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I. Pop - One of the best experts on this subject based on the ideXlab platform.
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Non-Darcy mixed convection of hybrid nanofluid with Thermal Dispersion along a vertical plate embedded in a porous medium
International Communications in Heat and Mass Transfer, 2020Co-Authors: Najiyah Safwa Khashi’ie, Norihan Md. Arifin, I. PopAbstract:Abstract The mixed convection flow of Cu-Al2O3/water nanofluid along a vertical plate embedded in a porous medium is numerically analyzed. Non-Darcy equation for porous medium with the Thermal Dispersion representation is used to model the present boundary layer problem. The reduced ordinary differential equations are computed using the bvp4c solver. The validation analysis shows a positive agreement between previous published and present results in few cases. The results imply that in the opposing buoyancy region, the dual solutions are expected, and the laminar boundary layer flow starts separating from the plate. The use of hybrid Cu-Al2O3/water nanofluid and increment of Thermal Dispersion parameter can extend the separation point. Moreover, the heat transfer rate and skin friction coefficient of Cu-Al2O3/water are greater than the pure water and Cu/water. The opposing flow shows a distinct behavior from the aiding flow.
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Free convection in a porous wavy cavity filled with a nanofluid using Buongiorno's mathematical model with Thermal Dispersion effect
Applied Mathematics and Computation, 2017Co-Authors: Mikhail A. Sheremet, Cornelia Revnic, I. PopAbstract:Abstract A numerical study of natural convection inside a porous wavy cavity filled with a nanofluid under the effect of Thermal Dispersion has been carried out using the Forchheimer–Buongiorno approach. The left boundary of the cavity is a wavy isoThermal wall while the rest are flat isoThermal walls. All boundaries are assumed to be impermeable to the base fluid and nanoparticles. The governing equations formulated in dimensionless stream function, temperature and nanoparticle volume fraction variables have been solved using implicit finite difference schemes of the second order accuracy. The effects of the Rayleigh number, undulation number, Thermal Dispersion parameter and flow inertia parameter on the average Nusselt number along the hot bottom wall, as well as on the streamlines, isotherms and isoconcentrations have been analyzed. It has been revealed the heat transfer enhancement with Rayleigh number, undulation number and Dispersion parameter. While convective flow is attenuated with a growth of undulation number, Dispersion parameter and flow inertia parameter. More essential homogenization of nanoparticles distribution inside the cavity occurs with an increase in Rayleigh number and a decrease in undulation number.
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Effect of Thermal Dispersion on transient natural convection in a wavy-walled porous cavity filled with a nanofluid: Tiwari and Das’ nanofluid model
International Journal of Heat and Mass Transfer, 2016Co-Authors: Mikhail A. Sheremet, I. Pop, Norfifah BachokAbstract:Abstract Transient natural convection in a porous wavy-walled cavity filled with a nanofluid has been studied numerically. The domain of interest is bounded by vertical flat and horizontal wavy walls having constant temperatures. The unsteady governing equations formulated in dimensionless stream function and temperature, within the Darcy–Boussinesq approximation and the mathematical nanofluid model proposed by Tiwari and Das in the presence of Thermal Dispersion with corresponding initial and boundary conditions have been solved numerically using an iterative implicit finite-difference method. The main objective is to investigate the effect of the dimensionless time, Thermal Dispersion parameter and solid volume fraction parameter of nanoparticles on the fluid flow and heat transfer characteristics. Results are presented in the form of streamlines, isotherms and distributions of the average Nusselt number at the bottom wavy wall.
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Non-Darcy mixed convection flow with Thermal Dispersion on a vertical cylinder in a saturated porous medium
Acta Mechanica, 1993Co-Authors: M. Kumari, G. Nath, I. PopAbstract:The non-Darcy mixed convection flow on a vertical cylinder embedded in a saturated porous medium has been studied taking into account the effect of Thermal Dispersion. Both forced flow and buoyancy force dominated cases with constant wall temperature condition have been considered. The governing partial differential equations have been solved numerically using the Keller box method. The results are presented for the buoyancy parameter which cover the entire regime of mixed convection flow ranging from pure forced convection to pure free convection. The effect of Thermal Dispersion is found to be more pronounced on the heat transfer than on the skin friction and it enhances the heat transfer but reduces the skin friction.
E. G. Bautista - One of the best experts on this subject based on the ideXlab platform.
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Thermal Dispersion driven by the spontaneous imbibition process
Applied Mathematical Modelling, 2010Co-Authors: O. Bautista, Federico Méndez, E. G. BautistaAbstract:Abstract In this work, we have theoretically analyzed the Thermal Dispersion process under the influence of the spontaneous imbibition of a liquid trapped in a capillary element, considering the presence of a uniform temperature gradient. The capillary element is represented by a porous medium which is initially found at temperature T0 and pressure P0. Suddenly, the lower part of the porous medium touches a liquid reservoir at temperature Tl and pressure P0. This contact between both phases, in turn causes spontaneously the imbibition process. Using a one-dimensional formulation of the average conservation laws, we derive the corresponding nondimensional momentum and energy equations. The numerical solutions permit us to evaluate the position and velocity of the imbibition front as well as the temperature profiles and Nusselt numbers. The above results are shown by taking into account the influence of three dimensionless parameters: the ratio of the characteristic Thermal time to the characteristic imbibition time, β, the ratio of the hydrostatic head of the imbibed liquid to the characteristic pressure difference for the imbibition front, α, and the ratio of the dispersive Thermal diffusivity to the effective Thermal diffusivity of the medium, Ω. The predictions show that temperature profiles and the heat transfer process are strongly dependent on Thermal Dispersion effects, indicating a clear deviation in comparison with the case of Ω = 0 that represents the absence of the Thermal Dispersion.
O. Bautista - One of the best experts on this subject based on the ideXlab platform.
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Thermal Dispersion driven by the spontaneous imbibition process
Applied Mathematical Modelling, 2010Co-Authors: O. Bautista, Federico Méndez, E. G. BautistaAbstract:Abstract In this work, we have theoretically analyzed the Thermal Dispersion process under the influence of the spontaneous imbibition of a liquid trapped in a capillary element, considering the presence of a uniform temperature gradient. The capillary element is represented by a porous medium which is initially found at temperature T0 and pressure P0. Suddenly, the lower part of the porous medium touches a liquid reservoir at temperature Tl and pressure P0. This contact between both phases, in turn causes spontaneously the imbibition process. Using a one-dimensional formulation of the average conservation laws, we derive the corresponding nondimensional momentum and energy equations. The numerical solutions permit us to evaluate the position and velocity of the imbibition front as well as the temperature profiles and Nusselt numbers. The above results are shown by taking into account the influence of three dimensionless parameters: the ratio of the characteristic Thermal time to the characteristic imbibition time, β, the ratio of the hydrostatic head of the imbibed liquid to the characteristic pressure difference for the imbibition front, α, and the ratio of the dispersive Thermal diffusivity to the effective Thermal diffusivity of the medium, Ω. The predictions show that temperature profiles and the heat transfer process are strongly dependent on Thermal Dispersion effects, indicating a clear deviation in comparison with the case of Ω = 0 that represents the absence of the Thermal Dispersion.
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Influence of Thermal Dispersion on spontaneous imbibition process in a homogeneous porous medium
2008Co-Authors: O. Bautista, Federico Méndez, E. BautistaAbstract:In this work we analyze the effect of Thermal Dispersion on spontaneous imbibition process of a fluid in a homogeneous porous medium, considering that it is subject to the presence of a temperature gradient. We assume that the porous medium is found initially at temperature T0 and pressure P0; suddenly the lower part touches a liquid reservoir with temperature T1 and pressure P0 and begins the spontaneous imbibition process into de porous medium. The physical influence of three nondimensional parameters such as the ratio of the characteristic Thermal time to the characteristic imbibition time, β, the ratio of the hydrostatic head of the imbibided fluid to the characteristic pressure difference between the imbibition front and the dry zone of the porous medium, α, and Ω defined as the ratio of Thermal Dispersion effect to Thermal diffusivity of the medium, serve us to evaluate the position and velocity of the imbibition front as well as the temperature profiles and the corresponding Nusselt number in the wetting zone. In particular for small values of time, we recover the well known Washburn law. The numerical predictions show that the imbibition and temperature profiles depend strongly on the above nondimensional parameters, revealing a clear deviation from the simple Washburn law.
Omar Rafae Alomar - One of the best experts on this subject based on the ideXlab platform.
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Analysis of variable porosity, Thermal Dispersion, and local Thermal non-equilibrium on two-phase flow inside porous media
Applied Thermal Engineering, 2019Co-Authors: Omar Rafae AlomarAbstract:Abstract This work involves the numerical simulations of two-phase flow inside porous media and the associated phase change processes in order to investigate the effects of Thermal Dispersion and variable porosity near the wall boundary. The modified enthalpy formulation has been employed. The mathematical model for the conservation of energy is based on the assumption of Local Thermal Non-Equilibrium (LTNE) condition. The relevant parameters such as free stream porosity, pore diameter, Thermal conductivity of the solid phase, heat flux and Reynolds number have been used to analyse the significance of the above mentioned effects. The governing equations have been discretised using the Finite Volume Method (FVM). The developed two-dimensional code has been validated against experimental data, which definitely display that there is a good agreement between them. The numerical results indicated that considering the effects of Thermal Dispersion and variable porosity is significant, particularly near the heated wall. It is also observed that those two effects become more pronounced for the large values of pore diameter, free stream porosity and Reynolds number. The effect of variations in the free stream porosity, Reynolds number and the pore diameter becomes substantial near the wall when Thermal Dispersion and variable porosity effects are included, whereas the effect of variations in the heat flux and Thermal conductivity of the solid phase have minor influence on the temperature distribution near the heated wall. It is evident that adding the effect of variable porosity and Thermal Dispersion have significant impact on the initiation and termination of phase change process, especially in the superheated vapour region as compared to the results that obtained by excluding those two effects. In general, it has been found that the present model provides a lower maximum fluid temperature near the wall as compared to that obtained by excluding those effects. Therefore, excluding these effects may lead to inaccurate predictions of two-phase flow with phase change process inside porous media. Most importantly, the Thermal Dispersion in the transverse direction plays an important role in the Dispersion phenomenon inside porous media owing to the Thermal boundary layer growth is more dependent on the transverse diffusion as compared to the axial diffusion.
Akira Nakayama - One of the best experts on this subject based on the ideXlab platform.
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Thermal Dispersion in Porous Media—A Review on the Experimental Studies for Packed Beds
Applied Mechanics Reviews, 2013Co-Authors: Turkuler Ozgumus, Moghtada Mobedi, Unver Ozkol, Akira NakayamaAbstract:Thermal Dispersion is an important topic in the convective heat transfer in porous media. In order to determine the heat transfer in a packed bed, the effective Thermal conductivity including both stagnant and Dispersion Thermal conductivities should be known. Several theoretical and experimental studies have been performed on the determination of the effective Thermal conductivity. The aim of this study is to review the experimental studies done on the determination of the effective Thermal conductivity of the packed beds. In this study, firstly brief information on the definition of the Thermal Dispersion is presented and then the reported experimental studies on the determination of the effective Thermal conductivity are summarized and compared. The reported experimental methods are classified into three groups: (1) heat addition/removal at the lateral boundaries, (2) heat addition at the inlet/outlet boundary, (3) heat addition inside the bed. For each performed study, the experimental details, methods, obtained results, and suggested correlations for the determination of the effective Thermal conductivity are presented. The similarities and differences between experimental methods and reported studies are shown by tables. Comparison of the correlations for the effective Thermal conductivity is made by using figures and the results of the studies are discussed.
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Effects of Thermal Dispersion on heat transfer in cross-flow tubular heat exchangers
Heat and Mass Transfer, 2011Co-Authors: Yoshihiko Sano, Fujio Kuwahara, Moghtada Mobedi, Akira NakayamaAbstract:Effects of Thermal Dispersion on heat transfer and temperature field within cross-flow tubular heat exchangers are investigated both analytically and numerically, exploiting the volume averaging theory in porous media. Thermal Dispersion caused by fluid mixing due to the presence of the obstacles plays an important role in enhancing heat transfer. Therefore, it must be taken into account for accurate estimations of the exit temperature and total heat transfer rate. It is shown that the Thermal Dispersion coefficient is inversely proportional to the interstitial heat transfer coefficient. The present analysis reveals that conventional estimations without consideration of the Thermal Dispersion result in errors in the fluid temperature development and underestimation of the total heat transfer rate.
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an equation for Thermal Dispersion flux transport and its mathematical modelling for heat and fluid flow in a porous medium
Journal of Fluid Mechanics, 2006Co-Authors: Akira Nakayama, Fujio Kuwahara, Y KodamaAbstract:It is shown for the first time that the gradient diffusion hypothesis often adopted for Thermal Dispersion heat flux in heat transfer within porous media can be derived from a transport equation for the Thermal Dispersion heat flux based on the Navier–Stokes and energy equations. The transport equation valid for both Thermal equilibrium and non-equilibrium cases is mathematically modelled so that all unknown spatial correlation terms, associated with redistribution and dissipation of the Dispersion heat flux, are expressed in terms of determinable variables. The unknown coefficients are determined analytically by considering of macroscopically unidirectional flow through a tube as treated by Taylor. Taylor’s expression for the Dispersion has been generated from the transport equation. Both laminar and turbulent flow cases are investigated to obtain two distinct limiting expressions for low- and high-P´ eclet-number regimes. The results obtained for the Taylor diffusion problem are translated to the case of heat and fluid flow in a packed bed, to obtain the corresponding expressions for the axial Dispersion coefficient in a packed bed. The resulting expression for the highP´ eclet-number case agrees well with the empirical formula, validating of the present transport analysis.
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A Numerical Study of Thermal Dispersion in Porous Media
Journal of Heat Transfer, 1996Co-Authors: Fujio Kuwahara, Akira Nakayama, Hitoshi KoyamaAbstract:Thermal Dispersion in convective flow in porous media has been numerically investigated using a two-dimensional periodic model of porous structure. A macroscopically uniform flow is assumed to pass through a collection of square rods placed regularly in an infinite space, where a macroscopically linear temperature gradient is imposed perpendicularly to the flow direction. Due to the periodicity of the model, only one structural unit is taken for a calculation domain to resolve an entire domain of porous medium. Continuity, Navier-Stokes and energy equations are solved numerically to describe the microscopic velocity and temperature fields at a pore scale. The numerical results thus obtained are integrated over a unit structure to evaluate the Thermal Dispersion and the molecular diffusion due to tortuosity. The resulting correlation for a high-Peclet-number range agrees well with available experimental data.
