Analyses of free convection flow of variable spaced plates embedded in a porous medium

Transport Processes in a Rapidly Changing World.- Modelling of Transport Phenomena in Porous Media.- Fundamentals of Mechanics of Saturated Porous Media: Basic Equations and Waves.- The Stability of Convective Flows in Porous Media.- Free Convection Heat and Mass Transfer in a Porous Medium.- Natural Convection in a Vertical Porous Annulus.- Non-Darcy Natural Convection in Saturated Porous Media.- Mixed Convection in Saturated Porous Media.- Forced Convective Flow and Heat Transfer Through a Porous Medium Exposed to a Flat Plate or a Channel.- Forced Convection Heat Transfer in a Porous Medium.- Radiation Transport in Porous or Fibrous Media.- Fundamentals of Drying of Capillary-Porous Bodies.- Heat Transfer During Unsaturated Flow in Porous Media.- Buoyancy-Induced Flow and Heat Transfer in Saturated Fissured Media.- Effect of Randomness on Heat and Mass Transfer in Porous Media.- Analytical Solutions to Transient Convective Mass Transfer Within Porous Media.- Natural Convection in Porous Media with Variable Porosity and Thermal Dispersion Effects.- Convective Flow Interaction and Heat Transfer Between Fluid and Porous Layers.- Temperature Distribution in a Porous Slab with Random Thermophysical Characteristic.- Forced Convection in Packed Tubes and Channels with Variable Porosity and Thermal Dispersion Effects.- Transient Double Diffusive Convection in a Horizontal Fluid Layer Situated on top of a Porous Substrate.- Drying of Wood Residues in a Fixed Bed.- Heat and Mass Transfer in Adsorbent Beds.- Solidification of a Binary Mixture Saturating a Bed of Glass Spheres.- Melting in the Presence of Natural Convection in a Saturated Porous Medium.- Air-Water Two-Phase Flow Pressure Drop in Large Scale Porous Media.- Boiling and Dryout in Unconsolidated Porous Media.- Heat Transfer from a Surface Covered with Hair.- Measurements of Thermal Conductivity in Porous Media.- Determination of Velocity Vectors in Porous Media with Fluorescent Particle Image Velocimetry (FPIV).- Non Invasive Measurement Techniques in Porous Media.- Flash Method of Measuring Thermal Diffusivity and Conductivity.- Mechanics, Heat and Mass Transfer in Saturated Porous Media. Application to Petroleum Technology.- Drying Complex Porous Materials-Modelling and Experiments.- Some Geophysical Problems Involving Convection in Porous Media.- Porous Surface Boiling and Its Application to Cooling Microelectronic Chips.- Heat and Mass Transfer in Spouted Beds.- Liquid Seeping into Porous Ground.- Future Research Needs in Convective Heat and Mass Transport in Porous Media.

The optimization of a magnetohydrodynamic flow of Al2O3–water nanofluid was carried out numerically considering the combined effects of various parameters such as porous medium permeability, Forchheimer drag, slip length, conduction–radiation parameter and nanoparticle volume fraction on heat transfer and entropy generation. The numerical computations were made by using the shooting technique together with Runge–Kutta–Fehlberg method, and the results were compared with already published studies obtaining a very good agreement. Here, optimal operating conditions with minimum entropy and maximum or minimum heat transfer not yet reported in previous similar configurations were reached and the effects of porous medium in the presence of combined convective–radiative boundary conditions and nonlinear radiation heat flux were analyzed. Results showed that the global entropy increased with the porous medium permeability, while it decreased with the inertia parameter. In addition, optimum values of slip length and nanoparticle volume fraction that minimize the global entropy, were found. These optimum values of both quantities moved to higher values as the porous medium permeability increased. The Nusselt number was also explored for different conditions. Optimum values of Grashof number and conduction–radiation parameter with maximum heat transfer, as well as slip length with minimum heat transfer were found. These optimum values of Grashof moved to lower values as the permeability increased, while their optimum values shifted toward higher values with the inertia parameter. The obtained optimum values of slip length with minimum heat transfer moved to higher values when the permeability increased. Finally, four different models were defined to show the effects of uncertainties in thermophysical properties of nanofluid on heat transfer and entropy generation. These models were obtained from the combination of two relations used for both the dynamic viscosity and the thermal conductivity of nanofluid. It was seen that, independent of the model, optimal operating conditions were achieved for the explored values.

The article studies the impact of chemically reactive species on the transportation of heat and mass in a polymer-added liquid past a linearly stretching surface inserted in a porous medium taking Soret and Dufour effects into consideration. The Oldroyd-B model is opted to examine polymer insertion in the base liquid. Polymer concentration is represented by γ ( 0 < γ < 1 ) , where γ = 0 represents the absence of polymers. Rapid changes in boundary layer locality cause polymers to elongate, which adds an extra term in the momentum equation. Problem defining partial differential equations are converted to a set of ordinary differential equations by introducing suitable similarity variables. Drag force, mass transfer rate (MTR) and heat transfer rate (HTR) at the wall are studied and numerical solutions are attained by applying the shooting scheme with the fourth-order Runge–Kutta method. Diminution in drag force and heat transfer while expansion in mass transportation at surface is noticed and the polymer insertion is found to be the significant reason for this. The influence of chemically reactive species on MTR and HTR is also investigated when Dufour and Soret effects are also taken into consideration.

The effect of thermal and mass stratification on mixed convection boundary layer flow over a vertical flat plate embedded in a porous medium saturated by a nanofluid has been investigated. The vertical plate is maintained at uniform and constant heat, mass and nanoparticle fluxes, and the behavior of the porous medium is described by the Darcy model. The model considered for nanofluids incorporates the effects of Brownian motion and thermophoresis. In addition, the thermal energy equations include regular diffusion and cross-diffusion terms. A suitable coordinate transformation is introduced, and the obtained system of non-similar, coupled and non-linear partial differential equations is solved numerically. The influence of pertinent parameters on the non-dimensional velocity, temperature, concentration and nanoparticle volume fraction are discussed. In addition, the variation of heat, mass and nanoparticle transfer rates at the plate are exhibited graphically for different values of physical parameters.

Conjugated, mixed convection-conduction heat transfer along a cylindrical fin in a porous medium

Second-law analysis (SLA) is an important concept in thermodynamics, which basically assesses energy by its value in terms of its convertibility from one form to another.[...]

Using the sum of latent and sensible heat fluxes and back radiation between the ocean and the atmosphere to express the total heat transfer, Q(T), the annual and interannual variations of QT over the North Pacific were calculated and analysed. The total heat transfer is positive (atmosphere gains heat from the ocean) for all seasons and all regions of the North Pacific and there is a close relationship with the main ocean currents. The area of maximum heat transfer is the Kuroshio area with an annual variation mainly determined by the Asian monsoon circulation. The maximum heat transfer is in January and the minimum, in June. Conversely, the maximum total heat transfer to the air over the Gulf of Alaska occurs in October. This follows from the interaction of the annual cycle of the oceanic thermal content (which is a maximum in late summer) and the occurrence of stormy conditions in the late fall. The QT over the California Current area is about 70% of that over the Kuroshio at the same latitude on the other side of the basin. The spectrum of the anomalies from the 30-year mean annual cycle show low frequency variations of period about 5 years in the Kuroshio area and about 2 years in the Alaska and California areas. After filtering out the monthly fluctuations, it was found that the Kuroshio area heat transfer was correlated with variations across the central North Pacific to about 170 degrees W. The remainder of the basin, including the area of the North Equatorial Current, was correlated with heating variations in both the California and Alaska Current regions.

Convective heat transfer in a vertical anisotropic porous layer

An analytical approach using the least-squares method (LSM) has been carried out to study the effect of thermal radiation on the flow and heat transfer in a thin liquid film over an unsteady stretching sheet embedded in a porous medium. Similarity transformations were used to convert the momentum, continuity and energy equations describing the problem, which are coupled nonlinear partial differential equations into a set of nonlinear ordinary differential equations. The resulting set of Ordinary Differential Equation (ODE) is then solved analytically by the least-squares method. By comparing the results of the applied method with previously published work the accuracy of the proposed method has been verified. Finally the effects of different outstanding parameters in this particular case such as the Darcy parameter, the radiation parameter and the Prandtl number on the flow velocity and temperature profiles are communicated.

The problem of free convection flow of a non-Newtonian power law fluid along an isothermal vertical flat plate embedded in the porous medium is considered in the present study. The physical coordinate system is shown schematically in Fig 1. In the present study, it is assumed that the modified Darcy law and the boundary layer approximation are applicable. This implies that the present solutions are valid at a high Rayleigh number. With these simplifications, the governing partial nonlinear differential equations can be transformed into a set of coupled ordinary differential equations which can be solved by the fourth-order Runge-Kutta method. Algebraic equations for heat transfer rate and boundary layer thickness as a function of the prescribed wall temperature and physical properties of liquid-porous medium are obtained. The similarity solutions can be applied to problems in geophysics and engineering. The primary purpose of the present study is to predict the characteristics of steady natural convection heat transfer using the model of the flow of a non-Newtonian power law fluid in a porous medium given by Dharmadhikari and Kale (1985). Secondly, the effects of the new power law index n on heat transfer are investigated.

This paper examines the problem of mass transfer on MHD unsteady free convective flow of a polar fluid through a porous medium of variable permeability bounded by an infinite horizontal porous plate in slip flow regime.The permeability of the porous medium decreases exponentially with time about a constant mean.Using perturbation technique the expressions for the velocity distribution, mean angular velocity of rotation of particles, concentration distribution and skin friction are obtained.The effects of permeability parameter K 0 , Magnetic parameter M, Prandtl number P r , Schimdt number S c ,and Grashof number G r ,Modified Grashof number G m entering into the problem on velocity, temperature distribution and concentration distribution are shown graphically and discussed numerically.It can be observed that this velocity decreases with the increase in M, P r, S c and increases with the increase in K 0 , G r , G m .Temperature and Concentration decreases with the increase in the value of P r and S c respectively.

In this study, the effects of magnetic field on nanofluid flow, heat, and mass transfer between two horizontal coaxial cylinders are studied using a two-phase model. The effect of viscous dissipation is also taken into account. By using the appropriate transformation for the velocity, temperature, and concentration, the basic equations governing the flow, heat, and mass transfer are reduced to a set of ordinary differential equations. These equations subject to the associated boundary conditions are solved numerically using the fourth-order Runge–Kutta method. The effects of Hartmann number, Reynolds number, Schmidt number, Brownian parameter, thermophoresis parameter, Eckert number, and aspect ratio on flow, heat, and mass transfer are examined. Results show that the Nusselt number has a direct relationship with the aspect ratio and Hartmann number but it has a reverse relationship with the Reynolds number, Schmidt number, Brownian parameter, thermophoresis parameter, and Eckert number.

The objective is to study the effects of thermal radiation and chemical reaction on mass transfer on unsteady free convection flow past an exponentially accelerated infinite vertical plate through porous medium in the presence of magnetic field. The fluid is considered here as absorbing/emitting radiation but a non-scattering medium. The plate temperature is raised linearly with time and the concentration level near the plate is raised to C   . We use proper transformations to make the governing equations dimensionless. The dimensionless governing equations are reduced to a set of ordinary differential equations. Then we solve these equations with the help of transformed boundary conditions. The effect of various parameters such as Grashof number, Modified Grashof number, Schmidt number, Prandtl number, Magnetic parameter, time, accelerating parameter, Dimensionless porous medium factor and Dimensionless chemical reaction parameter on velocity profiles, temperature profiles, concentration profiles, skin friction profiles, rate of heat transfer profiles and rate of mass transfer profiles are shown graphically.

The problem of boundary layer flow and heat transfer induced due to nanofluid over a vertical plate is investigated. The transport equations employed in the analysis include the effect of Brownian motion and thermophoresis. We used a convective heating boundary condition instead of a widely employed thermal conduction of constant temperature or constant heat flux. The solution for the temperature and nanoparticle concentration depends on six parameters, viz., convective heating parameter A, Prandtl number Pr, Lewis number Le, Brownian motion Nb, buoyancy ratio parameter Nr, and the thermophoresis parameter Nt. Similarity transformation is used to convert the governing nonlinear boundary-layer equations into coupled higher order ordinary differential equations. These equations were solved numerically using Runge-Kutta fourth order method with shooting technique. The effects of the governing parameters on flow field and heat transfer characteristics were obtained and discussed. Numerical results are obtained for velocity, temperature, and concentration distribution as well as the local Nusselt number and Sherwood number. It is found that the local Nusselt number and Sherwood number increase with an increase in convective parameter A and Lewis number Le. Likewise, the local Sherwood number increases with an increase in both A and Le. A comparison with the previous study available in literature has been done and we found an excellent agreement with them.

The objective of this paper is to analyze the effects of heat and mass transfer in the presence of thermal radiation, internal heat generation and Dufour effect on an unsteady magneto-hydrodynamic mixed convection stagnation point flow towards a vertical plate embedded in a porous medium. The non-linear partial differential equations governing the flow are transformed into a set of ordinary differential equations using suitable similarity variables and then solved numerically using shooting method together with Runge- Kutta algorithm. The effects of the various parameters on the velocity, temperature and concentration profiles are depicted graphically and values of skin- friction coefficient, Nusselt number and Sherwood number for various values of physical parameters are tabulated and discussed. It is observed that the temperature increases for increasing values of the internal heat generation, thermal radiation and the Dufour number and hence thermal boundary layer thickness increases.