Augmentation of heat transfer from a solid cylinder wrapped with a porous layer

In the present study, the heat transfer from a porous wrapped solid cylinder is considered. The heated cylinder is placed horizontally and is subjected to a uniform cross-flow. The aim is to investigate the heat transfer augmentation through the inclusion of a porous wrapper. The porous layer is of foam material with high porosity and thermal conductivity. The mixed convection is studied for different values of flow parameters such as Reynolds number (based on radius of solid cylinder and stream velocity), Grashof number, permeability and thermal conductivity of the porous material. The optimal value of porous layer thickness for heat transfer augmentation and its dependence on other properties of the porous foam is obtained. The flow field is analyzed through a single domain approach in which the porous layer is considered as a pseudo-fluid and the composite region as a continuum. A pressure correction based iterative algorithm is used for computation. Our results show that a thin porous wrapper of high thermal conductivity can enhance the rate of heat transfer substantially. Periodic vortex shedding is observed from the porous shrouded solid cylinder for high values of Reynolds number. The frequency of oscillation due to vortex shedding is dampened due to the presence of the porous coating. Beyond a critical value of the porous layer thickness, the average rate of heat transfer approaches asymptotically the value corresponding to the case where the heated cylinder is embedded in an unbounded porous medium.     

Convective heat transfer over a heated square porous cylinder in a channel

A numerical study is made of the unsteady flow and convection heat transfer for a heated square porous cylinder in a channel. The general Darcy–Brinkman–Forchheimer model is adopted for the porous region. The parameters studies including porosity, Darcy number, and Reynolds number on heat transfer performance have been explored in detail. The results indicate that the average local Nusselt number is augmented as the Darcy number increases. The average local Nusselt number increases as Reynolds number increases; in particular, the increase is more obvious at a higher Darcy number. In contrast, the porosity has slight influence on heat transfer.     

Unsteady natural convection from a horizontal annulus filled with a porous medium

The unsteady natural convection flow from a horizontal cylindrical annulus filled with a non-Darcy porous medium has been studied. The unsteadiness in the problem arises due to the impulsive change in the wall temperature of the outer cylinder. The Navier–Stokes equations along with the energy equation governing the unsteady natural convection flow have been solved by the finite-volume method. The effect of time variation on the heat transfer is more pronounced only in a small time interval immediately after the start of the impulsive motion and the steady state is reached after certain time. The results show that the annulus completely filled with a porous medium has the best insulating effectiveness. Convection in the horizontal annulus is confined mostly at top and bottom regions. Hence, only these regions should be insulated. In case of annulus partially filled with a porous material, insulating the region near the outer cylinder is more effective than insulating the region near the inner cylinder. The effect of Darcy number on the heat transfer is more pronounced than that of the Grashof number.     

Heat transfer in a conical cylinder with porous medium

In this paper, numerical study of heat transfer in a conical annular cylinder fixed with saturated porous medium is presented. The heat transfer is assumed to take place by natural convection and radiation. The inner surface of conical cylinder is maintained at uniform wall temperature. The governing partial differential equations are non-dimensionalised using suitable non-dimensional parameters and then solved by using finite element method. The porous medium is divided using triangular elements with uneven element size. A computer software is used to solve the coupled momentum and energy equations in an iterative manner. The results are discussed for various values of geometric and physical parameters of porous medium with emphasis on cone angle of the cylinder. It is seen that the cone angle plays a vital role in heat transfer from the hot surface to porous medium.     

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.     

Transient forced convection heat transfer from a circular cylinder embedded in a porous medium

Studies of the transient heat transfer past a circular cylinder in a steady-state viscous flow are presented for some fluid saturated fibrous porous media. Numerical results have been obtained according to the Darcy-Brinkman model by means of the finite element method. Analysis of the influence of the Darcy and Peclet numbers on the mean Nusselt number exhibits the successive conduction, transition and convection regimes. The duration necessary to reach the steady-state convection heat transfer appears as a function of the Peclet and Darcy numbers.     

Natural convection in a concentric annulus with a porous sleeve

Analytical solutions obtained through perturbation method and Fourier transform are presented for natural convection in concentric cylinders with a porous sleeve. The porous sleeve is press-fitted to the inner surface of the outer cylinder. Both the inner and outer cylinders are kept at constant temperatures with the inner surface at a slightly higher temperature than that of the outer. The main objective of the present study is to investigate the buoyancy-induced flow as affected by the presence of the porous layer. A parametric study has been performed to investigate the effects of Rayleigh number, Darcy number, porous sleeve thickness, and relative thermal conductivity on the heat transfer results.     

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.     

Generation of entropy during forced convection of heat in nanofluid stagnation-point flows over a cylinder embedded in porous media

Thermodynamics and heat transfer of an impinging nanofluid flow upon a cylinder with constant surface temperature and embedded in porous media are investigated. Numerical solutions reveal the flow velocity and temperature fields as well as the Nusselt number. These are then used to calculate the rate of entropy generation within the system by viscous and heat transfer irreversibilities. It is demonstrated that changes in the concentration of nanoparticles modify the thermal and hydrodynamic boundary layers and hence can alter the Nusselt number and entropy generation considerably. However, the shear stress on the surface of the cylinder is observed to be less affected by the variations in the concentration of nanoparticles. Further, the Reynolds number and non-uniform transpiration are shown to affect the Nusselt number and entropy generation. It is argued that the influences of Reynolds number on the boundary layer thickness can majorly modify the irreversibility and Bejan number.     

Transient natural convection and heat transfer during the storage of granular media

Transient heat transfer in an originally isothermal cylinder filled with a porous medium after sudden change of wall temperature is studied experimentally and computationally. Lab-scale experiments with water as the interstitial fluid are used in order to imitate the conditions prevailing in large, air-filled industrial silos. The proposed model assumes isotropy of the porous medium, local thermal equilibrium between the phases, Darcy flow and applicability of the Boussinesq approximation. Its predictions are in satisfactory agreement with the experimental results. Simulations reveal the role of dimensionless parameters like the modified porous media Rayleigh number and the cylinder aspect ratio. A criterion for neglecting the influence of natural convection on heat transfer is established.     

Transient heat transfer in air saturated porous media in a short cylinder

The rate of heat transfer occurring in a fluid saturated porous media contained in a short cylinder has been experimentally studied. The experiments considered the situations of heating and cooling the porous bed from an initially uniform temperature to the imposed boundary temperature to steady-state. A modified Rayleigh and a modified absolute Nusselt number were used to correlate the experimental results. Comparison was made to a finite difference simulation.     

Simulation of a porous medium (PM) engine using a two-zone combustion model

Porous medium (PM) engine was a new type engine based on the technique of combustion in porous medium, which can realize homogeneous and stable combustion. In this paper, the combustion and working processes of a specific PM engine were simulated by a two-zone model considering the influences of the mass distribution, heat transfer from the cylinder wall, mass exchange between zones and the heat transfer in porous medium. Influences of operating parameters, e.g. intake temperature and pressure, compression ratio, the excess air ratio on the performance of the PM engine were discussed. It was found out that the porous medium, acting as a heat recuperator, can significantly enhance the evaporation of liquid fuel and preheat the mixture, which promotes the ignition and combustion in the cylinder; and that the initial PM temperature and the compression ratio are critical factors controlling the compression ignition of the mixture.     

Effects of porosity and thickness of porous sheets on heat transfer enhancement in a cross flow over heated cylinder

An experimental study is carried out to investigate the thermal impact of wrapping an aluminum porous sheet over a circular tube in a heat convection configuration. The experimental apparatus consists of a heated horizontal cylinder with a constant heat flux. The cylinder is then covered with porous sheets of different thicknesses. The tube is exposed to a cross flow of air at different speeds which corresponds to different Reynolds numbers. The effect of the added porous layer on the pressure loss over the cylinder was also investigated. It is observed that heat transfer is greatly enhanced with the addition of the porous layer. Also, the addition of the porous layer doesn’t appear to increase the pressure loss.     

NON-DARCIAN FORCED CONVECTION ANALYSIS IN AN ANNULUS PARTIALLY FILLED WITH A POROUS MATERIAL

Numerical solutions are presented for fully developed forced convection in concentric annuli partially filled with a porous medium. The porous medium is attached at the inner cylinder, which is maintained at uniform heat flux or at uniform wall temperature while the outer cylinder is adiabatic. The Brinkman-Forchheimer-extended Darcy model was used to model the flow inside the porous medium. The dependence of the fluid flow and heat transfer on several parameters of the problem is thoroughly documented. The inertia coefficient at which the inertial effects reduce the flow rate by 5% is determined as a function of the Darcy number for various thicknesses of the porous substrate. It is also shown that a critical thickness at which the value of the Nusselt number reaches a minimum does not exist if the effective thermal conductivity of the fluid-saturated porous medium is much higher than the fluid conductivity.     

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.     

Natural convection heat transfer from a horizontal cylinder embedded in a porous medium

This paper presents the results of an experimental investigation of heat transfer by natural convection from a horizontal cylinder embedded in porous media consisting of randomly packed glass spheres saturated by either water or silicone oil. It is shown that the overall range of the Rayleigh number, Ra, can be divided into two subregions, called ‘low’ and ‘high’, in each of which the Nusselt number, Nu, behaves differently. It is demonstrated that the low Ra region corresponds to Darey flow and the high to Forchheimer flow. Correlation equations for Nu for the Darcy regime are presented that account for viscous dissipation, and others for the Forchheimer regime that involve the first and second Forchheimer coefficients. The variation of properties with temperature and the wall effect on porosity (and consequently on heat transfer) are considered. The paper includes information concerning the resistance to flow in porous media that was obtained in conjunction with the heat transfer study.     

Effects of buoyancy and conjugate heat transfer on non-Darcy mixed convection about a vertical slender hollow cylinder embedded in a porous medium with high porosity

This study investigates mixed convection heat transfer about a vertical slender hollow cylinder in the buoyancy and conjugate heat transfer effects in the porous medium with high porosity. The non-similar solutions using the Keller box method are obtained. The wall conduction parameter p, the porous medium parameter k₁, the Forchheimer parameter F∗ and the Richardson number are the main parameters. For various values of these parameters the local skin friction and local heat transfer parameters are determined. The validity of the methodology is checked by comparing the results with those available in the open literature and a fairly good agreement is observed. Finally, it is determined that the local skin friction and the local heat transfer coefficients increase with an increase buoyancy parameter Ri, porous medium parameter k₁, Forchheimer parameter F∗ and decrease with conjugate heat transfer parameter p.     

Natural convection of a non-Newtonian fluid about a horizontal cylinder and a sphere in a porous medium

The problem of natural convection of a non-Newtonian fluid about a horizontal isothermal cylinder and an isothermal sphere in the porous medium is considered. The present study is based on the boundary layer approximation and only suitable for a high Rayleigh number. Similarity solutions are obtained by using the fourth order Runge-Kutta method. The effects of the wall temperature T_W and the new power-law index n on the characteristics of heat transfer are discussed.     

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.     

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.