cu nanoparticles is greater for opposing lid-driven case. [DOI: 10.1115/1.4033211]

Mixed Convection in Lid-Driven Trapezoidal Cavities with an Aiding or Opposing Side Wall

Mixed convection heat transfer and fluid flow fields inside a lid-driven trapezoidal cavity were studied numerically. The cavity horizontal walls were thermally insulated while the inclined side walls were maintained isothermally at different temperatures. Forced convection was induced by moving the hotter right inclined side wall. The problem is formulated using the stream function–vorticity procedure. Together with the established boundary conditions on the right moving wall, the problem is solved by the finite difference method. The Richardson number Ri (0.01–10) and inclination angle of the side walls Φ (66–80°) were considered as pertinent parameters and investigated in two lid-driven cases: aiding and opposing directions. The results show that the behavior of Nusselt number is different from Richardson number depending on the direction of the lid. The inclination angle of the side walls was found to have a significant effect on Nusselt number when Ri was relatively low (≤1); otherwise, a negligible effect of Φ on Nusselt number was recorded.

Mixed convection in a partially layered porous cavity with an inner rotating cylinder

ABSTRACT In this study, mixed convection in a cavity that has a fluid and superposed porous medium with an adiabatic rotating cylinder is numerically investigated. The bottom horizontal wall is heated and the top horizontal wall is cooled while the remaining walls are assumed to be adiabatic. An adiabatic rotating cylinder is inserted inside the cavity. The governing equations are solved by the Galerkin weighted residual finite element method. The effects of Rayleigh number (between 103 and 106), angular rotational speed of the cylinder (between 0 and 6,000), Darcy number (between 10−5 and 10−2), cylinder sizes (between R = 0.1 and R = 0.3) and three different vertical locations of the cylinder on the fluid flow and heat transfers characteristics are numerically investigated. It is observed that the cylinder size has a profound effect on the local and averaged heat transfer. The local and averaged heat transfers generally increase and the convection is more effective in the upper half of the cavity as the Rayleigh number and Darcy number enhance. The averaged heat transfers increases with the cylinder size until Ra = 105. The averaged heat transfer increases almost linearly with the angular rotational velocity of the cylinder and the increase rate becomes higher as the cylinder size increases. The local and averaged heat transfers enhances/deteriorate as the cylinder approaches the upper/lower wall of the cavity.

Numerical analysis of natural convection of Cu–water nanofluid filling triangular cavity with semicircular bottom wall

AbstractThis study provides numerical analysis of the free convection of copper–water-based nanofluid filling a triangular cavity with semicircular bottom wall. The cavity sidewalls are maintained at cold temperature, while the semicircular wall is maintained at hot temperature. The other wall segments are thermally insulated. To control the energy transport within the cavity, a uniform magnetic field is applied horizontally. The physical domain is discretized according to the control volume finite element method which has been used to solve the governing equations. The physical and geometrical aspects of the current problem are investigated by inspecting the impacts of Rayleigh number, Hartman number, aspect ratio and the volume fraction of the Cu nanoparticles. Decreasing the radius of the hot semicircle enlarges the average Nusselt number at the absence of the magnetic field. When the magnetic field is applied, this effect is conversed within Ra ≤ 104. This conversed impact does not hold up when Ra is raised to 105. The numerical results are correlated in a sophisticated correlation of the average Nusselt number with other parameters.

Mixed Convection in a Ventilated Cavity Filled with a Triangular Porous Layer

Mixed convection in a square cavity having a triangular porous layer and a local heater has been investigated numerically. The governing partial differential equations with corresponding boundary conditions have been solved by the finite difference method using the dimensionless stream function, vorticity and temperature formulation. The effects of the Richardson number (

Numerical Investigation of Mixed Convection and Entropy Generation in a Wavy-Walled Cavity Filled with Nanofluid and Involving a Rotating Cylinder

{ Ri} = 0.01 - 10