Mathematical models and numerical solutions of Williamson fluid flow under influences of various ... more Mathematical models and numerical solutions of Williamson fluid flow under influences of various boundary conditions provide important support to experimental studies in the solar energy field.
Forced convection of Williamson fluid flow in porous media under constant surface heat flux condi... more Forced convection of Williamson fluid flow in porous media under constant surface heat flux conditions is investigated numerically. A model of Darcy–Forchheimer–Brinkman is used and the corresponding governing equations are expressed in dimensionless forms and solved numerically using bvp4c with MATLAB package. Boundary layer velocity, shear stress, and temperature profiles, in addition to the local Nusselt number parameter over a horizontal plate, are found. The effects of the Forchheimer parameter, Nusselt number, Darcy parameter, porous inertia, and Williamson parameter on the velocity profiles, temperature profiles, coefficient of friction, and coefficient of heat transfer are investigated. The results showed that as the Darcy parameter increases, boundary layer velocity and shear stress increase, while the temperature and Nusselt number decrease. In addition, as Williamson's parameter increases, velocity within the boundary layer, shear stress, and Nusselt number decrease w...
Williamson fluid flux and heat transfer characteristics over horizontal plate via a saturated por... more Williamson fluid flux and heat transfer characteristics over horizontal plate via a saturated porous medium at constant surface temperature are examined in this study to determine the impact of forced viscous dissipation. The flow is modeled using a Darcy-Forchheimer-Brinkman model based on conservation laws and associated governing equations. Using appropriate dimensionless variables, the modeled governed equations are transformed into dimensionless differential forms. The higher constrained coupled non-linear differential equations have been reduced to the first order differential equations to find a reliable numerical solution. The Runge-Kutta method and the built-in Matlab function bvp4c are applied in the shooting method to produce a numerical solution. The impact of λ x , ϵ, ζ x , β x on the velocity profile, temperature, shear stress, and skin friction are illustrated graphically. It is found that the increasing of the Darcy number leads to enhance both velocity and shear stress while the temperature and the Nusselt number are diminished inside the boundary layer. Additionally, it is found that the raising Williamson's parameter causes the temperature to rise while decreasing velocity, shear stress, heat transfer coefficient, and Nusselt number inside the boundary layer. The method applied in the current work is supported by earlier research.
A 2-dimensional model is developed to investigate fluid flow in a magneto-hydrodynamic (MHD) micr... more A 2-dimensional model is developed to investigate fluid flow in a magneto-hydrodynamic (MHD) microp-ump. The transient, laminar, incompressible, and developing flow equations are numerically solved using the finite difference method and the SIMPLE algorithm. The micropump is driven using the Lorentz force, which is induced as a result of interaction between an applied electric field and a perpendicular magnetic field. The effect of Hartmann number on the transient velocity profile and the entrance region length is stud-ied. It is found that controlling the electrical conductivity and magnetic flux density will allow controlling the entrance region length.
Magnetohydrodynamic (MHD) forced convection heat transfer from radiate surfaces in the presence o... more Magnetohydrodynamic (MHD) forced convection heat transfer from radiate surfaces in the presence of a uniform transverse magnetic eld, with conductive fluid suction or injection from a porous plate is considered. A set of solutions to the non-linear equations is presented using the Keller box method. It is found that increasing the magnetic influence number decreases both the velocity boundary layer thickness and the heat transfer rates from the porous plate, also increasing the radiation-conduction parameter, Eckert numbers, dimensionless temperature ratios, which heated the fluid, and decreases heat transfer rates. Dierent velocity and temperature proles, local coecient of friction, and local Nusselt numbers for dierent dimensionless groups are drawn.
Description/Abstract The Office of Environmental Restoration and Waste Management (OEM) is respon... more Description/Abstract The Office of Environmental Restoration and Waste Management (OEM) is responsible for the management and the cleanup of radioactive, hazardous, and mixed wastes generated by US Department of Energy (DOE) operations. The Office of ...
The effects of oscillating plate temperature on transient mixed convection heat transfer from a p... more The effects of oscillating plate temperature on transient mixed convection heat transfer from a porous vertical surface embedded in a saturated porous medium with internal heat generation or absorption are studied. The governing equations are transformed into dimenionless form by a set of variables and solved using the Galerkine finite element method. As the energy generation increases, the temperature near
Abstract. The viscoelastic boundary layer flow and mixed convection heat transfer near a vertical... more Abstract. The viscoelastic boundary layer flow and mixed convection heat transfer near a vertical isothermal surface have been examined in this paper. The governing equations are formulated and solved numerically using an explicit finite difference technique. The velocity and temperature profiles, boundary layer thicknesses, Nusselt numbers and the local skin friction coefficients are shown graphically for different values of the viscoelsatic parameter. In general, it is found that the velocity decreases inside the boundary layer as the viscoelsatic parameter is increased and consequently, the local Nusselt number decreases. This is due to higher tensile stresses between viscoelsatic fluid layers which has a retardation effects on the motion of these layers and consequently, on the heat transfer rates for the mixed convection heat transfer problem under investigation. A Comparison with available published results on special cases of the problem shows excellent agreement.
Abstract. The viscoelastic boundary layer flow and mixed convection heat transfer near a vertical... more Abstract. The viscoelastic boundary layer flow and mixed convection heat transfer near a vertical isothermal surface have been examined in this paper. The governing equations are formulated and solved numerically using an explicit finite difference technique. The velocity and temperature profiles, boundary layer thicknesses, Nusselt numbers and the local skin friction coefficients are shown graphically for different values of the viscoelsatic parameter. In general, it is found that the velocity decreases inside the boundary layer as the viscoelsatic parameter is increased and consequently, the local Nusselt number decreases. This is due to higher tensile stresses between viscoelsatic fluid layers which has a retardation effects on the motion of these layers and consequently, on the heat transfer rates for the mixed convection heat transfer problem under investigation. A Comparison with available published results on special cases of the problem shows excellent agreement.
In recent years, the dynamics of micropolar fluids, originated from the theory of Eringen, has be... more In recent years, the dynamics of micropolar fluids, originated from the theory of Eringen, has been a popular area of research. As the fluids con-sist of randomly oriented molecules, and as each volume element of the fluid has translational as well as rotational motions, the analysis of physical prob-lems in these fluids has revealed several interesting phenomena, which are not found in Newtonian fluids. The present study presents a numerical study for transient natural convection heat transfer of a micropolar boundary layer flow near a vertical isothermal surface. The governing equations are formulated and solved numerically using the MackCormak’s technique. A comparison with previously published results on special cases of the problem shows ex-cellent agreement. Representative results for the velocity, micro-rotation and temperature profiles are shown graphically for different values of material pa-rameters. In general, it is found that the temperature increases inside the boundar...
The evacuated tube solar collector is considered an efficient, convenient, and economical option ... more The evacuated tube solar collector is considered an efficient, convenient, and economical option used to convert solar energy into heat. In this work, enhancement of evacuated tubes solar collector performance and the potential for energy storage by using Al2O3 water-based nanofluid embedded in Graphite as a saturated porous media was presented and studied theoretically. The Governing equations derived from the principles of conservation of mass, momentum, and energy were written in a dimensionless form, and solved these equations analytically for the fully developed region, and numerically throughout the entrance region, and the heat flux data for Amman, Jordan was used in this study. The analysis of the effect of different parameters as porosity, pore diameter, nanoparticles solid volume fraction, pressure, and radius of conduit on temperature variation through the pipe and Nusselt number was done. The results show that the flow of nanofluid in porous media enhances the evacuated ...
In this paper, the magnetohydrodynamic mixed convection flow about an isothermal cone embedded in... more In this paper, the magnetohydrodynamic mixed convection flow about an isothermal cone embedded in a saturated porous medium is considered. The Darcian model including the viscous dissipation effects in the energy equation is used. The governing equations are transformed by using a set of nonsimilarity variables and solved by using Keller box method. The entire mixed convection regime is covered by nonsimilarity parameter χ, where χ=0 corresponds to pure free convection and χ=1 corresponds to pure forced convection. Numerical results for the dimensionless velocity and temperature profiles and the local Nusselt number for various values of the mixed convection parameter χ, the cone angle parameter m, the magnetic field strength parameter H, and the modify Gebhart number Ge * are drawn. It is found that increasing the magnetic strength decreased the heat transfer rates, while increasing the cone angle increased the heat transfer rates.
Turkish Journal of Engineering and Environmental Sciences, 2008
A 2-dimensional model is developed to investigate fluid flow in a magneto-hydrodynamic (MHD) micr... more A 2-dimensional model is developed to investigate fluid flow in a magneto-hydrodynamic (MHD) micropump. The transient, laminar, incompressible, and developing flow equations are numerically solved using the finite difference method and the SIMPLE algorithm. The micropump is driven using the Lorentz force, which is induced as a result of interaction between an applied electric field and a perpendicular magnetic field. The effect of Hartmann number on the transient velocity profile and the entrance region length is studied. It is found that controlling the electrical conductivity and magnetic flux density will allow controlling the entrance region length.
A rigid frame, cylindrical capillary theory of sound propagation in porous media that includes th... more A rigid frame, cylindrical capillary theory of sound propagation in porous media that includes the nonlinear effects of the Forchheimer type is laid out by using variational solutions. It is shown that the five main parameters governing the propagation of sound waves in a fluid contained in rigid cylindrical tubes filled with a saturated porous media are shear wave number, μ ω ρ / R s = , reduced frequency parameter, a wR k = , porosity, e , Darcy number, K R Da = , and Forchheimer number, F s C C 2 * = . The manner in which the flow influences the attenuation and the phase velocities of the forward and backward propagating isentropic acoustic waves is deduced. It is found that the inclusion of the solid matrix increases wave’s attenuations and phase velocities for both forward and backward sound waves, while increasing the porosity and the reduced frequency number decreased attenuation and phase velocities. The effect of the steady flow is found to decrease the attenuation and phas...
World Academy of Science, Engineering and Technology, International Journal of Mechanical, Aerospace, Industrial, Mechatronic and Manufacturing Engineering, 2014
This work deals with heat and mass transfer by steady laminar boundary layer flow of a Newtonian,... more This work deals with heat and mass transfer by steady laminar boundary layer flow of a Newtonian, viscous fluid over a vertical flat plate with variable surface heat flux embedded in a fluid saturated porous medium in the presence of thermophoresis particle deposition effect. The governing partial differential equations are transformed into no-similar form by using special transformation and solved numerically by using an implicit finite difference method. Many results are obtained and a representative set is displaced graphically to illustrate the influence of the various physical parameters on the wall thermophoresis deposition velocity and concentration profiles. It is found that the increasing of thermophoresis constant or temperature differences enhances heat transfer rates from vertical surfaces and increase wall thermophoresis velocities; this is due to favorable temperature gradients or buoyancy forces. It is also found that the effect of thermophoresis phenomena is more pro...
Magnetohydrodynamic (MHD) forced convection heat transfer from radiate surfaces in the presence o... more Magnetohydrodynamic (MHD) forced convection heat transfer from radiate surfaces in the presence of a uniform transverse magnetic field, with conductive fluid suction or injection from a porous plate is considered. A set of solutions to the non-linear equations is presented using the Keller box method. It is found that increasing the magnetic influence number decreases both the velocity boundary layer thickness and the heat transfer rates from the porous plate, also increasing the radiation-conduction parameter, Eckert numbers, dimensionless temperature ratios, which heated the fluid, and decreases heat transfer rates. Different velocity and temperature profiles, local coefficient of friction, and local Nusselt numbers for different dimensionless groups are drawn.
Mathematical models and numerical solutions of Williamson fluid flow under influences of various ... more Mathematical models and numerical solutions of Williamson fluid flow under influences of various boundary conditions provide important support to experimental studies in the solar energy field.
Forced convection of Williamson fluid flow in porous media under constant surface heat flux condi... more Forced convection of Williamson fluid flow in porous media under constant surface heat flux conditions is investigated numerically. A model of Darcy–Forchheimer–Brinkman is used and the corresponding governing equations are expressed in dimensionless forms and solved numerically using bvp4c with MATLAB package. Boundary layer velocity, shear stress, and temperature profiles, in addition to the local Nusselt number parameter over a horizontal plate, are found. The effects of the Forchheimer parameter, Nusselt number, Darcy parameter, porous inertia, and Williamson parameter on the velocity profiles, temperature profiles, coefficient of friction, and coefficient of heat transfer are investigated. The results showed that as the Darcy parameter increases, boundary layer velocity and shear stress increase, while the temperature and Nusselt number decrease. In addition, as Williamson's parameter increases, velocity within the boundary layer, shear stress, and Nusselt number decrease w...
Williamson fluid flux and heat transfer characteristics over horizontal plate via a saturated por... more Williamson fluid flux and heat transfer characteristics over horizontal plate via a saturated porous medium at constant surface temperature are examined in this study to determine the impact of forced viscous dissipation. The flow is modeled using a Darcy-Forchheimer-Brinkman model based on conservation laws and associated governing equations. Using appropriate dimensionless variables, the modeled governed equations are transformed into dimensionless differential forms. The higher constrained coupled non-linear differential equations have been reduced to the first order differential equations to find a reliable numerical solution. The Runge-Kutta method and the built-in Matlab function bvp4c are applied in the shooting method to produce a numerical solution. The impact of λ x , ϵ, ζ x , β x on the velocity profile, temperature, shear stress, and skin friction are illustrated graphically. It is found that the increasing of the Darcy number leads to enhance both velocity and shear stress while the temperature and the Nusselt number are diminished inside the boundary layer. Additionally, it is found that the raising Williamson's parameter causes the temperature to rise while decreasing velocity, shear stress, heat transfer coefficient, and Nusselt number inside the boundary layer. The method applied in the current work is supported by earlier research.
A 2-dimensional model is developed to investigate fluid flow in a magneto-hydrodynamic (MHD) micr... more A 2-dimensional model is developed to investigate fluid flow in a magneto-hydrodynamic (MHD) microp-ump. The transient, laminar, incompressible, and developing flow equations are numerically solved using the finite difference method and the SIMPLE algorithm. The micropump is driven using the Lorentz force, which is induced as a result of interaction between an applied electric field and a perpendicular magnetic field. The effect of Hartmann number on the transient velocity profile and the entrance region length is stud-ied. It is found that controlling the electrical conductivity and magnetic flux density will allow controlling the entrance region length.
Magnetohydrodynamic (MHD) forced convection heat transfer from radiate surfaces in the presence o... more Magnetohydrodynamic (MHD) forced convection heat transfer from radiate surfaces in the presence of a uniform transverse magnetic eld, with conductive fluid suction or injection from a porous plate is considered. A set of solutions to the non-linear equations is presented using the Keller box method. It is found that increasing the magnetic influence number decreases both the velocity boundary layer thickness and the heat transfer rates from the porous plate, also increasing the radiation-conduction parameter, Eckert numbers, dimensionless temperature ratios, which heated the fluid, and decreases heat transfer rates. Dierent velocity and temperature proles, local coecient of friction, and local Nusselt numbers for dierent dimensionless groups are drawn.
Description/Abstract The Office of Environmental Restoration and Waste Management (OEM) is respon... more Description/Abstract The Office of Environmental Restoration and Waste Management (OEM) is responsible for the management and the cleanup of radioactive, hazardous, and mixed wastes generated by US Department of Energy (DOE) operations. The Office of ...
The effects of oscillating plate temperature on transient mixed convection heat transfer from a p... more The effects of oscillating plate temperature on transient mixed convection heat transfer from a porous vertical surface embedded in a saturated porous medium with internal heat generation or absorption are studied. The governing equations are transformed into dimenionless form by a set of variables and solved using the Galerkine finite element method. As the energy generation increases, the temperature near
Abstract. The viscoelastic boundary layer flow and mixed convection heat transfer near a vertical... more Abstract. The viscoelastic boundary layer flow and mixed convection heat transfer near a vertical isothermal surface have been examined in this paper. The governing equations are formulated and solved numerically using an explicit finite difference technique. The velocity and temperature profiles, boundary layer thicknesses, Nusselt numbers and the local skin friction coefficients are shown graphically for different values of the viscoelsatic parameter. In general, it is found that the velocity decreases inside the boundary layer as the viscoelsatic parameter is increased and consequently, the local Nusselt number decreases. This is due to higher tensile stresses between viscoelsatic fluid layers which has a retardation effects on the motion of these layers and consequently, on the heat transfer rates for the mixed convection heat transfer problem under investigation. A Comparison with available published results on special cases of the problem shows excellent agreement.
Abstract. The viscoelastic boundary layer flow and mixed convection heat transfer near a vertical... more Abstract. The viscoelastic boundary layer flow and mixed convection heat transfer near a vertical isothermal surface have been examined in this paper. The governing equations are formulated and solved numerically using an explicit finite difference technique. The velocity and temperature profiles, boundary layer thicknesses, Nusselt numbers and the local skin friction coefficients are shown graphically for different values of the viscoelsatic parameter. In general, it is found that the velocity decreases inside the boundary layer as the viscoelsatic parameter is increased and consequently, the local Nusselt number decreases. This is due to higher tensile stresses between viscoelsatic fluid layers which has a retardation effects on the motion of these layers and consequently, on the heat transfer rates for the mixed convection heat transfer problem under investigation. A Comparison with available published results on special cases of the problem shows excellent agreement.
In recent years, the dynamics of micropolar fluids, originated from the theory of Eringen, has be... more In recent years, the dynamics of micropolar fluids, originated from the theory of Eringen, has been a popular area of research. As the fluids con-sist of randomly oriented molecules, and as each volume element of the fluid has translational as well as rotational motions, the analysis of physical prob-lems in these fluids has revealed several interesting phenomena, which are not found in Newtonian fluids. The present study presents a numerical study for transient natural convection heat transfer of a micropolar boundary layer flow near a vertical isothermal surface. The governing equations are formulated and solved numerically using the MackCormak’s technique. A comparison with previously published results on special cases of the problem shows ex-cellent agreement. Representative results for the velocity, micro-rotation and temperature profiles are shown graphically for different values of material pa-rameters. In general, it is found that the temperature increases inside the boundar...
The evacuated tube solar collector is considered an efficient, convenient, and economical option ... more The evacuated tube solar collector is considered an efficient, convenient, and economical option used to convert solar energy into heat. In this work, enhancement of evacuated tubes solar collector performance and the potential for energy storage by using Al2O3 water-based nanofluid embedded in Graphite as a saturated porous media was presented and studied theoretically. The Governing equations derived from the principles of conservation of mass, momentum, and energy were written in a dimensionless form, and solved these equations analytically for the fully developed region, and numerically throughout the entrance region, and the heat flux data for Amman, Jordan was used in this study. The analysis of the effect of different parameters as porosity, pore diameter, nanoparticles solid volume fraction, pressure, and radius of conduit on temperature variation through the pipe and Nusselt number was done. The results show that the flow of nanofluid in porous media enhances the evacuated ...
In this paper, the magnetohydrodynamic mixed convection flow about an isothermal cone embedded in... more In this paper, the magnetohydrodynamic mixed convection flow about an isothermal cone embedded in a saturated porous medium is considered. The Darcian model including the viscous dissipation effects in the energy equation is used. The governing equations are transformed by using a set of nonsimilarity variables and solved by using Keller box method. The entire mixed convection regime is covered by nonsimilarity parameter χ, where χ=0 corresponds to pure free convection and χ=1 corresponds to pure forced convection. Numerical results for the dimensionless velocity and temperature profiles and the local Nusselt number for various values of the mixed convection parameter χ, the cone angle parameter m, the magnetic field strength parameter H, and the modify Gebhart number Ge * are drawn. It is found that increasing the magnetic strength decreased the heat transfer rates, while increasing the cone angle increased the heat transfer rates.
Turkish Journal of Engineering and Environmental Sciences, 2008
A 2-dimensional model is developed to investigate fluid flow in a magneto-hydrodynamic (MHD) micr... more A 2-dimensional model is developed to investigate fluid flow in a magneto-hydrodynamic (MHD) micropump. The transient, laminar, incompressible, and developing flow equations are numerically solved using the finite difference method and the SIMPLE algorithm. The micropump is driven using the Lorentz force, which is induced as a result of interaction between an applied electric field and a perpendicular magnetic field. The effect of Hartmann number on the transient velocity profile and the entrance region length is studied. It is found that controlling the electrical conductivity and magnetic flux density will allow controlling the entrance region length.
A rigid frame, cylindrical capillary theory of sound propagation in porous media that includes th... more A rigid frame, cylindrical capillary theory of sound propagation in porous media that includes the nonlinear effects of the Forchheimer type is laid out by using variational solutions. It is shown that the five main parameters governing the propagation of sound waves in a fluid contained in rigid cylindrical tubes filled with a saturated porous media are shear wave number, μ ω ρ / R s = , reduced frequency parameter, a wR k = , porosity, e , Darcy number, K R Da = , and Forchheimer number, F s C C 2 * = . The manner in which the flow influences the attenuation and the phase velocities of the forward and backward propagating isentropic acoustic waves is deduced. It is found that the inclusion of the solid matrix increases wave’s attenuations and phase velocities for both forward and backward sound waves, while increasing the porosity and the reduced frequency number decreased attenuation and phase velocities. The effect of the steady flow is found to decrease the attenuation and phas...
World Academy of Science, Engineering and Technology, International Journal of Mechanical, Aerospace, Industrial, Mechatronic and Manufacturing Engineering, 2014
This work deals with heat and mass transfer by steady laminar boundary layer flow of a Newtonian,... more This work deals with heat and mass transfer by steady laminar boundary layer flow of a Newtonian, viscous fluid over a vertical flat plate with variable surface heat flux embedded in a fluid saturated porous medium in the presence of thermophoresis particle deposition effect. The governing partial differential equations are transformed into no-similar form by using special transformation and solved numerically by using an implicit finite difference method. Many results are obtained and a representative set is displaced graphically to illustrate the influence of the various physical parameters on the wall thermophoresis deposition velocity and concentration profiles. It is found that the increasing of thermophoresis constant or temperature differences enhances heat transfer rates from vertical surfaces and increase wall thermophoresis velocities; this is due to favorable temperature gradients or buoyancy forces. It is also found that the effect of thermophoresis phenomena is more pro...
Magnetohydrodynamic (MHD) forced convection heat transfer from radiate surfaces in the presence o... more Magnetohydrodynamic (MHD) forced convection heat transfer from radiate surfaces in the presence of a uniform transverse magnetic field, with conductive fluid suction or injection from a porous plate is considered. A set of solutions to the non-linear equations is presented using the Keller box method. It is found that increasing the magnetic influence number decreases both the velocity boundary layer thickness and the heat transfer rates from the porous plate, also increasing the radiation-conduction parameter, Eckert numbers, dimensionless temperature ratios, which heated the fluid, and decreases heat transfer rates. Different velocity and temperature profiles, local coefficient of friction, and local Nusselt numbers for different dimensionless groups are drawn.
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