Compressible boundary layer flow with non-uniform slot injection (or suction) over i) a cylinder and ii) a sphere

Non-similar solutions of steady two-dimensional and axi-symmetric compressible laminar boundary layer flows with non-uniform slot injection (or suction) have been obtained, from the starting point of the stream-wise co-ordinate to the exact point of separation. The difficulties arising at the starting point of the stream-wise co-ordinate, and at the edges of the slot and at the point of separation have been overcome by applying the method of quasi-linear implicit finite difference scheme, along with an appropriate selection of finer step size along the stream-wise direction. It is observed that the separation can be delayed by a non-uniform slot suction and also by moving the slot downstream but the effect of non-uniform slot injection is just the opposite. The increase of total enthalpy at the wall causes the separation to occur earlier while cooling delays it. The increase of Mach number shifts the point of separation upstream due to the adverse pressure gradient

Self-similar solution of the unsteady flow in the stagnation point region of a rotating sphere with a magnetic field

The unsteady flow and heat transfer of a viscous incompressible electrically conducting fluid in the forward stagnation point region of a rotating sphere in the presence of a magnetic field are investigated in this study. The unsteadiness in the flow field is caused by the velocity at the edge of the boundary layer and the angular velocity of the rotating sphere, both varying continuously with time. The system of ordinary differential equations governing the flow is solved numerically. For some particular cases, an analytical solution is also obtained. It is found that the surface shear stresses in x- and y-directions and the surface heat transfer increase with the acceleration, the magnetic and the rotation parameters whether the magnetic field is fixed relative to the fluid or body, except that the surface shear stress in x-direction and the surface heat transfer decrease with increasing the magnetic parameter when the magnetic field is fixed relative to the body. For a certain value of the acceleration parameter, the surface shear stress in the x-direction vanishes while the surface shear stress in the y-direction and the surface heat transfer remain finite. Also, below a certain value of the acceleration parameter, reverse flow occurs in the x-component of the velocity profile

Numerical study of heat transfer characteristics of the micropolar boundary layer near a stagnation point on a moving wall

The present paper presents a numerical study of heat transfer of a micropolar boundary layer flow near a stagnation point on a moving wall. The governing differential equations are solved numerically and the temperature profiles are shown graphically for different values of material parameters and wall velocity. The heat transfer rate has been obtained for both the isothermal and the adiabatic case. It is concluded that the temperature in the boundary layer increases for the micropolar flows, as compared to the Newtonian flows

Free convection flow of two immiscible viscous liquids through parallel permeable beds: use of Brinkman equation

The present paper deals with an analytical study of free convection in fully developed laminar, free convection flow of two viscous, immiscible, incompressible liquids bounded above and blow by two parallel naturally permeable beds of high porosity and finite thickness. The momentum transfer in the free flow region is governed by Navier-Stokes equations and the flow in the porous medium is governed by Brinkman equation. The flow domain is divided into four regions and exact solutions of the momentum and energy equations are obtained for each region under appropriate matching and boundary conditions. The effects of various parameters on the velocity and temperature fields are discussed with the help of graphs while the effects on skin-friction and heat transfer are discussed with the help of tables

Mathematical modelling of gradually varied flow in open channels: corrections to the Chow and Bresse integration derivations

We present a re-examination of the gradually varied flow problem for open channels. A close study of the classical study by Bresse (1860) [1] and Bakhmeteff (1912) [2] and later Chow (1955) [4] has shown that their standard computations contain some errors. The objective is to clarify this error in open channel hydrodynamics and thereby assist engineers and modelers engaged in this area of research

Hydrodynamic stability of viscous flow between curved porous channel with radial flow

A linear stability analysis has been presented for the flow between long concentric stationary porous cylinders driven by constant azimuthal pressure gradient, when a radial flow through the permeable walls of the cylinders is present. The radial Reynolds number, based on the radial velocity at the inner cylinder and the inner radius is varied from −100 to 30. The linearized stability equations form an eigenvalue problem which are solved using a numerical technique based on classical Runge–Kutta scheme combined with a shooting method, termed as unit disturbance method. It is observed that radially outward flow and strong inward flow have a stabilizing effect, while weak inward flow has a destabilizing effect on the stability. Profiles of the relative amplitude of the perturbed radial velocities show that radially outward flow shifts the vortices toward the outer cylinder, while radially inward flow shifts the vortices toward the inner cylinder

Three-dimensional heat and mass transfer flow of a viscous fluid with periodic suction velocity

In this paper, three-dimensional unsteady free convection and mass transfer flow of an incompressible, viscous liquid through a porous medium past an infinite vertical porous plate is presented. It is considered that the plate is subjected to a time-dependent periodic suction velocity normal to the plate. Approximate solutions for the velocity, temperature, and concentration fields are obtained by using the series expansion method and considering ε as a reference parameter. Expressions for the skin friction, rate of heat transfer, and mass transfers are also derived. The results obtained are discussed for the cooling and heating cases of the porous plate

Effects of nonuniformly heated wall(s) on a natural-convection flow in a square cavity filled with a porous medium

The influence of uniform and nonuniform heating of wall(s) on natural-convection flow in a square cavity filled with a porous matrix has been studied numerically by using the penalty finite-element method with biquadratic rectangular elements. In the present investigation, the left vertical wall and the bottom wall are uniformly and nonuniformly heated, while the right vertical wall is maintained at constant cold temperature and the top wall is well insulated. The Darcy-Forchheimer model is used to simulate the momentum transfer in the porous medium. The present numerical approach yields consistent performance over the range of parameters (Rayleigh number Ra, 103 ≤ Ra ≤ 106, Darcy number Da, 10-5 ≤ Da ≤ 10-3, and Prandtl number Pr, 0.71 ≤ Pr ≤ 10) in order to obtain the solutions in terms of stream functions, temperature profiles, and Nusselt numbers. Nonuniform heating of the bottom wall produces greater heat transfer rate at the center of the bottom wall than the uniform heating case for all Rayleigh numbers, but average Nusselt number shows overall lower heat transfer rate for the nonuniform heating case. Critical Rayleigh numbers for conduction-dominant heat transfer cases have been obtained. For convection-dominated regimes the power-law correlations between average Nusselt number and Rayleigh numbers are presented