Mikhail A. Sheremet

Mixed convection in a lid-driven square cavity filled by a nanofluid

Steady laminar mixed convection inside a lid-driven square cavity filled with water based nanofluid is studied numerically. The cavity is subjected to the moving upper and lower walls. The top and bottom moving walls are maintained at constant temperatures and nanoparticle volume fractions. The vertical walls of the cavity are thermally insulated. The appliance of the numerical analysis was finite difference method with upwind scheme treatments of the convective terms included in the momentum and energy equations. The governing parameters are the Reynolds, Grashof, Prandtl and Lewis numbers along with the buoyancy-ratio, the Brownian motion, the thermophoresis and the moving parameters. The effects of these parameters on the local Nusselt, local Sherwood, the mean Nusselt and Sherwood numbers, as well as on the developments of streamlines, isotherms and isoconcentrations have been analyzed. The results have shown that these parameters have substantial effects on the flow and heat transfer characteristics. The comparison with known results from the open literature shows excellent agreement.

Unsteady Conjugate Natural Convection in a Vertical Cylinder Partially Filled with a Porous Medium

Transient natural convection in a vertical cylinder containing both a fluid layer overlying a horizontal porous layer saturated with the same fluid and heat-conducting solid shell of finite thickness in conditions of convective heat exchange with an environment has been studied numerically. The Beavers-Joseph empirical boundary condition is considered at the fluid-porous interface with the Darcy model for the porous layer and the Boussinesq approximation for the pure fluid. The governing equations formulated in dimensionless variables, such as the stream function, the vorticity, and the temperature have been solved by a finite difference method. Particular efforts have been focused on the effects of five types of influential factors, such as the Darcy number 10−5 ≤ Da ≤ 10−3, the porous layer height ratio 0 ≤ d/L ≤ 1, the solid shell thickness ratio 0.1 ≤ l/L ≤ 0.3, the thermal conductivity ratio 1 ≤ k1,3 ≤ 20, and the dimensionless time 0 ≤ τ ≤ 1000 on the fluid flow and heat transfer. Comprehensive analysis of an effect of these key parameters on the Nusselt number at the bottom wall, on the average temperature in the cavity, and on the maximum absolute value of the stream function has been conducted.

Free convection in a triangular cavity filled with a porous medium saturated by a nanofluid

Purpose – Steady-state free convection heat transfer in a right-angle triangular porous enclosure filled by a nanofluid using the mathematical nanofluid model proposed by Buongiorno has been numerically analyzed. The paper aims to discuss this issue. Design/methodology/approach – The nanofluid model takes into account the Brownian diffusion and thermophoresis effects. The governing equations formulated in terms of the vorticity-stream function variables were solved by finite difference method. Findings – It has been found that the average Nusselt number is an increasing function of the Rayleigh and Lewis numbers and a decreasing function of Brownian motion, buoyancy-ratio and thermophoresis parameters. At the same time the average Sherwood number is an increasing function of the Rayleigh and Lewis numbers, Brownian motion and thermophoresis parameters and a decreasing function of buoyancy-ratio parameter. Originality/value – The present results are new and original for the heat transfer and fluid flow in ...

Numerical simulation of turbulent natural convection combined with surface thermal radiation in a square cavity

Purpose – The purpose of this paper is to present transient turbulent natural convection with surface thermal radiation in a square differentially heated enclosure using non-primitive variables like stream function and vorticity. Design/methodology/approach – The governing equations formulated in dimensionless variables “stream function, vorticity and temperature,” within the Boussinesq approach taking into account the standard two equation k-e turbulence model with physical boundary conditions have been solved using an iterative implicit finite-difference method. Findings – It has been found that using of the presented algebraic transformation of the mesh allows to effectively conduct numerical analysis of turbulent natural convection with thermal surface radiation. It has been shown that the average convective Nusselt number increases with the Rayleigh number and decreases with the surface emissivity, while the average radiative Nusselt number is an increasing function of these key parameters. It has be...

Convective heat transfer of ferrofluid in a lid-driven cavity with a heat-conducting solid backward step under the effect of a variable magnetic field

ABSTRACT The effect of variable magnetic field on the mixed convective flow of a ferrofluid within a lid-driven cavity has been analyzed numerically. A heat-conducting solid block is located in the bottom part of the cavity. Governing partial differential equations have been formulated taking into account that the magnetic source is a point source located over the moving lid. Analysis has been performed for a wide range of Hartmann number, nanoparticles volume fraction, and magnetic number. It has been found that the growth of the magnetic number leads to the heat transfer enhancement.

Free convection in a square porous cavity filled with a nanofluid using thermal non equilibrium and Buongiorno models

Purpose – The purpose of this paper is to theoretically analysis the steady-state natural convection flow and heat transfer of nanofluids in a square enclosure filled with a porous medium saturated with a nanofluid considering local thermal non-equilibrium (LTNE) effects. Different local temperatures for the solid phase of the nanoparticles, the solid phase of porous matrix and the liquid phase of the base fluid are taken into account. Design/methodology/approach – The Buongiorno’s model, incorporating the Brownian motion and thermophoresis effects, is utilized to take into account the migration of nanoparticles. Using appropriate non-dimensional variables, the governing equations are transformed into the non-dimensional form, and the finite element method is utilized to solve the governing equations. Findings – The results show that the increase of buoyancy ratio parameter (Nr) decreases the magnitude of average Nusselt number. The increase of the nanoparticles-fluid interface heat transfer parameter (Nh...

Effect of surface radiation on transient natural convection in a wavy-walled cavity

ABSTRACT Transient natural convection in a differentially heated square cavity that has one vertical wavy wall has been studied numerically. The domain of interest is bounded by vertical isothermal walls and horizontal adiabatic walls. The governing equations formulated in dimensionless stream function, vorticity, and temperature, within the Boussinesq approximation with corresponding initial and boundary conditions, have been solved using an iterative implicit finite-difference method. The main objective is to investigate the effect of the dimensionless time 0 ≤ τ ≤ 0.4, Rayleigh number 104 ≤Ra ≤ 106, surface emissivity 0 ≤ ε < 1, undulations number 1 ≤ κ ≤ 6, and shape parameter 0.6 ≤ a ≤ 1.4 on fluid flow and heat transfer. Results are presented in the form of streamlines, isotherms, and distribution of average total Nusselt number at the wavy wall.

Natural convection combined with thermal radiation in a square cavity filled with a viscoelastic fluid

The purpose of this paper is to study natural convective heat transfer and viscoelastic fluid flow in a differentially heated square cavity under the effect of thermal radiation.,The cavity filled with a viscoelastic fluid is heated uniformly from the left wall and cooled from the right side while insulated from horizontal walls. Governing partial differential equations formulated in non-dimensional stream function, vorticity and temperature with corresponding boundary conditions have been solved by finite difference method of second order accuracy. The effects of Rayleigh number (Ra = 1e+3−1e+5), radiation parameter (Rd = 0 − 10), Prandtl number (Pr = 1 − 30) and elastic number (E = 0.0001 − 0.001) on flow patterns, temperature fields, average Nusselt number at hot vertical wall and rate of fluid flow have been studied.,It has been found that a growth of elastic number leads to the heat transfer reduction and convective flow attenuation. The heat conduction is a dominating heat transfer mechanism for high values of radiation parameter.,The originality of this work is to analyze heat transfer and fluid flow of a viscoelastic fluid inside a differentially heated cavity. The results would benefit scientists and engineers to become familiar with the flow and heat behavior of non-Newtonian fluids, and the way to predict the properties of this flow for possibility of using viscoelastic fluids in compact heat exchangers, electronic cooling systems, polymer engineering, etc.

Radiation effect on conjugate turbulent natural convection in a cavity with a discrete heater

A numerical study of a conjugate turbulent natural convection with thermal surface radiation inside a square cavity with heat-conducting solid walls and a local heat source has been performed. Two-dimensional equations for conservation of mass, momentum and energy using k turbulence model with a heat conduction equation inside the solid walls and corresponding boundary conditions have been solved using the finite difference method. The developed numerical method can be widely used in some engineering problems, such as the simulation of heat and mass transfer in heat-generating elements in power engineering. Discrete heater has been simulated by a heat source of constant temperature centrally located on the bottom wall. Numerical solutions have been obtained for Ra=109 and different values of surface emissivity (0<1) and thermal conductivity ratio (10 1,2 1000). It has been found that an increase in surface emissivity and thermal conductivity ratio leads to a growth of the average total Nusselt number, while a rise of surface emissivity only illustrates a reduction of the average convective Nusselt number. The obtained numerical results are useful for predicting the convective and radiative heat transfer in domain similar to the one under consideration.