Asymptotic Profiles for the Blasius and Sakiadis flows in a Darcy–Brinkman Isotropic Porous Medium Either with Uniform Suction or with Zero Transverse Velocity

The Blasius and Sakiadis flows with uniform suction or with zero transverse velocity, at the asymptotic state, in a Darcy–Brinkman porous medium are investigated in this note. Exact analytical solutions are derived for velocity as well as for the integral quantities. It is found that both the dimensional and non-dimensional displacement thickness, momentum thickness, energy thickness and the absolute wall shear stress are identical in both Blasius and Sakiadis flows at the asymptotic state.     

The Blasius and Sakiadis flow with variable fluid properties

A theoretical study of the effect of variable fluid properties on the classical Blasius and Sakiadis flow is presented in this paper. The investigation concerns engine oil, water and air taking into account the variation of their physical properties with temperature. The results are obtained with the numerical simulation of the governing equations and cover large temperature differences. Velocity and temperature profiles are presented, as well as values of wall shear stress and wall heat transfer, for a variety of temperatures between the plate and the ambient fluid. It is found that the variation of fluid properties and especially viscosity have a strong influence on the results. The results of oil and water are, in general, similar and are generalized to liquids whereas air results are different and are generalized to gases. Except of the new results found in the present work some inaccurate results existing in the literature have been identified.     

Heat transfer,development length,and friction factor correlations for the asymptotic region of a laminar arc constrictor

A rigorous equilibrium model is formulated for the laminar flow of plasma through the heating region of a constricted arc plasma generator. The resulting equations are solved for an argon gas using an implicit finite-difference scheme, and the wall shear stress and heat transfer are computed from momentum and energy balances for a wide range of flow rates and arc currents. Friction factors based on this method are in agreement with empirical values to within approximately 10 per cent, and heat transfer calculations agree with the orders of magnitude predicted by a simplified arc model. A dimensionless number peculiar to the constricted arc, the so-called Ohmic heating parameter, is used to correlate the mean Nusselt numbers in the asymptotic arc regime. When the fluid properties are based on the mean temperature, the product of friction factor and Reynolds number is found to be a constant for currents below 200 Amp and to vary with the Ohmic heating parameter for larger currents. Correlations are also presented for the thermal development length, and the agreement with experiment is good.     

Magnetic field effect on heat transfer and fluid flow characteristics of blood flow in multi-stenosis arteries

Heat and fluid flow characteristics of blood flow in multi-stenosis arteries in the presence of magnetic field is considered. A mathematical model of the multi-stenosis inside the arteries is introduced. A finite difference scheme is used to solve the governing equations in terms of vorticity-stream function along with their boundary conditions. The effect of magnetic field and the degree of stenosis on wall shear stress and Nusselt number is investigated. It was found that magnetic field modifies the flow patterns and increases the heat transfer rate. The severity of the stenosis affects the wall shear stress characteristics significantly. The magnetic field torque will increase the thermal boundary layer thickness and the temperature gradient in the streaming blood, and hence increasing the local Nusselt number     

A comparative assessment of fluid flow and heat transfer parameters in laminar flow around a circular cylinder and a sphere

Theoretical studies have been carried out for a comparative assessment of hydrodynamic boundary layer thickness, displacement thickness and shear stress at the wall for laminar flow around a circular cylinder and a sphere with the help of the approximate method due to Karman and Pohlhausen for two dimensional flow and the method as applied to bodies of revolution based on the work of F. W. Scholkemeier, respectively. Thermal boundary layer thickness and Nusselt number have been evaluated around the surface of the solids. Comparison is made with available solutions. The graphical presentation of the results depicts a concise and relative assessment of fluid flow and heat-transfer parameters for flow around cylinder and sphere.     

A Legendre wavelet spectral collocation technique resolving anomalies associated with velocity in some boundary layer flows of Walter-B liquid

A Legendre wavelet spectral collocation method is proposed here to solve three boundary layer flow problems of Walter-B fluid namely the stagnation point flow, Blasius flow and Sakiadis flow. In the proposed method, we first transform the boundary value problems into initial value problems using shooting method. We then split the semi infinite domain into subintervals and the governing initial value problems are transformed to system of algebraic equations in each subinterval. The solutions of these algebraic equations yield an approximate solution of the differential equation in each subinterval. The overshoot in the velocity profile associated with the stagnation point and Blasius flows and undershoot in the Sakiadis flow is controlled. Physically realistic solutions are presented for both weakly and strongly viscoelastic parameters. The residual error validates the correctness, convergence and accuracy of the obtained solutions.     

非稳态Couette流动阶段的边界位移与黏性能量耗散

本文研究了牛顿流体非稳态Couette流动阶段的边界位移与流体黏性摩擦能耗.在上边界始终保持静止,下边界以恒定速度或恒定内壁剪切应力突然运动的情况下,建立了Couette非稳态流动的数学模型.求解定解问题,获得流体速度分布函数;通过渐近分析,获得不同边界条件下流动充分发展的临界时间,进而获得非稳态过程中的边界位移量.利用边界剪切应力和位移量的结果,计算非稳态过程中移动平板做功;再结合流体动能增加量,计算得出不同边界条件下非稳态流动阶段流体黏性摩擦能耗.     

Boundary layer development on a continuous moving surface with a parallel free stream due to impulsive motion

The development of the momentum and thermal boundary layers over a semi-infinite flat plate has been studied when the external stream as well as the plate are impulsively moved with constant velocities. At the same time the temperature of the wall is suddenly raised from T_∞, the temperature of the surrounding fluid, toT _w and maintained at this temperature. The problem has been formulated in a new system of scaled coordinates such that fort?=0 it reduces to Rayleigh type of equation and fort? → ∞ it reduces to Blasius or Sakiadis type of equation. A new scale of time has been used which reduces the region of integration from an infinite region to a finite region which reduces the computational time considerably. The governing singular parabolic partial differential equations have been solved numerically using an implicit finite difference scheme. For some particular cases, analytical solutions have been obtained. The results show that there is a smooth transition from Rayleigh solution to Blasius or Sakiadis solution as the dimensionless timeξ increases from zero to one. The shear stress at the wall is negative for the friction parameterλ<0.5, positive forλ>0.5 and zero forλ=0.5. The zero shear stress at the wall does not imply separation but corresponds to the parallel flow. The surface heat transfer is strongly dependent on the Prandtl numberPr and increases with it. Also forPr<Pr ₀, the surface heat transfer is enhanced as the friction parameterλ increases, but forPr>Pr ₀ it get reduced.     

Effects of viscous dissipation and boundary conditions on forced convection in a channel occupied by a saturated porous medium

Forced convection with viscous dissipation in a parallel plate channel filled by a saturated porous medium is investigated numerically. Three different viscous dissipation models are examined. Two different sets of wall conditions are considered: isothermal and isoflux. Analytical expressions are also presented for the asymptotic temperature profile and the asymptotic Nusselt number. With isothermal walls, the Brinkman number significantly influences the developing Nusselt number but not the asymptotic one. At constant wall heat flux, both the developing and the asymptotic Nusselt numbers are affected by the value of the Brinkman number. The Nusselt number is sensitive to the porous medium shape factor under all conditions considered.     

Non-Newtonian Behavior of Ballistic Gelatin at High Shear Rates

A coordinated modeling and experimental effort to investigate the shear stress-shear strain rate response of ballistic gelatin is presented. A power-law constitutive model that captures non-Newtonian shear-thickening behavior, the evolution of viscosity, and the momentum diffusion at high shear rates is adopted. A simple asymptotic relationship between the maximum wall shear stress and the maximum striking wall velocity is derived in the high diffusion rate regime for a shear flow between two parallel plates. Experimental investigation is conducted on double lap-shear test fixture with gelatin specimens of different thicknesses subjected to high strain rate input on the inner surface, generated by a polymer split Hopkinson pressure bar. This test fixture allows measurement of transmitted shear stress as well as visualization of momentum diffusion through gelatin when imaged by a high speed camera. Gelatin specimens of various thicknesses were used for extracting the power-law model parameters. It is found that ballistic gelatin behaves as a shear-thickening fluid at high shear rates with a power-law exponent of 2.22.     

Radiation effects on combined convection over a vertical flat plate embedded in a porous medium of variable porosity

The present paper is concerned with the study of radiation effects on the combined (forced-free) convection flow of an optically dense viscous incompressible fluid over a vertical surface embedded in a fluid saturated porous medium of variable porosity with heat generation or absorption. The effects of radiation heat transfer from a porous wall on convection flow are very important in high temperature processes. The inclusion of radiation effects in the energy equation leads to a highly non-linear partial differential equations which are transformed to a system of ordinary differential equations using non-similarity transformation. These equations are then solved numerically using implicit finite-difference method subject to appropriate boundary and matching conditions. A parametric study of the physical parameters such as the particle diameter-based Reynolds number, the flow based Reynolds number, the Grashof number, the heat generation or absorption co-efficient and radiation parameter is conducted on temperature distribution. The effects of radiation and other physical parameters on the local skin friction and on local Nusselt number are shown graphically. It is interesting to observe that the momentum and thermal boundary layer thickness increases with the radiation and decrease with increase in the Prandtl number.     

Blood flow in stenosed arteries with radially variable viscosity, peripheral plasma layer thickness and magnetic field

A novel approach of combined mathematical and computational models has been developed to investigate the oscillatory two-layered flow of blood through arterial stenosis in the presence of a transverse uniform magnetic field applied. Blood in the core region and plasma fluid in the peripheral layer region are assumed to obey the law of Newtonian fluid. An analytical solution is obtained for velocity profile and volumetric flow rate in the peripheral plasma region and also wall shear stress. Finite difference method is employed to solve the momentum equation for the core region. The numerical solutions for velocity, flow rate and flow resistance are computed. The effects of various parameters associated with the present flow problem such as radially variable viscosity, hematocrit, plasma layer thickness, magnetic field and pulsatile Reynolds number on the physiologically important flow characteristics namely velocity distribution, flow rate, wall shear stress and resistance to flow have been investigated. It is observed that the velocity increases with the increase of plasma layer thickness. An increase or a decrease in the velocity and wall shear stress against the increase in the value of magnetic parameter (Hartmann number) and hematocrit is dependent on the value of t. An increase in magnetic field leads to an increase in the flow resistance and it decreases with the increase in the plasma layer thickness and pulsatile Reynolds number. The information concerning the phase lag between the flow characteristics and how it is affected by the hematocrit, plasma layer thickness and Hartmann number has, for the first time, been added to the literature.     

Heat transfer for non-Newtonian laminar flow in internally finned pipes with uniform temperature

An analysis is presented for fully developed laminar convective heat transfer of non-Newtonian power-law fluids in pipes with internal longitudinal fins and uniform outside wall temperature. The governing momentum and energy equations have been solved numerically, with the influence of fin conductance. The distributions of fin temperature, fluid temperature and local heat flux (both at finned and unfinned surfaces) are presented. These are shown to be strongly dependent on finned pipe geometry, fluid flow behavior index and the fin conductance. Values of overall Nusselt number indicated significant heat transfer enhancement over finless pipes. The flow behavior index affects the no. of fins which maximizes the overall Nusselt number.     

Radiation effects on the thermal boundary layer flow over a moving plate with convective boundary condition

The steady laminar boundary layer flow over a moving plate in a moving fluid with convective surface boundary condition and in the presence of thermal radiation is investigated in this paper. Under certain conditions, the present problem reduces to the classical Blasius and Sakiadis problems. The effects of radiation and convective parameters on the thermal field are thoroughly examined and discussed. Dual solutions are found to exist when the plate and the fluid move in the opposite directions.     

Magnetohydrodynamic flow over a vertical stretching surface with suction and blowing

An analysis is presented to investigate the flow and heat transfer characteristics of a vertical stretching surface with suction and blowing, and variable magnetic effects. The magnetic field of variable intensity is applied perpendicular to the surface. The range of the magnetic parameter M investigated is 0.1 to 1.0. The flow is considered steady, incompressible, and three-dimensional. The governing momentum and energy equations are solved numerically. Numerical results are presented for velocity distribution, temperature distribution, surface shear stress, and wall heat transfer rate. Discussion is provided for the effect of the magnetic field strength on the velocity and temperature fields. Received on 26 November 1997     

Two-fluid non-linear model for flow in catheterized blood vessels

Blood flow through a catheterized artery is analyzed, assuming the flow is steady and blood is treated as a two-fluid model with the suspension of all the erythrocytes in the core region as a Casson fluid and the plasma in the peripheral region as a Newtonian fluid. The expressions for velocity, flow rate, wall shear stress and frictional resistance are obtained. The variations of these flow quantities with yield stress, catheter radius ratio and peripheral layer thickness are discussed. It is noticed that the velocity and flow rate decrease while the wall shear stress and resistance to flow increase when the yield stress or the catheter radius ratio increases while all the other parameters were held fixed. It is found that the velocity and flow rate increase while the wall shear stress and frictional resistance decrease with the increase of the peripheral layer thickness. The estimates of the increase in the frictional resistance are significantly very small for the present two-fluid model than those of the single-fluid Casson model.     

MHD natural convection flow with radiative heat transfer past an impulsively moving plate with ramped wall temperature

Influence of radiation on unsteady hydromagnetic natural convection transient flow near an impulsively moving vertical flat plate with ramped wall temperature in a porous medium is studied. Exact solution of momentum and energy equations, under Boussinesq approximation, is obtained in closed form by Laplace transform technique. The variations in fluid velocity and temperature are shown graphically whereas numerical values of skin friction and Nusselt number are presented in tabular form.     

A Two-Layer Mathematical Model of Blood Flow in Porous Constricted Blood Vessels

In this paper, we discussed a mathematical model for two-layered non-Newtonian blood flow through porous constricted blood vessels. The core region of blood flow contains the suspension of erythrocytes as non-Newtonian Casson fluid and the peripheral region contains the plasma flow as Newtonian fluid. The wall of porous constricted blood vessel configured as thin transition Brinkman layer over layered by Darcy region. The boundary of fluid layer is defined as stress jump condition of Ocha-Tapiya and Beavers–Joseph. In this paper, we obtained an analytic expression for velocity, flow rate, wall shear stress. The effect of permeability, plasma layer thickness, yield stress and shape of the constriction on velocity in core & peripheral region, wall shear stress and flow rate is discussed graphically. This is found throughout the discussion that permeability and plasma layer thickness have accountable effect on various flow parameters which gives an important observation for diseased blood vessels.     

Influence of magnetic field and thermal radiation by natural convection past vertical cone subjected to variable surface heat flux

A numerical study is performed to examine the heat transfer characteristics of natural convection past a vertical cone under the combined effects of magnetic field and thermal radiation.The surface of the cone is subjected to a variable surface heat flux.The fluid considered is a gray,absorbing-emitting radiation but a non-scattering medium.With approximate transformations,the boundary layer equations governing the flow are reduced to non-dimensional equations valid in the free convection regime.The dimensionless governing equations are solved by an implicit finite difference method of Crank-Nicolson type which is fast convergent,accurate,and unconditionally stable.Numerical results are obtained and presented for velocity,temperature,local and average wall shear stress,and local and average Nusselt number in air and water.The present results are compared with the previous published work and are found to be in excellent agreement.