Incompressible fluid flow and heat transfer through a nonsaturated porous medium

This work studies a nonsaturated flow and the heat transfer associated phenomenon of a newtonian fluid through a rigid porous matrix, using a mixture theory approach in its modelling. The mixture consists of three overlapping continuous constituents: a solid (porous medium), a liquid and an inert gas, included to account for the compressibility of the system as a whole. A set of four nonlinear partial differential equations describe the problem whose hydrodynamical part is approximated by means of a Glimm's scheme combined with an operator splitting technique.     

Heat transfer in a viscoelastic boundary layer flow through a porous medium

This paper examines the viscoelastic fluid flow and heat transfer characteristics in a saturated porous medium over an impermeable stretching surface with frictional heating and internal heat generation or absorption. The heat transfer analysis has been carried out for two different heating processes, namely (i) with prescribed surface temperature (PST-case) and (ii) prescribed surface heat flux (PHF-case). The governing equations for the boundary layer flow problem result similar solutions. For the specified five boundary conditions, it is not possible to solve directly the resulting sixth-order nonlinear ordinary differential equation. For the present incompressible boundary layer flow problem with constant physical parameters, the momentum equation is decoupled from the energy equation. Two closed–form solutions for the momentum equation are obtained and identified the realistic solution of the physical problem. Exact solution for the velocity field and the skin-friction are obtained. Also, the solution for the temperature and the heat transfer characteristics are obtained in terms of Kummers function. Asymptotic results for the temperature function for large Prandtl numbers are presented. The work due to deformation in the energy equation, which is essential and escaped from the attention of researchers while formulating the visco-elastic boundary layer flow problems, is considered. Drastic variation in the values of heat transfer coefficient is observed when the work due to deformation is ignored.The authors would like to thank the reviewers for their valuable comments/ suggestions to improve the clarity of the paper.     

On boundary conditions for fluid flow in porous media

We continue the study undertaken in [11] of boundary conditions at the surface between a porous medium and a free fluid flow. Two different kinds of phenomena may appear, according to the direction of the averaged gradient of pressure in the porous medium, oblique or normal to the surface. General results about the matching of the different flow regions and boundary conditions are given, as well as examples. The interface layer in the case of a normal gradient of pressure is studied in detail.     

MHD flow and heat transfer due to ecentric rotations of a porous disc and a fluid at infinity

An exact solution of the steady 3-dimensional Navier-Stokes equations and the energy equation is derived for the case of flow due to non-coaxilly rotations of a porous disc and a fluid at infinity in the presence of a uniform transverse magnetic field. It is observed that asymptotic solution exists for the velocity profile both in the case of suction and blowing. Further, it is seen that the velocity boundary layer shows a thickness of 0 (1/) in case of suction and it is of 0 (1/γ) in the case of blowing. While, the thermal boundary layer exhibits a double-deck structure of 0 (1/SP_r) and 0 (1/) in case SP_r − ≠ 0 and single-deck structure of 0 (1/) in case SP_r = = 0. Here a, γ depends on suction S, magnetic parameter N and P_r the Prandtl number.     

Open-cell porous metals for thermal management applications: fluid flow and heat transfer

Porous metals are produced by a wide range of industrially applied techniques, and the resulting porous structure is a characteristic of the manufacturing method chosen. This review firstly provides an overview of the different techniques to manufacture open-cell porous metals, highlighting the distinction between the resulting porous structures. The effects of the structural parameters on the fluid flow properties and heat transfer in porous metals are also discussed. It was evident from literature that there exist optimum structural parameters which offered maximum thermal exchange performance. Therefore, the last part of this review outlines the current research on porous metals for thermal management applications, which focuses on optimising the design of the porous metal structure to improve the heat transfer performance.

This review was submitted as part of the 2016 Materials Literature Review Prize of the Institute of Materials, Minerals and Mining run by the Editorial Board of MST. Sponsorship of the prize by TWI Ltd is gratefully acknowledged     

Heat and mass transfer in a binary laminar boundary layer with free convection on a vertical porous surface

An approximate analytical solution of heat and mass transfer in a binary laminar boundary layer with free convection on a vertical surface is presented. The numerical solution is compared with an approximate analytical solution obtained by another method.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 21, No. 1, pp. 19–28, July, 1971.     

Mixture theory for a thermoelasto-plastic porous solid considering fluid flow and internal mass exchange

A thermoelastic–plastic body consisting of two phases, a solid and a fluid, each comprising two constituents is considered where one constituent in one phase is allowed to exchange mass with another constituent (of the same substance) in the other phase. A large strain setting is adopted and the formulation applies to general anisotropy and the existence of residual stresses. Generalized forms of Fourier’s, Fick’s and Darcy’s laws are derived and also the stresses on the constituent, phase and mixture level are established; in addition, the evolution law for general plasticity is given. Finally, and in particular, a general evolution law for the rate of deformation tensor related to mass exchange is proposed and this leads to general absorption and desorption evolution laws for mass exchange between two constituents (of the same substance), one belonging to the solid phase and the other to the fluid phase. Equilibrium curves for absorption and desorption also emerge from the theory.     

Heat and mass transfer on a stretching sheet with a magnetic field in a visco-elastic fluid flow through a porous medium with heat source or sink

A mathematical model will be analyzed in order to study the role of an applied magnetic field on heat and mass transfer in a visco-elastic fluid flow through a porous medium with a stretching sheet in the presence of such effect as heat generation or absorption. A similarity transformation is used to reduce the governing partial differential equations into ordinary ones, which are solved numerically by shooting method. Numerical results for the velocity, temperature and concentration profiles as well as for the local skin friction, Nusselt number and Sherwood number are obtained and reported graphically for various parametric conditions to show interesting aspects of the solution.     

Slip effects on the peristaltic flow of a non-Newtonian Maxwellian fluid

Summary In real systems there is always a certain amount of slip, which, however, is hard to detect experimentally because of the required space resolution. In this paper, we analyze the effect of slip boundary conditions on the dynamics of fluids in porous media by studying the flow of a Newtonian and non-Newtonian Maxwellian fluid in an axisymmetric cylindrical tube (pore), in which the flow is induced by traveling transversal waves on the tube wall. Like in peristaltic pumping, the traveling transversal waves induce a net flow of the liquid inside the pore. The viscosity as well as the compressibility of the liquid is taken into account. This problem has numerous applications in various branches of science, including stimulation of fluid flow in porous media under the effect of elastic waves and studies of blood flow dynamics in living creatures. The Navier-Stokes equations for an axisymmetric cylindrical pore are solved by means of a perturbation analysis, in which the ratio of the wave amplitude to the radius of the pore is small parameter. In the second order approximation, a net flow induced by the traveling wave is calculated for various values of the compressibility of the liquid, relaxation time and Knudsen number. The calculations disclose that the compressibility of the liquid, Knudsen number of slip flow and non-Newtonian effects in presence of peristaltic transport have a strong influence of the net flow rate. The effects of all parameters of the problem are numerically discussed and graphically explained.     

Heat transfer in a transient boundary layer on a porous plate

We present the results of an experimental study and a procedure for calculation of the effect of intense injection of various coolants on stability loss in laminar flow and on heat transfer in a transient boundary layer on a porous plate in a longitudinal flow.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 33, No. 2, pp. 197–203, August, 1977.     

Heat transfer in channels with porous inserts during forced fluid flow

General analytic expressions are obtained to calculate heat transfer and temperature fields in a plane channel with a porous insert with allowance for the effective thermal conductivity of the heat carrier and the distribution of heat between the skeleton of the insert and the fluid in the boundary pores.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 56, No. 1, pp. 36–44, January, 1988.     

Transient convective mass transfer at a disc rotating in a non-newtonian fluid

Results are shown of a theoretical and experimental study concerning the transient convective mass transfer at a disc rotating in a non-Newtonian fluid.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 22, No. 3, pp. 441–449, March 1972.     

An XFEM model for cracked porous media: effects of fluid flow and heat transfer

In this work, a numerical model is developed to investigate the influence of fluid flow and heat transfer on the thermo-mechanical response of a cracked porous media. The fluid flow, governed by the Darcy’s law, is discretized with the nonconforming finite element method. Time splitting is used with the energy conservation equation to solve the fluid and the solid phases separately. A combination of Discontinuous Galerkin (DG) and multi-point flux approximation methods is used to solve the advection-diffusion heat transfer equation in the fluid phase. While the conductive heat transfers equation in the solid phase is solved using the eXtended finite element method (XFEM) to better handle the temperature discontinuities and singularities caused by the cracks. Further, the resulted temperature is used as body force to solve the thermo-mechanical problem using the XFEM. In the post processing stage, the thermal stress intensity factor is computed using the interaction integral technique at each time step and used to validate the obtained results. A good agreement was found when the results were compared with the existing ones in the literature.     

Unsteady incompressible boundary layer flow of a micropolar fluid at a stagnation point

The flow, heat and mass transfer on the unsteady laminar incompressible boundary layer in micropolar fluid at the stagnation point of a 2-dimensional and an axisymmetric body have been studied when the free stream velocity and the wall temperature vary arbitrarily with time. The partial defferential equations governing the flow have been solved numerically using a quasilinear finite-difference scheme. The skin friction, microrotation gradient and heat transfer parameters are found to be strongly dependent on the coupling parameter, mass transfer and time, whereas the effect of the microrotation parameter on the skin friction and heat transfer is rather weak, but microrotation gradient is strongly affected by it. The Prandtl number and the variation of the wall temperature with time affect the heat-transfer very significantly but the skin friction and micrortation gradient are unaffected by them.     

Heat and mass transfer as a means of flow mode management in a supersonic boundary layer

This paper continues the studies cycle of flow management simulation methods in boundary layers of compressible gas. The influence of distributed heat and mass transfer on the stability characteristics of supersonic boundary layers is considered at Mach numbers M = 2.0 and 5.35. At high Mach numbers, waves of vortex nature and unstable acoustic oscillations emerge. Resistance to both types of disturbances is studied. Both normal injection, with normal mean velocity, V, being the only nonzero component, and injection at other angles, including tangential with the longitudinal component of mean velocity, U, being the only nonzero component on the wall, are simulated. It is shown that a tangential streamwise injection causes significant flow stabilization in relation to vortex and acoustic modes. This mode management provides thermal protection of the streamlined surface under aerodynamic heating, and is able to expand the laminar flow mode region. Cooled gas injection suppresses vortex disturbances and amplifies acoustic waves, while injected heated gas influences boundary layer stability in the opposite way. The performed studies anticipate that an injection of homogeneous cold gas would be similar to an extraneous heavy gas injection, and that injected heated gas would behave similarly to injected light gas.     

Effects of mass transfer on a resonance instability in the laminar boundary layer flow over a rotating-disk

In this paper the linear stability properties of the magnetohydrodynamic flow of an incompressible, viscous and electrically conducting fluid are investigated for the boundary-layer due to an infinite permeable rotating-disk. The fluid is subjected to an external magnetic field perpendicular to the disk. The interest lies also in finding out the effects of uniform suction or injection. In place of the traditional linear stability method, a theoretical approach is adopted here based on the high-Reynolds-number triple-deck theory. It is demonstrated that the nonstationary perturbations evolve in accordance with an eigenrelation analytically obtained.     

The effect of mass transfer on steady two-dimensional rimming flow

Motivated by applications in rapidly rotating machinery, the standard lubrication model of two-dimensional thin-film flow on the inside of a rotating circular cylinder is adapted in a simple manner to incorporate the effect of mass flux into the free surface of the film. A numerical attack, validated against published results for the zero-mass-flux case, is used to study the case of constant mass fraction with non-zero injection into and extraction from the film, this representing the steady-state operating condition in an aero-engine. It is found that increasing mass flux inhibits the formation of the steep fronts on the film surface, thus reducing the chances of droplets being stripped away from the film when there is a core flow present, and that recirculation zones may be suppressed by an increase in the Bond number, thus reducing the chances of oil degradation in rapidly rotating machinery.     

An unsteady flow due to eccentrically rotating porous disk and a fluid at infinity

An exact solution of the unsteady Navier-Stokes equations is obtained for the flow due to non-coaxial rotations of a porous disk, executing non-torsional oscillations in its own plane, and a fluid at infinity. It is shown that the infinite number of solutions existing for a flow confined between two disks reduce to a single unique solution in the case of a single disk. The adjustment of the unsteady flow near the rotating disk to the flow at infinity rotating about a different axis is explained.