Hall effects on oscillating flow due to eccentrically rotating porous disk and a fluid at infinity

Hall effects on the viscous incompressible fluid due to non-coaxial rotations of an oscillating porous disk and a fluid at infinity are studied. The velocity field, shear stresses and temperature distribution are obtained in closed form. It is found that with increase in frequency parameter, the primary velocity increases near the disk and becomes almost stationary away from the disk. The secondary velocity also increases with increase in frequency parameter. It is seen that with increase in Hall parameter, the primary velocity increases near the disk and decreases away from the disk. The reversed effect is observed for the secondary velocity. The shear stresses at the disk are also obtained. It is found that the shear stresses due to the primary and the secondary velocities decrease with increase in Hall parameter. The heat transfer characteristic is also studied on taking viscous dissipation into account. It is found that the mean temperature at the disk decreases with increase in Hall parameter.     

Heat transfer enhancement with deformation of the velocity profile

The problem of enhancing the heat transfer in channels and boundary layers by the appropriate deformation of the fluid velocity profile is considered. The resulting additional hydraulic losses, the price of heat transfer enhancement, are determined. The possibilities of controlling heat transfer by redistributing the fluid velocity in channels are demonstrated with reference to flows at low Prandtl numbers. Laminar and turbulent liquid and gas flows with heat transfer in channels and boundary layers are numerically modeled on the basis of modern models of turbulence (flow development in channels with different initial velocity profiles, flows with wall roughness and boundary layer flows with forces acting on the flow to cause deformation of the velocity profile). In all cases it is found that the heat transfer can be enhanced only at the expense of a considerable increase in the hydaulic losses. A class of self-similar thermal problems for flows in plane diffusers is formulated. The eigenfunctions — temperature modes — for various velocity profiles are determined with allowance for the nonuniqueness of the solution of the classical dynamical problem for a plane diffuser and the corresponding heat transfer coefficients are found.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.4, pp. 94–105, May–June, 1993.The authors are grateful to A. Yu. Klimenko for useful discussions.     

Investigation on convective heat transfer over a rotating disk with discrete pins

A three-dimensional numerical study on the flow and heat transfer characteristics over a rotating disk surface with discrete pins was conducted by the use of RNG k–ε turbulent model. And some experiments were also made for validation. The effects of rotating angular speed and pin configuration on the temperature maps and convective heat transfer characteristics on the rotating surface were analyzed. As the increase of rotating velocity, the impingement of pumping jet on the centre of rotating disk becomes stronger and the transition from laminar to turbulent occurs at the outer radius of rotating disk, which resulting in heat transfer enhancement. The pins on the disk make the pumping action of a rotating disk weaker. Simultaneously, they also act as perturbing elements to the cyclone flow near the rotating disk surface, making the overall heat transfer to be enhanced. The needle pins have higher convective heat transfer capacity than the discrete ring pins with the same extend pin areas.     

Rotating disk heat transfer in a fluid swirling as a forced vortex

The paper represents results of an exact solution of a laminar heat transfer problem for a rotating disk in a fluid co-rotating with the disk as a solid body. The angular speed of the fluid is less than the angular speed of the disk. Disks surface temperature varies radially accordingly to a power law. Results for the laminar regime are compared with computations for turbulent heat transfer obtained using an integral method developed earlier. On the basis of the exact solution for laminar flow and basic ideas of the integral methods solution for turbulent flow, an integral method for laminar regime is designed and an approximate analytical solution of the considered problem is derived. Inaccuracies of the laminar approximate solution over the main range of variation of the influencing parameters and Prandtl numbers from 0.71 to 1 do not exceed 2.5%. It is shown that the dependence of the Nusselt number on the ratio of the angular speeds of disk and fluid varying from 0 to 0.3 is weak and has a point of maximum within this region for laminar flow. The obtained results are important in predictions of fluid flow and heat transfer in different types of rotating machinery.     

Dynamics of Sutterby fluid flow due to a spinning stretching disk with non-Fourier/Fick heat and mass flux models

The magnetohydrodynamic Sutterby fluid flow instigated by a spinning stretchable disk is modeled in this study. The Stefan blowing and heat and mass flux aspects are incorporated in the thermal phenomenon. The conventional models for heat and mass flux, i.e., Fourier and Fick models, are modified using the Cattaneo-Christov(CC)model for the more accurate modeling of the process. The boundary layer equations that govern this problem are solved using the apt similarity variables. The subsequent system of equations is tackled by the Runge-Kutta-Fehlberg(RKF) scheme. The graphical visualizations of the results are discussed with the physical significance. The rates of mass and heat transmission are evaluated for the augmentation in the pertinent parameters. The Stefan blowing leads to more species diffusion which in turn increases the concentration field of the fluid. The external magnetism is observed to decrease the velocity field. Also,more thermal relaxation leads to a lower thermal field which is due to the increased time required to transfer the heat among fluid particles. The heat transport is enhanced by the stretching of the rotating disk.     

Buoyancy-affected laminar film condensation

The flow and heat transfer in a laminar condensate flim on an isothermal vertical plate is modelled mathematically. The strict Boussinesq approximation is adopted to account for buoyancy due to local temperature variations within the film. A similarity transformation reduces the governing boundary-layer type equations to a coupled set of ordinary differential equations and the resulting three-parameter twopoint boundary value problem is solved numerically for Prandtl numbers,Pr, ranging from 0.001 to 1000 and Jakob numbers,Ja, between 0.0001 and 1.5. The principal effects of the favourable buoyancy are to reduce the thickness of the condensate film and increase the film velocity at the smooth liquid-vapour interface, whereas the friction and heat transfer at the plate are enhanced. In accordance with the classical Nusselt theory, it is found that the temperature varies nearly linearly across the film. The computed similarity profiles for velocity reveal, however, substantial departures from the parabolic distribution assumed in the simplified Nusselt analysis.     

Double diffusive convection of anomalous density fluids in a porous cavity

A numerical study has been performed to analyze the combined effect of temperature and species gradients on the buoyancy-driven natural convection flow of cold water near its density extremum contained in a porous cavity. The governing equations are descretized using the finite volume method. The results of the investigation are presented in the form of steady-state streamlines, velocity vectors, isotherms, and isoconcentrationlines. The results are discussed for different porosities, Darcy numbers, and Grashof numbers. The heat and mass transfer rates calculated are found to behave nonlinearly with hot wall temperature. The heat and mass transfer are increased with increasing Darcy number and porosity. It is found that the convective heat and mass transfer rate are greatly affected by the presence of density maximum.     

Unsteady heat transfer from a rotating disk to fluids with low Prandtl numbers

Summary An analysis is presented concerning unsteady heat transfer from a rotating disk to a low Prandtl number fluid under the condition of a step change in surface temperature with time. Entire time history results for the surface heat flux are given for Prandtl numbers up to 0.04, and these results are obtained by means of a first-order perturbation about the solution for zero Prandtl number. Steady-state heat transfer predicted by this method agrees almost precisely with exact values.     

Numerical study of flow and heat transfer during oscillatory blood flow in diseased arteries in presence of magnetic fields

A problem motivated by the investigation of the heat and mass transfer in the unsteady magnetohydrodynamic(MHD) flow of blood through a vessel is solved numerically when the lumen of the vessel has turned into the porous structure.The time-dependent permeability and the oscillatory suction velocity are considered.The computational results are presented graphically for the velocity,the temperature,and the concentration fields for various values of skin friction coefficients,Nusselt numbers,and Sherwood numbers.The study reveals that the flow is appreciably influenced by the presence of a magnetic field and also by the value of the Grashof number.     

Utilization of Maxwell-Cattaneo law for MHD swirling flow through oscillatory disk subject to porous medium

The present study aims to investigate the salient features of incompressible,hydromagnetic, three-dimensional flow of viscous fluid subject to the oscillatory motion of a disk. The rotating disk is contained in a porous medium. Furthermore, a time-invariant version of the Maxwell-Cattaneo law is implemented in the energy equation. The flow problem is normalized by obtaining similarity variables. The resulting nonlinear system is solved numerically using the successive over-relaxation method. The main results are discussed through graphical representations and tables. It is perceived that the thermal relaxation time parameter decreases the temperature curves and increases the heat transfer rate. The oscillatory curves for the velocity field demonstrate a decreasing tendency with the increasing porosity parameter values. Two-and three-dimensional flow phenomena are also shown through graphical results.     

Numerical study of the flow and heat transfer in a Reiner-Rivlin fluid on a rotating porous disk

An unsteady flow and heat transfer to an infinite porous disk rotating in a Reiner—Rivlin non-Newtonian fluid are considered. The effect of the non-Newtonian fluid characteristics and injection (suction) through the disk surface on velocity and temperature distributions and heat transfer is considered. Numerical solutions are obtained over the entire range of the governing parameters.Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 1, pp. 85–95, January–February, 2005.     

Analysis of laminar thermal entrance region of elliptical and rectangular channels with Kantorowich method

The Kantorowich method of variational calculus is introduced to solve the problem of laminar forced heat convection in a channel of an arbitrary cross section. Employing this procedure, the development of the temperature field and the heat transfer data in the thermal entrance region of elliptical and rectangular channels are determined, assuming a linear variation of wall temperature in the direction of flow. The uniform and the fully developed velocity profiles are considered. The local Nusselt numbers are tabulated for different aspect ratios.     

A Simple Hysteretic Constitutive Model for Unsaturated Flow

The present study covers the problem of rotation of a porous disk under a viscous incompressible fluid that fills the half-space above the disk, which is the generalization of the von Karman’s problem. It is found that, instead of solving the exact problem, which is rather complicated by coupling the motions of the free fluid and that contained inside the permeable disk, it is sufficient to solve a much simpler problem of the motion of the free fluid placed onto a permeable plane. Assuming the flow in the permeable disk is described by the Brinkman equations, we obtain a self-similar formulation of the problem. Employing this formulation, we also show that the boundary condition associated with continuity of the tangential strains and tangential velocity components is satisfied at the fluid–porous body interface. The coefficient for the vertical velocity component is furthermore obtained. Various extreme cases are identified.     

Free Convection Heat Transfer over a Vertical Cylinder in a Saturated Porous Medium Using a Local Thermal Non-equilibrium Model

In this article, free convection heat transfer over a vertical cylinder with variable surface temperature distributions in a porous medium is analyzed. It is assumed that the fluid and solid phases are not in local thermal equilibrium and, therefore, a two-temperature model of heat transfer is applied. The coupled momentum and energy equations are presented and then they are transformed into ordinary differential equations. The similarity equations are solved numerically. The resulting velocity, streamlines, temperature distributions for fluid and solid phases are shown for different values of parameters entering into the problem. The calculated values of the local Nusselt numbers for both solid and fluid phases are also shown.     

Combined effects of rotation and translation on a MHD flow due to compressible viscous fluid

Summary The modification of an axi-symmetric viscous flow due to a relative rotation of a disk or fluid by a translation of the boundary are studied. The fluid is taken to be compressible and electrically conducting. The equations governing the motion are solved iteratively through a central-difference scheme. The effect of an axial magnetic field and disk temperature on the flow and heat transfer are included in the present analysis. The translation of the disk or fluid generates a velocity field at each plane parallel to the disk (secondary flow). The cartesian components of the velocity due to the secondary flow are oscillatory in nature when a rigid body rotation of the free stream along with a translation of the disk is considered. The magnetic field damps out the velocity field, and reduces the thickness of the boundary layer. The cross component of wall shear due to secondary flow acts in a direction opposite to the rotation of the disk or fluid for all cases of the motion. The rise in disk temperature produces an increment in the magnitude of the wall shear associated with the secondary flow.     

Numerical Simulation of Turbulent Flow and Heat Transfer in a Three-Dimensional Channel Coupled with Flow Through Porous Structures

This study investigates numerically the turbulent flow and heat transfer characteristics of a T-junction mixing, where a porous media flow is vertically discharged in a 3D fully developed channel flow. The fluid equations for the porous medium are solved in a pore structure level using an Speziale, Sarkar and Gatski turbulence model and validated with open literature data. Overall, two types of porous structures, consisted of square pores, are investigated over a wide range of Reynolds numbers: an in-line and a staggered pore structure arrangement. The flow patterns, including the reattachment length in the channel, the velocity field inside the porous medium as well as the fluctuation velocity at the interface, are found to be strongly affected by the velocity ratio between the transversely interacting flow streams. In addition, the heat transfer examination of the flow domain reveals that the temperature distribution in the porous structure is more uniform for the staggered array. The local heat transfer distributions inside the porous structure are also studied, and the general heat transfer rates are correlated in terms of area-averaged Nusselt number accounting for the effects of Reynolds number, velocity ratio as well as the geometrical arrangement of the porous structures.     

Fully Developed Forced Convection Heat Transfer in a Porous Channel with Asymmetric Heat Flux Boundary Conditions

An analytical study is performed on steady, laminar, and fully developed forced convection heat transfer in a parallel plate channel with asymmetric uniform heat flux boundary conditions. The channel is filled with a saturated porous medium, and the lower and upper walls are subjected to different uniform heat fluxes. The dimensionless form of the Darcy–Brinkman momentum equation is solved to determine the dimensionless velocity profile, while the dimensionless energy equation is solved to obtain temperature profile for a hydrodynamically and thermally fully developed flow in the channel. Nusselt numbers for the lower and upper walls and an overall Nusselt number are defined. Analytical expressions for determination of the Nusselt numbers and critical heat flux ratio, at which singularities are observed for individual Nusselt numbers, are obtained. Based on the values of critical heat flux ratio and Darcy number, a diagram is provided to determine the direction of heat transfer between the lower or upper walls while the fluid is flowing in the channel.     

Natural convection heat transfer from a thin rectangular fin with a line source at the base — a finite difference solution

This paper presents an analysis of the problem of a thin fin of finite thermal conductivity, with an isothermal line source at the base, dissipating heat to the surrounding air by natural convection. The horizontal surface to which the fin is attached is adiabatic so that heat is dissipated only through the fin. The temperature and velocity distributions in the field, the temperature profile in the fin, local Nusselt numbers along the fin and the average heat transfer coefficient of the fin are obtained by solving the governing equations in the field and the heat transfer equation in the fin simultaneously, using an explicit unsteady Finite Difference formulation leading to the steady state result. Numerical experiments are performed to study the influence of parameters namely the fin height, temperature of the heating source and the fin material on the average heat transfer coefficient. Comparison is made with fins of infinite thermal conductivity and the vertical isothermal flat plate.     

Rarefied gas flow in a channel with specular‐diffuse boundary conditions for arbitrary knudsen numbers. Onsager relations

The problem of a rarefied gas flow in a channel for arbitrary Knudsen numbers has been solved analytically for the first time in the case where the scattering of gas molecules on the channel walls can be described by speculardiffuse boundary conditions. The mean free path of gas molecules is assumed to be constant, i.e., the collision frequency is proportional to molecular velocity. The gas moves under the action of a streamwise temperature gradient. Exact relations for heat and mass fluxes and for meanmass velocity are obtained. It is shown that the Onsager relations are valid within the entire range of Knudsen numbers in the problem of heat and mass transfer in a channel. The dependence of heat and mass fluxes on the Knudsen number (channel thickness) is analyzed. A comparison with available results is performed.