Study of mixed convection in an annular vertical cylinder filled with saturated porous medium,using thermal non-equilibrium model

The present study deals with numerical investigation of effects of different parameters on enhancement or retardation of the heat transfer rate in an annular vertical cylinder filled with saturated porous medium. The heat transfer is assumed to take place by mixed convection mode. The thermal non-equilibrium approach is considered. The inner surface of the annular cylinder is maintained at constant wall temperature whereas the outer surface remains at ambient temperature. The governing partial differential equations are solved using finite element method. The results are discussed for the effects of Peclet number, interphase heat transfer co-efficient and thermal conductivity ratio.     

Soret and Dufour effects on free convection boundary layers over an inclined wavy surface in a porous medium

This work studies the heat and mass transfer characteristics of natural convection near a vertical wavy cone in a fluid saturated porous medium with Soret and Dufour effects. The surface of the wavy cone is kept at constant temperature and concentration. The governing equations are transformed into a set of coupled differential equations, and the obtained boundary layer equations are solved by the cubic spline collocation method. The heat and mass transfer characteristics are presented as functions of Soret parameter, Dufour parameter, half angle of the cone, Lewis number, buoyancy ratio, and dimensionless amplitude. Results show that an increase in the Dufour parameter tends to decrease the local Nusselt number, and an increase in the Soret parameter tends to decrease the local Sherwood number. Moreover, a greater half angle of the cone leads to a greater fluctuation of the local Nusselt and Sherwood numbers with the streamwise coordinates.     

Magnetohydrodynamic Slip Flow and Heat Transfer in a Porous Medium over a Stretching Cylinder: Homotopy Analysis Method

This study considers magnetohydrodynamic flow and heat transfer outside a hollow stretching cylinder immersed in a fluid saturated porous medium of sparse distribution of particles with high permeability. Partial slip boundary conditions for the velocity and temperature fields are assumed at the stretching surface of the cylinder. Using similarity transformations, the nonlinear partial differential equations governing the flow and heat transfer are converted into nonlinear ordinary differential equations which are then solved by the homotopy analysis method. The effects of the pertinent parameters on the velocity and temperature profiles are investigated and discussed graphically.     

Natural convection heat and mass transfer from a vertical truncated cone in a porous medium saturated with a non-Newtonian fluid with variable wall temperature and concentration

This work presents a boundary-layer analysis about the natural convection heat and mass transfer near a vertical truncated cone with variable wall temperature and concentration in a porous medium saturated with non-Newtonian power-law fluids. A coordinate transform is used to obtain the nonsimilar governing equations, and the transformed boundary-layer equations are solved by the cubic spline collocation method. Results for local Nusselt numbers are presented as functions of power-law indexes, surface temperature and concentration exponents, buoyancy ratios, and Lewis numbers. The heat and mass transfer rates of the truncated cones with higher surface temperature and concentration exponents are higher than those with lower exponents. Moreover, an increase in the power-law index of fluids tends to decrease the heat and mass transfer from a vertical truncated cone in a porous medium saturated with non-Newtonian power-law fluids.     

Mixed convection within a porous heat generating horizontal annulus

A numerical investigation of mixed convection in a horizontal annulus filled with a uniform fluid-saturated porous medium in the presence of internal heat generation is carried out. The inner cylinder is heated while the outer cylinder is cooled. The forced flow is induced by the cold outer cylinder rotating at a constant angular velocity. The flow field is modeled using a generalized form of the momentum equation that accounts for the presence of porous medium viscous, Darcian and inertial effects. Discretization of the governing equations is achieved using a finite element scheme based on the Galerkin method of weighted residuals. Comparisons with previous works are performed and the results show excellent agreement. The effects of pertinent parameters such as the internal Rayleigh number, the Darcy number, the annulus gap, and the Richardson number on the flow and heat transfer characteristics are considered in the present study. The obtained results depict that the Richardson number plays a significant role on the heat transfer characterization within the annulus. The present results show that an increase in Reynolds number has a significant effect on the flow patterns within the annulus with respect to two-eddy, one-eddy and no-eddy flows. Categorization of the flow regimes according to the number of eddies is established on the Ra-Re plane for various Rayleigh numbers.     

A boundary layer analysis of heat transfer by free convection from permeable horizontal cylinders of elliptic cross-section in porous media using a thermal non-equilibrium model

This work uses a thermal non-equilibrium model to study the free convection boundary layer flow driven by temperature gradients near a permeable horizontal cylinder of elliptic cross-section with constant wall temperature in a fluid-saturated porous medium. A coordinate transformation is used to obtain the nonsimilar boundary layer equations. The transformed boundary layer equations are then solved by the cubic spline collocation method. Results for the local Nusselt numbers are presented as functions of the porosity scaled thermal conductivity ratio, the heat transfer coefficient between solid and fluid phases, the transpiration parameter, and the aspect ratio when the major axis of the elliptical cylinder is vertical (slender orientation) and horizontal (blunt orientation). An increase in the porosity scaled thermal conductivity ratio or the heat transfer coefficient between the solid and fluid phases increases the heat transfer rates. Moreover, the use of suction (positive transpiration parameter) tends to increase the heat transfer rates between the porous medium and the surface.     

Impingement of hollow cone spray on hot porous medium

To have a good understanding of the formation of homogenous mixture in a porous medium engine, the interaction between hollow cone spray and hot porous medium was studied numerically by using an improved version of KIVA-3V code. The improved KIVA-3V code is incorporated with an impingement model, heat transfer model and linearized instability sheet atomization (LISA) model to simulate the hollow cone spray. The reasonability of the impingement model and heat transfer model was validated. With a simple model to describe the structure of the porous medium, the interaction between hollow cone spray and hot porous medium was simulated under different ambient pressures and spray cone angles. Computational results show that the fuel spray could be divided into smaller ones, which provides conditions for the quick evaporation of fuel droplets and the mixing of fuel vapor with air. Differences in ambient pressure and spray cone angle affect the distribution of droplets in the porous medium.     

Double-diffusive natural convection along a vertical wavy truncated cone in non-Newtonian fluid saturated porous media with thermal and mass stratification

This paper studies the double-diffusive natural convection near a vertical wavy truncated cone in a non-Newtonian fluid saturated porous medium with thermal and mass stratification. The surface of the truncated cone is kept at constant wall temperature and concentration. A coordinate transformation is employed to transform the complex wavy surface to a smooth surface, and the obtained boundary-layer equations are then solved by the cubic spline collocation method. Effects of thermal and concentration stratification parameters, Lewis number, buoyancy ratio, power-law index, and wavy geometry on the heat and mass transfer characteristics are studied. Results show that the streamwise distributions of the local Nusselt number and the local Sherwood number are harmonic curves with a wave number twice the wave number of the surface of the vertical wavy truncated cone. An increase in the power-law index leads to a smaller fluctuation of the local Nusselt and Sherwood numbers. Moreover, increasing the thermal and concentration stratification parameter decreases the buoyancy force and retards the flow, thus decreasing the heat and mass transfer rates between the fluid and the wavy surface of the vertical truncated cone.     

Non-Darcy hydromagnetic free convection from a cone and a wedge in porous media

Continuum equations governing non-Darcy hydromagnetic free convection flow of an electrically conducting and heat-generating fluid over a vertical cone and a wedge adjacent to a porous medium are developed. These equations account for such effects as buoyancy, boundary and inertia effects of porous media, Hartmann effects of magnetohydrodynamics, and heat generation or absorption of fluid. Similarity variables were employed for the case of variable surface temperature and the resulting ordinary differential equations are solved numerically by an implicit, iterative, finite-difference method. Flow and heat transfer numerical results are obtained for various combinations of physical parameters. Graphical results illustrating interesting features of the physics of the problem are presented and discussed.     

Similarity solutions for pressure-driven boiling flows in capillary porous media

A similarity transformation has been proposed to study the two-phase boundary layer equations derived by Wang and Beckermann for capillary porous media. By virtue of the present transformation, the set of governing equations and boundary conditions for the pressure-driven boiling flow over a body of arbitrary shape reduces to the one for the flow over a flat plate. The dryout heat fluxes for pressure-driven boiling flows over a plate, a wedge, a cone, a sphere and a horizontal circular cylinder are correlated with the fluid thermophysical properties and porous medium parameters. The study confirms that the capillary force plays an important role in boiling flows in porous media.     

Soret and Dufour effects on heat and mass transfer by natural convection from a vertical truncated cone in a fluid-saturated porous medium with variable wall temperature and concentration

This work studies the Soret and Dufour effects on the natural convection heat and mass transfer near a vertical truncated cone with variable wall temperature and concentration in a fluid-saturated porous medium. A coordinate transform is used to obtain the nonsimilar governing equations, and the transformed boundary layer equations are solved by the cubic spline collocation method. Results for local Nusselt number and the local Sherwood number are presented as functions of Soret parameters, Dufour parameters, surface temperature and concentration exponents, buoyancy ratios, and Lewis numbers. Results show that increasing the Dufour parameter tends to decrease the local Nusselt number, while it tends to increase the local Sherwood number. An increase in the Soret number leads to an increase in the Nusselt number and a decrease in the Sherwood number from a vertical truncated cone in a fluid-saturated porous medium. The local Nusselt number and the local Sherwood number of the truncated cones with higher surface temperature and concentration exponents are higher than those with lower exponents.     

Non-Darcy Non-Newtonian Free Convection Flow Over a Horizontal Cylinder in a Saturated Porous Medium

Steady state solutions are obtained for non-Darcy free convection flow along a horizontal cylinder in a non-Newtonian fluid saturated porous medium. The boundary-layer equations governing the flow are solved numerically by using an implicit finite-difference method developed by Keller. Numerical results are obtained for the velocity and heat transfer at the wall for various values of the parameters namely, the Ergun number, Rayleigh number, power-law index and transpiration parameter.     

Comparative analysis of a Sisko nanofluid over a stretching cylinder through a porous medium

The present article examines the Sisko nanofluid flow and heat transfer through a porous medium due to a stretching cylinder using Buongiorno's model for nanofluids. Suitable similarity transformations are used to transform the governing boundary layer equations of fluid flow into nonlinear ordinary differential equations. The finite difference method is used to solve coupled nonlinear differential equations with MATLAB software. The impact of different parameters viz., the Sisko material parameter, porosity parameter, curvature parameter, thermophoresis parameter, and Brownian diffusion parameter on the velocity and temperature distribution are presented graphically. Moreover, the effect of the involved parameters on the heat transfer rate is also studied and presented through table values. It is noticed from the numerical values that the porosity parameter reduces the velocity while enhancing the temperature. The curvature parameter enhances the velocity throughout the fluid regime and reduces the temperature near the surface while enhancing the temperature far away from the surface. The study reveals that the thermophoresis and Brownian diffusion parameters that characterize the nanofluid flow reduce the wall heat transfer rate, while the curvature parameter enhances it. This investigation of wall heating/cooling has essential applications in solar porous water absorber systems, chemical engineering, metallurgy, material processing, and so forth.     

Darcian mixed convection along slender vertical cylinders with variable surface heat flux embedded in a porous medium

The problem of mixed convection flow along a vertical slender circular cylinder with variable surface heat flux embedded ina fluid-porous medium has been studied. The effects of mixed convection, surface curvature and buoyancy parameters are analyzed for the case of power-law variation in surface heat flux. The numerical solution of the transformed governing equations has been obtained using the Keller box method to demonstrate the important influence of these parameters on the flow and heat transfer characteristics     

HEAT AND MASS TRANSFER FROM A PERMEABLE CYLINDER IN A POROUS MEDIUM WITH MAGNETIC FIELD AND HEAT GENERATION/ABSORPTION EFFECTS

We formulate the problem of coupled heat and mass transfer by natural convection from a horizontal cylinder embedded in a uniform porous medium in the presence of an external magnetic field and internal heat generation or absorption effects. The cylinder surface is maintained at a constant temperature and a constant concentration and is permeable to allow for possible fluid wall suction or blowing. The resulting governing equations are nondimensionalized and transformed into a nonsimilar form and then solved numerically by an implicit, iterative, finite-difference method. Comparisons with previously published work are performed and excellent agreement is obtained. A parametric study of the physical parameters is conducted and a representative set of numerical results for the stream function, temperature, concentration profiles, and the Nusselt and Sherwood numbers is illustrated graphically to show interesting features of the solutions.     

Non-Darcian effects on natural convection heat transfer in a wavy porous enclosure

A numerical investigation is carried out to analyze natural convection heat transfer inside a cavity with a sinusoidal vertical wavy wall and filled with a porous medium. The vertical walls are isothermal while the top and bottom horizontal straight walls are kept adiabatic. The transport equations are solved using the finite element formulation based on the Galerkin method of weighted residuals. The validity of the numerical code used is ascertained by comparing our results with previously published results. The importance of non-Darcian effects on convection in a wavy porous cavity is analyzed in this work. Different flow models for porous media such, as Brinkman-extended Darcy, Forchheimer-extended Darcy, and the generalized flow models, are considered. Results are presented in terms of streamlines, isotherms, and local heat transfer. The implications of Rayleigh number, number of wavy surface undulation and amplitude of the wavy surface on the flow structure and heat transfer characteristics are investigated in detail while the Prandtl number is considered equal to unity.     

Soret and Dufour effects on free convection along a vertical wavy surface in a fluid saturated Darcy porous medium

In this article, free convection of heat and mass transfer along a vertical wavy surface in a Newtonian fluid saturated Darcy porous medium is studied by considering cross diffusion (namely the Soret and the Dufour effects) in the medium. The vertical wavy wall and the flow governing equations are transformed to a plane geometry case by using a suitable transformation. Then a similarity solution to this problem is presented under the large Darcy–Rayleigh number assumption. The governing partial differential equations are reduced to a set of ordinary differential equations that are integrated using numerical methods to study the nature of the non-dimensional heat and mass transfer coefficients in the medium. The results are presented for a range of the flow governing parameters such as the diffusivity ratio parameter, the buoyancy ratio parameter, the Soret parameter, the Dufour parameter and the amplitude of the wavy surface.     

Spectral relaxation method analysis of Casson nanofluid flow over stretching cylinder with variable thermal conductivity and Cattaneo–Christov heat flux model

This article deals with non‐Newtonian Casson nanofluid flow and heat transfer over stretching cylinder in a porous medium. The mode of heat transfer is presented considering temperature‐dependent thermal conductivity by integrating the Cattaneo–Christov heat flux and mass flux models. Boundary layer theory is applied to develop the governing partial differential equations from the physical problem. Employing proper similarity transformation, the governing boundary layer equations are transformed into dimensionless system of nonlinear ordinary differential equations. Then, the resulting problem is numerically solved by means of spectral relaxation method. The convergence analysis of the proposed numerical scheme is presented via a table, which confirms almost the 10th order of approximation is enough for the convergence of the skin friction coefficient, local heat transfer, and mass transfer rates. The effects of various embedded parameters on velocity, temperature, and concentration profiles as well as skin friction coefficient, surface heat and mass transfer rates are examined through graphs and tables. The findings reveal that the growth of permeability and velocity slip parameters appears to decelerate the velocity distributions of fluid. Thermal boundary layer thickness tends to develop with greater values of permeability and Brownian motion parameters. Also, the local heat transfer rate is less with Fourier's law of heat conduction than Cattaneo–Christov heat flux model. Furthermore, the validity and accuracy of the present result is checked with the available literature, and very sound agreement has been obtained.     

Impingement of hollow cone spray on hot porous medium

To have a good understanding of the formation of homogenous mixture in a porous medium engine, the interaction between hollow cone spray and hot porous medium was studied numerically by using an improved version of KIVA-3V code. The improved KIVA-3V code is incorporated with an impingement model, heat transfer model and linearized instability sheet atomization (LISA) model to simulate the hollow cone spray. The reasonability of the impingement model and heat transfer model was validated. With a simple model to describe the structure of the porous medium, the interaction between hollow cone spray and hot porous medium was simulated under different ambient pressures and spray cone angles. Computational results show that the fuel spray could be divided into smaller ones, which provides conditions for the quick evaporation of fuel droplets and the mixing of fuel vapor with air. Differences in ambient pressure and spray cone angle affect the distribution of droplets in the porous medium. __________ Translated from Chinese Internal Combustion Engine Engineering, 2007, 28(4): 28-31 [译自: 内燃机工程]     

Natural convection heat transfer from an inclined wavy plate in a bidisperse porous medium

This work studies the natural convection heat transfer from an inclined wavy plate in a bidisperse porous medium with uniform wall temperature. The two-velocity two-temperature formulation is used to derive the governing equations of this system. The Prandtl coordinate transformation is used to transform the wavy surface into a regular plane, and the obtained equations are then simplified further by the order-of-magnitude analysis to give the boundary layer equations. The cubic spline collocation method is used to solve the boundary layer governing equations. The effects of dimensionless amplitude, angle of inclination, inter-phase heat transfer parameter, modified thermal conductivity ratio, and permeability ratio on the heat transfer and flow characteristics are studied. Increasing the modified thermal conductivity ratio and the permeability ratio can effectively enhance the natural convection heat transfer of the inclined plate in bidisperse porous media. Moreover, the thermal non-equilibrium effects are significant for low values of the inter-phase heat transfer parameter. As the dimensionless amplitude increases, both the fluctuations of the local Nusselt number for the f-phase and the p-phase with the streamwise coordinate are enhanced.