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.     

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.     

About enhancement of heat transfer over a circular cylinder embedded in a porous medium

Studies of the steady viscous flow and heat transfer past a circular cylinder 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. Forced convection is analyzed by assuming a solid matrix of constant porosity and permeability in a Péclet number range without any effect of thermal dispersion. Analysis of the influence of the Darcy number on isotherms, streamlines, and velocity contours shows the conditions of the enhancement of heat transfer from the cylinder to the surrounding porous medium.     

Combined forced and natural convection heat transfer from a horizontal cylinder embedded in a porous medium

This paper reports the results of an experimental study of heat transfer by combined forced and natural convection from a horizontal cylinder embedded in a porous medium composed of randomly packed glass spheres saturated with water. The direction of the flow of water was horizontal and normal to the longitudinal axis of the cylinder. The diameter of the cylinder, D, was 11.45mm and the equivalent diameter of the glass spheres was 3.072mm. It is shown that the condition Gr_k/Re²_D ⩽ 0.5 represents a conservative criterion for segregating heat transfer data that are predominantly governed by forced convection from those in which natural convection effects are significant. A correlation hypothesis for convection heat transfer which is based upon four assumptions, primary among which is that the flow can be (conceptually) regarded as being composed of ‘coarse’ and ‘fine’ components, is presented. This hypothesis is shown to provide a basis for successfully correlating a set of experimental heat transfer data that extends from the Darcy regime into the turbulent regime and spans the intervening Forchheimer and transition regimes. It is suggested that the correlation procedure adopted here may yield useful results if applied to other geometries such as, for example, forced convection heat transfer in ducts packed with porous media.     

Heat transfer in a medium with a density gradient

This paper presents a theory of heat transfer in an inhomogeneous medium. Numerical results indicate that the density and thermal conductivity of the medium cannot be assumed to be constant, as such an assumption would lead to results which differed considerably from reality. Moreover, the theory provides a new approach to thickness optimisation for passive buildings by introducing a spatial variation in the density of the building material.     

Heat transfer enhancement in a channel with a built-in square cylinder

A two dimensional numerical investigation of the unsteady laminar flow pattern and forced convective heat transfer in a channel with a built-in square cylinder is presented. The channel in the entrance region has a length to plate spacing of ten. The computations were made for several Reynolds number and two square cylinder sizes. Hydrodynamic behavior and heat transfer results are obtained by solution of the complete Navier-Stokes and energy equation. The results show that these flow exhibits laminar self-sustained oscillations for Reynolds numbers above the critical one. This study shows that oscillatory separated flows result in a significant heat transfer enhancement but also in a significant pressure drop increase.     

Heat and mass transfer in three‐dimensional flow through a porous medium with periodic permeability

In this paper, a theoretical study of a three‐dimensional mixed convective mass transfer flow past a semi‐infinite vertical plate embedded in a porous medium has been presented. The novelty of the present work is to analyze the influence of periodic permeability on the flow and transport characteristics in the presence of viscous dissipation and chemical reaction. The equations governing the flow, heat, and mass transfer are solved analytically by using asymptotic series expansion method. The variations in fluid velocity, temperature, and concentration fields due to change of various physical parameters are demonstrated graphically, whereas the numerical values of skin friction and the rate of mass transfer at the plate are compiled in tabular form. It is found that fluid velocity is increased for increasing permeability. Further, it is seen that concentration level of the fluid drops due to chemical reaction.     

Heat transfer by radiation and natural convection through a vertical annulus embedded in porous medium

The effect of radiation and natural convection in a saturated porous medium embedded in a vertical annular cylinder has been investigated. Finite element method has been used to solve the governing equations. Influence of aspect ratio (A) and radius ratio (R) on Nusselt number is presented. The effect of radiation on heat transfer behavior is discussed. Results for two limiting cases of vertical cylinder and vertical plate embedded in saturated porous medium are presented. It is seen that average Nusselt number (N¯u) increases significantly with radiation parameter (Rd). N¯u attains maximum value at an aspect ratio of around one. N¯u always decreases with decrease in radius ratio.     

Heat transfer in channel flow around a rectangular cylinder

Heat transfer and flow visualization experiments have been made in a channel with a rectangular cylindrical section having various width-to-height ratios. Vortices were observed to shed periodically from the cylinder and then reattach to the channel wall. This reattachment of the vortices induces a periodic fluctuation in heat flux at the wall and enhances the heat transfer in the downstream region of the cylinder. The streamwise position of the maximum Nusselt number moves downstream with decreasing width-to-height ratio, b/h, of the cylinder. When b/h = 2.0, however, the heat flux periodicity disappears because the wake narrows intermittently owing to reattachment of the separated flows to the upper and lower surfaces of the cylinder. © 1998 Scripta Technica. Heat Trans Jpn Res, 27(1): 84–97, 1998     

Heat transfer from a cylinder in axial turbulent flows

Local convective heat transfer coefficients were measured on a two-diameter long cylinder in axial flows of air at conditions unexplored so far, by using thermochromic liquid crystals (TLC) coated on an electrically heated strip-foil consisting bonded to the external surfaces. The Reynolds numbers (Re) based on the cylinder diameter were between 8.9 × 10⁴ and 6.17 × 10⁵, and the flow in front of the cylinder was modified in some cases by the use of a turbulence generating grid, or by circular disc inserts of two sizes placed upstream of the cylinder. These created a major change in the local convective heat transfer coefficient distribution on the cylinder. Increase of the turbulence intensity from Tu < 0.1% to Tu = 6.7% at the same Re increased the average calculated Nusselt number Nu over the cylinder by 25%, and decreased the Nu non-uniformity over the surface. One of the flow modification inserts also reduced significantly the Nu non-uniformity. The position of flow reattachment was measured using tufts. Our heat transfer data agree well with the small amount if data published of others, when extrapolated to their conditions. Correlations between the Nu and Re in the form Nu = CRe^e were established and presented for the average Nu on the front, middle and rear cylinder surfaces, and the variation of the local exponent e was shown along the cylinder. Introducing a new technique, a TLC-coated heated flat plate mounted in the flow above the cylinder in the meridional plane was demonstrated to help visualize the flow field above the cylinder. A track of maximum convective coefficients on this plate was found similar in position to the stream line dividing the forward and backward flows in a case measured for the separated flow in a past study.     

Transpiration-induced buoyancy effect around a horizontal cylinder embedded in a porous medium

Laminar free convection around a long porous limiting cylindrical surface arising from the buoyancy forces created by temperature as well as by transpiration-induced concentration gradients is investigated. All the fluid properties except for the temperature and concentration-dependent body forces are assumed to be constant in the analysis. The dimensionless non-linear coupled boundary-layer equations embody the following parameters: (1) Pr, the Prandtl number, (2) Sc, the Schmidt number and (3) R, the ratio of the concentration to the thermal buoyancy forces. Numerical results for the local Nusselt number, the local wall shear stress and the local Sherwood number are displayed graphically for the transpiration-induced convective diffusion of hydrogen, water vapour and naphthalene into an air-saturated porous medium. The dimensionless thermal, concentration and momentum boundary layer thicknesses, along with the cumulative tangential mass flow rate are given in tabular form. The analysis covers a wide range of blowing rates.     

Forced convection along a longitudinal cylinder embedded in a saturated porous medium

The thermal boundary layer along an isothermal cylinder in a porous 3edium is studied numerically by a finite difference scheme and also using the method of extended perturbation series. The series in terms of the transverse curvature parameter ξ extended to seven terms and is subsequently improved by applying the Shanks transformation twice and thrice, respectively. Results for heat transfer characteristics are found in very good agreement.     

Coupled heat and mass transfer by natural convection adjacent to a permeable horizontal cylinder in a saturated porous medium

The heat and mass transfer characteristics of free convection about a permeable horizontal cylinder embedded in porous media under the coupled effects of thermal and mass diffusion are numerically analyzed. The surface of the horizontal cylinder is maintained at a uniform wall temperature and uniform wall concentration. The transformed governing equations are obtained and solved by Keller box method. Numerical results for the dimensionless temperature profiles, the dimensionless concentration profiles, the Nusselt number and the Sherwood number are presented. Increasing the buoyancy ratio N and the transpiration parameter f_w increases the Nusselt number and the Sherwood number. For thermally assisting flow, when Lewis number Le increases, the Nusselt (Sherwood) number decreases (increases). Whereas, for thermally opposing flow, both the Nusselt number and the Sherwood number increase with increasing the Lewis number.     

Heat transfer on a radially rotating heated cylinder

Experiments are conducted to investigate the convective heat transfer on a radially rotating heated cylinder. In the experiment, one uses cold air-hot cylinder instead of hot air-cold blade in a real engine. The hollow bakelite test rotating cylinder is pasted with a heater made of 0.03 mm thin film of stainless steel. The maximum air stream velocity is 20 m/s with the corresponding Reynolds number of 1.2 × 10⁵ that is high enough to simulate the real turbine blade of Re ≈ 10⁵. The rotation-induced cross stream flow affect the heat transfer coefficient on the cylinder surface. The effect is more prominent for the cases with higher rotational speeds and lower Reynolds numbers. Due to rotation, the heat transfer enhancement at lower Reynolds number is greater than those at a higher one.     

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.     

Heat transfer in a confined rectangular cavity packed with porous media

This paper presents an experimental investigation of convective heat transfer in a confined rectangular cavity packed with porous media, on the opposing vertical walls of which different temperatures are imposed. Measurements are made for each of two kinds of solid particles using three kinds of fluids, i.e. water, transformer oil and ethyl alcohol. The present experiments cover a wide range of Rayleigh number Ra1 between 1 and 10⁵, Prandtl number Pr1 between 1 and 200 and geometrical aspect-ratio $\text{H}\text{W}$ between 5 and 26. The experimental results indicate that Nusselt number Nu1 is correlated by the following relationship: $\text{Nu1 = 0.627 Pr1}{}^{0.130}\text{(}\text{H}\text{W}\text{)}{}^{\mathrm{?0.527}}\text{Ra1}{}^{0.463}$     

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.