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Ioan Pop - One of the best experts on this subject based on the ideXlab platform.
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Free Convection inside a porous square cavity with convective boundary condition using spline functions
'Springer Science and Business Media LLC', 2021Co-Authors: Sanda Micula, Ioan PopAbstract:Abstract In this paper, we consider the problem of Free Convection in a square cavity filled with a porous medium with convective boundary condition on the left wall of the cavity. We first transform the governing equations transformed in terms of dimensionless variables and then solve them numerically using a cubic spline colocation method. We discuss the effects of two very important parameters, the Biot (Bi) and Rayleigh (Ra) numbers. We perform a comparison of the average Nusselt number N u ‾ $\overline{Nu}$ at the hot wall with results from the open literature. We can notice that the comparison is very good, which gives us strong confidence that this cubic spline collocation method works very efficiently for such problems. We also state that the present problem has not been considered before by any researcher
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Free Convection in Shallow and Slender Porous Cavities Filled by a Nanofluid Using Buongiorno's Model
Journal of Heat Transfer, 2014Co-Authors: Mikhail A Sheremet, Teodor Grosan, Ioan PopAbstract:A numerical study of the steady Free Convection flow in shallow and slender porous cavities filled by a nanofluid is presented. The nanofluid model takes into account the Brownian diffusion and the thermophoresis effects. The governing dimensional partial differential equations are transformed into a dimensionless form before being solved numerically using a finite difference method. Effort has been focused on the effects of four types of influential factors such as the aspect ratio, the Rayleigh and Lewis numbers, and the buoyancy-ratio parameter on the fluid flow and heat transfer characteristics.
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effect of the source term on steady Free Convection boundary layer flows over an vertical plate in a porous medium part i
Transport in Porous Media, 2007Co-Authors: E Magyari, Ioan Pop, Adrian PostelnicuAbstract:The problem of steady Free Convection boundary layer over a vertical isothermal impermeable flat plate which is embedded in a fluid-saturated porous medium with volumetric heat generation or absorption is studied in this paper using the Darcy equation model. The case of the externally prescribed source terms S = S(x,y) is considered in this paper. It is shown that the corresponding boundary value problem depends on the sign of the plate temperature, which implies that the source term breaks the usual upflow or downflow symmetry of the Free Convection problem. Looking for similarity solutions, analytical and numerical solutions of the transformed boundary value problem are obtained for several values of the problem parameters. It is also shown that, contrary to the widely spread opinion, the exponential form of the internal heat generation term is not a necessary requirement of similarity reduction.
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Free Convection in a wavy cavity filled with a porous medium
International Journal of Heat and Mass Transfer, 2005Co-Authors: Aydin Misirlioglu, Cihat A Baytas, Ioan PopAbstract:Abstract The steady-state Free Convection inside a cavity made of two horizontal straight walls and two vertical bent-wavy walls and filled with a fluid-saturated porous medium is numerically investigated in the present paper. The wavy walls are assumed to follow a profile of cosine curve. The horizontal walls are kept adiabatic, while the bent-wavy walls are isothermal but kept at different temperatures. The Darcy and energy equations (in non-dimensional stream function and temperature formulation) are solved numerically using the Galerkin Finite Element Method (FEM). Flow and heat transfer characteristics (isothermal, streamlines and local and average Nusselt numbers) are investigated for some values of the Rayleigh number, cavity aspect ratio and surface waviness parameter. The present results are compared with those reported in the open literature for a square cavity with straight walls. It was found that these results are in excellent agreement.
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transient Free Convection in a square cavity filled with a porous medium
International Journal of Heat and Mass Transfer, 2004Co-Authors: Nawaf H Saeid, Ioan PopAbstract:Abstract Transient Free Convection in a two-dimensional square cavity filled with a porous medium is numerically studied in this paper. The left vertical wall is suddenly heated to a constant temperature T h , while the right wall is suddenly cooled to a constant temperature T c by equal amount relative to an initially uniform temperature distribution. Both the horizontal walls are adiabatic. The finite volume numerical method is used to solve the non-dimensional governing equations. The results are obtained for the initial transient state up to the steady state, and for Rayleigh number values of 10 2 –10 4 . It is observed that the average Nusselt number showing an undershoot during the transient period and that the time required to reach the steady state is longer for low Rayleigh number and shorter for high Rayleigh number.
M. Sheikholeslami - One of the best experts on this subject based on the ideXlab platform.
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Free Convection of fe3o4 water nanofluid under the influence of an external magnetic source
Journal of Molecular Liquids, 2017Co-Authors: M. Sheikholeslami, D D GanjiAbstract:Abstract Influence of external magnetic source on Free Convection of ferrofluid is reported in this paper. Obtaining systems have been solved through Control volume based finite element method. Influences of Rayleigh, Hartmann numbers, size of inner cylinder and volume fraction of Fe 3 O 4 on hydrothermal characteristics are presented. Results indicate that both temperature gradient and nanofluid velocity decease with augment of Hartmann number. Thermal boundary layer thickness reduces with augment of r in . Nusselt number decreases with rise of Lorentz forces while it enhances with rise of buoyancy forces.
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transportation of mhd nanofluid Free Convection in a porous semi annulus using numerical approach
Chemical Physics Letters, 2017Co-Authors: M. Sheikholeslami, D D GanjiAbstract:Abstract Nanofluid Free Convection in presence of Lorentz forces in a permeable semi annulus is simulated using Control Volume based Finite Element Method. Impact of porous media on governing equations is considered by means of Darcy law. Brownian motion impact on properties of nanofluid is taken into account using Koo-Kleinstreuer-Li (KKL) model. Important parameters are inclination angle ( ξ ) , CuO-water volume fraction ( ϕ ) , Hartmann ( Ha ) and Rayleigh ( Ra ) numbers for porous medium. A formula for Nuave is provided. Results indicated that temperature gradient detracts with enhance of Ha but it enhances with rise of ξ , Ra . Heat transfer augmentation enhances with rise of Lorentz forces.
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influence of induced magnetic field on Free Convection of nanofluid considering koo kleinstreuer li kkl correlation
Applied Sciences, 2016Co-Authors: M. Sheikholeslami, Q Zaigham M Zia, R EllahiAbstract:In this paper, the influence of induced magnetic field on Free Convection of Al2O3-water nanofluid on permeable plate by means of Koo-Kleinstreuer-Li (KKL) model is reported. Impact of Brownian motion, along with the properties of nanofluid, are also taken into account. The resulting equations are solved utilizing Runge-Kutta integration method. Obtained results are examined for innumerable energetic parameters, namely Al2O3 volume fraction, suction parameter, and Hartmann and magnetic Prandtl numbers. Results indicate that the velocity profile reduces with rise of the suction parameter and magnetic Prandtl and Hartmann numbers but it increases with addition of nanoparticles. Shear stress enhances with rise of suction parameter, magnetic Prandtl and Hartmann numbers. Temperature gradient improves with augment of suction parameter.
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Free Convection of magnetic nanofluid considering mfd viscosity effect
Journal of Molecular Liquids, 2016Co-Authors: M. Sheikholeslami, M M Rashidi, Tasawar Hayat, D D GanjiAbstract:Abstract In this study effect of magnetic field dependent (MFD) viscosity on Free Convection heat transfer of nanofluid in an enclosure is investigated. The bottom wall has constant flux heating element. Single phase nanofluid model is utilized considering Brownian motion. Control Volume based Finite Element Method is applied to simulate this problem. The effects of viscosity parameter, Hartmann number and Rayleigh number on hydrothermal behavior have been examined. Results show that Nusselt number is an increasing function of Rayleigh number and volume fraction of nanoparticle while it is a decreasing function of viscosity parameter and Hartmann number. Also it can be found that reduction of Nusselt number due to MFD viscosity effect are more sensible for high Rayleigh number and low Hartmann number.
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mhd Free Convection in an eccentric semi annulus filled with nanofluid
Journal of The Taiwan Institute of Chemical Engineers, 2014Co-Authors: M. Sheikholeslami, M Gorjibandpy, D D GanjiAbstract:Abstract In this study magnetohydrodynamic effect on Free Convection of nanofluid in an eccentric semi-annulus filled is considered. The effective thermal conductivity and viscosity of nanofluid are calculated by the Maxwell–Garnetts (MG) and Brinkman models, respectively. Lattice Boltzmann method is applied to simulate this problem. This investigation compared with other works and found to be in excellent agreement. Effects of the Hartmann number, nanoparticle volume fraction, Rayleigh numbers and position of the inner circular cylinder on flow and heat transfer characteristics are examined. Also a correlation of Nusselt number corresponding to active parameters is presented. The results show that Nusselt number has direct relationship with nanoparticle volume fraction and Rayleigh number but it has inverse relationship with Hartmann number and position of inner cylinder at high Rayleigh number. Also it can be concluded that heat transfer enhancement increases with increase of Hartmann number and decreases with augment of Raleigh number.
Sharidan Shafie - One of the best experts on this subject based on the ideXlab platform.
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Unsteady Free Convection Flow between Two Vertical Parallel Plates with Newtonian Heating
MATEMATIKA, 2019Co-Authors: Fasihah Zulkiflee, Ahmad Qushairi Mohamad, Sharidan Shafie, Arshad KhanAbstract:Free Convection flow in a boundary layer region is a motion that results from the interaction of gravity with density differences within a fluid. These differences occur due to temperature or concentration gradients or due to their composition. Studies pertaining Free Convection flows of incompressible viscous fluids have received much attention in recent years both theoretically (exact or approximate solutions) and experimentally. The situation where the heat be transported to the convective fluid via a bounding surface having finite heat capacity is known as Newtonian heating (or conjugate convective flows). In this paper, the unsteady Free Convection flow of an incompressible viscous fluid between two parallel plates with Newtonian heating is studied. Appropriate non-dimensional variables are used to reduce the dimensional governing equations along with imposed initial and boundary conditions into dimensionless forms. The exact solutions for velocity and temperature are obtained using the Laplace transform technique. The corresponding expressions for skin friction and Nusselt number are also calculated. The graphical results are displayed to illustrate the influence of various embedded parameters such as Newtonian heating parameter and Grashof number. The results show that the effect of Newtonian heating parameter increases the Nusselt number but reduces the skin friction.
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exact solutions for Free Convection flow of nanofluids with ramped wall temperature
European Physical Journal Plus, 2015Co-Authors: Asma Khalid, Ilyas Khan, Sharidan ShafieAbstract:This article aims to study the unsteady Convection flow of nanofluids induced by Free Convection and the oscillating plate condition. The fluid is confined to the region over an infinite vertical flat plate with ramped wall temperature. Five different types of water-based nanofluids containing copper (Cu), silver (Ag), copper oxide (CuO), alumina ( Al2O3 and titanium oxide (TiO2 are chosen for this analysis. The Laplace transform technique is applied to obtain exact solutions of velocity and temperature for both cases of ramp and isothermal plate conditions. Ramp and isothermal solutions are compared graphically and it is found that the ramp velocity and the temperature are smaller in magnitude than isothermal velocity and temperature. Corresponding expressions for skin-friction and Nusselt number are also evaluated. The results are plotted for various physical parameters contained in the governing equations and discussed in details. Comparison with earlier results provides an excellent agreement.
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unsteady magnetohydrodynamic Free Convection flow of a second grade fluid in a porous medium with ramped wall temperature
PLOS ONE, 2014Co-Authors: Sohail Ahmad, Ilyas Khan, Dumitru Vieru, Sharidan ShafieAbstract:Magnetic field influence on unsteady Free Convection flow of a second grade fluid near an infinite vertical flat plate with ramped wall temperature embedded in a porous medium is studied. It has been observed that magnitude of velocity as well as skin friction in case of ramped temperature is quite less than the isothermal temperature. Some special cases namely: (i) second grade fluid in the absence of magnetic field and porous medium and (ii) Newtonian fluid in the presence of magnetic field and porous medium, performing the same motion are obtained. Finally, the influence of various parameters is graphically shown.
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closed form solutions for unsteady Free Convection flow of a second grade fluid over an oscillating vertical plate
PLOS ONE, 2014Co-Authors: Farhad Ali, Ilyas Khan, Sharidan ShafieAbstract:Closed form solutions for unsteady Free Convection flows of a second grade fluid near an isothermal vertical plate oscillating in its plane using the Laplace transform technique are established. Expressions for velocity and temperature are obtained and displayed graphically for different values of Prandtl number Pr, thermal Grashof number Gr, viscoelastic parameter α, phase angle ωτ and time τ. Numerical values of skin friction τ0 and Nusselt number Nu are shown in tables. Some well-known solutions in literature are reduced as the limiting cases of the present solutions.
Ilyas Khan - One of the best experts on this subject based on the ideXlab platform.
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exact solutions for Free Convection flow of generalized jeffrey fluid a caputo fabrizio fractional model
alexandria engineering journal, 2017Co-Authors: Muhammad Saqib, Farhad Ali, Ilyas Khan, Nadeem Ahmad Sheikh, Syed Aftab Alam JanAbstract:Abstract The present article reports the applications of Caputo-Fabrizio time-fractional derivatives. This article generalizes the idea of Free Convection flow of Jeffrey fluid over a vertical static plate. The Free Convection is caused due to the temperature gradient. Therefore, heat transfer is considered for Free Convection. The classical model for Jeffrey fluid is written in dimensionless form with the help of non-dimensional variables. Furthermore, the dimensionless model is converted into a fractional model called as a generalized Jeffrey fluid model. The governing equations of generalized Jeffrey fluid model have been solved analytically using the Laplace transform technique. The recovery of existing solutions in the open literature is possible through this work in terms of classical Jeffrey fluid, fractional Newtonian fluid as well as classical Newtonian fluid. For various embedded parameters, the physics of velocity and temperature profiles is studied by means of numerical computation. This report provides a detailed discussion as well as a graphical representation of the obtained results.
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application of caputo fabrizio derivatives to mhd Free Convection flow of generalized walters b fluid model
European Physical Journal Plus, 2016Co-Authors: Farhad Ali, Muhammad Saqib, Ilyas Khan, Nadeem Ahmad SheikhAbstract:The present article applies the idea of Caputo-Fabrizio time fractional derivatives to magnetohydrodynamics (MHD) Free Convection flow of generalized Walters’-B fluid over a static vertical plate. Free Convection is caused due to combined gradients of temperature and concentration. Hence, heat and mass transfers are considered together. The fractional model of Walters’-B fluid is used in the mathematical formulation of the problem. The problem is solved via the Laplace transform method. Exact solutions for velocity, temperature and concentration are obtained. The physical quantities of interest are examined through plots for various values of fractional parameter: \(\alpha\), Walters’-B parameter \(\Gamma\), magnetic parameter M , Prandtl number Pr, Schmidt number Sc, thermal Grashof number Gr and mass Grashof number Gm. As a special case, the published results from open literature are recovered.
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exact solutions for Free Convection flow of nanofluids with ramped wall temperature
European Physical Journal Plus, 2015Co-Authors: Asma Khalid, Ilyas Khan, Sharidan ShafieAbstract:This article aims to study the unsteady Convection flow of nanofluids induced by Free Convection and the oscillating plate condition. The fluid is confined to the region over an infinite vertical flat plate with ramped wall temperature. Five different types of water-based nanofluids containing copper (Cu), silver (Ag), copper oxide (CuO), alumina ( Al2O3 and titanium oxide (TiO2 are chosen for this analysis. The Laplace transform technique is applied to obtain exact solutions of velocity and temperature for both cases of ramp and isothermal plate conditions. Ramp and isothermal solutions are compared graphically and it is found that the ramp velocity and the temperature are smaller in magnitude than isothermal velocity and temperature. Corresponding expressions for skin-friction and Nusselt number are also evaluated. The results are plotted for various physical parameters contained in the governing equations and discussed in details. Comparison with earlier results provides an excellent agreement.
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unsteady magnetohydrodynamic Free Convection flow of a second grade fluid in a porous medium with ramped wall temperature
PLOS ONE, 2014Co-Authors: Sohail Ahmad, Ilyas Khan, Dumitru Vieru, Sharidan ShafieAbstract:Magnetic field influence on unsteady Free Convection flow of a second grade fluid near an infinite vertical flat plate with ramped wall temperature embedded in a porous medium is studied. It has been observed that magnitude of velocity as well as skin friction in case of ramped temperature is quite less than the isothermal temperature. Some special cases namely: (i) second grade fluid in the absence of magnetic field and porous medium and (ii) Newtonian fluid in the presence of magnetic field and porous medium, performing the same motion are obtained. Finally, the influence of various parameters is graphically shown.
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closed form solutions for unsteady Free Convection flow of a second grade fluid over an oscillating vertical plate
PLOS ONE, 2014Co-Authors: Farhad Ali, Ilyas Khan, Sharidan ShafieAbstract:Closed form solutions for unsteady Free Convection flows of a second grade fluid near an isothermal vertical plate oscillating in its plane using the Laplace transform technique are established. Expressions for velocity and temperature are obtained and displayed graphically for different values of Prandtl number Pr, thermal Grashof number Gr, viscoelastic parameter α, phase angle ωτ and time τ. Numerical values of skin friction τ0 and Nusselt number Nu are shown in tables. Some well-known solutions in literature are reduced as the limiting cases of the present solutions.
J. Zueco - One of the best experts on this subject based on the ideXlab platform.
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Hydromagnetic Free Convection flow with induced magnetic field effects
Meccanica, 2010Co-Authors: S. K. Ghosh, O. Anwar Bég, J. ZuecoAbstract:An exact solution is presented for the hydromagnetic natural Convection boundary layer flow past an infinite vertical flat plate under the influence of a transverse magnetic field with magnetic induction effects included. The transformed ordinary differential equations are solved exactly, under physically appropriate boundary conditions. Closed-form expressions are obtained for the non-dimensional velocity ( u ), non-dimensional induced magnetic field component ( B _ x ) and wall frictional shearing stress i.e. skin friction function ( τ _ x ) as functions of dimensionless transverse coordinate ( η ), Grashof Free Convection number ( G _ r ) and the Hartmann number ( M ). The bulk temperature in the boundary layer ( Θ ) is also evaluated and shown to be purely a function of M . The Rayleigh flow distribution ( R ) is derived and found to be a function of both Hartmann number ( M ) and the buoyant diffusivity parameter ( ϑ ^*). The influence of Grashof number on velocity, induced magnetic field and wall shear stress profiles is computed. The response of Rayleigh flow distribution to Grashof numbers ranging from 2 to 200 is also discussed as is the influence of Hartmann number on the bulk temperature. Rayleigh flow is demonstrated to become stable with respect to the width of the boundary layer region and intensifies with greater magnetic field i.e. larger Hartman number M , for constant buoyant diffusivity parameter ϑ ^*. The induced magnetic field ( B _ x ), is elevated in the vicinity of the plate surface with a rise in Free Convection (buoyancy) parameter G _ r , but is reduced over the central zone of the boundary layer regime. Applications of the study include laminar magneto-aerodynamics, materials processing and MHD propulsion thermo-fluid dynamics.
