An approximate method for the calculation of the incompressible laminar spanwise boundary layer on an infinite uniform yawed cylinder with distributed suction

This paper describes an approximate method to calculate the incompressible laminar spanwise boundary layer on an infinite yawed uniform cylinder with distributed suction. The calculation for the chordwise layer is supposed to be known. A similar method to calculate the laminar spanwise layer for a solid boundary is given by Rott and Crabtree, but for a porous boundary with suction no such method is known to the author at present except the one given in this paper. The present method is equally applicable to a solid boundary also. A comparison of the calculation by the present approximate method is made with the exact solutions of the spanwise layer with the chordwise velocity distribution U = Cx ^mat the edge of the layer, and the agreement is found to be quite satisfactory. Moreover, the method is very simple in operation.     

The transverse curvature effect on the incompressible laminar boundary layer for longitudinal flow over a cylinder

A solution to the partial differential equations governing incompressible laminar flow in the axial direction over a circular cylinder is presented. A method is employed which reduces the partial differential equations to a set of ordinary differential equations which are then solved consecutively. The solution is initiated at a leading edge and proceeds far downstream. Velocity profiles and values for the coefficient of skin friction, displacement thickness and momentum thickness are obtained. The results are compared to previously obtained solutions valid near the leading edge and asymptotic solutions valid far downstream.     

Solution of a laminar boundary layer flow via a numerical method

In this paper, the numerical solution of the Blasius problem is obtained using the collocation method based on rational Chebyshev functions. The Blasius equation is a nonlinear ordinary differential equation which arises in the boundary layer flow. The method reduces solving the equation to solving a system of nonlinear algebraic equations. The results presented here demonstrate reliability and efficiency of the method.     

Compressible laminar boundary layer behavior studied by a finite difference method

Zusammenfassung Die L?sung des Systems der nichtlinearen partiellen Differentialgleichungen der laminaren kompressiblen Grenzschicht bereitet erhebliche mathematische Schwierigkeiten. In dieser Arbeit wird ein Differenzenverfahren benutzt, um die Str?mung entlang einer gekrümmten Wand zu untersuchen. Analytische Bedingungen für seine Stabilit?t sind angegeben, und die Konvergenz der L?sung gegen die L?sung des Differentialgleichungssystems ist durch Vergleichsrechnungen mit verschiedener Schrittweite erprobt. Der Einfluss von beliebigen Druck- und Temperaturverteilungen ist an einer Reihe von Beispielen untersucht. Da das Verfahren Energiedissipation und Ver?nderlichkeit der Dichte und der Z?higkeit vollst?ndig berücksichtigt, sind seine Ergebnisse benutzt, um die Vereinfachungen kritisch zu diskutieren, die so oft angewendet werden, um die analytische L?sung des Problems zu erleichtern.

---

---

This research was supported by the Air Force Office of Scientific Research of the Air Research and Development Command under Contract AF 18(600)-1488.     

Investigation of secondary flow on an infinite yawed cylinder in a compressible stream

In this paper a study of the secondary flow on an infinite yawed cylinder in a compressible stream is made at stagnation for unit Prandtl number and for a given Mach number. The secondary flow profiles are calculated for different edge inclination angles. The chordwise and spanwise velocity profiles given by Crabtree¹ are used here in the calculation. It is found that the secondary flow profiles are the same for complementary edge inclination angles and they are maximum for the edge inclination angle of 45°. A comparison with the incompressible flow profiles² is made. It is found that the magnitude of the secondary flow profiles in a compressible stream is less than that in an incompressible stream for the same edge inclination angle.     

Heat transfer in MHD viscoelastic boundary layer flow over a stretching sheet with non-uniform heat source/sink

This paper presents the study of momentum and heat transfer characteristics in a hydromagnetic flow of viscoelastic liquid over a stretching sheet with non-uniform heat source, where the flow is generated due to a linear stretching of the sheet and influenced by uniform magnetic field applied vertically. Here an analysis has been carried out to study the effect of magnetic field on the visco-elastic liquid flow and heat transfer over a stretching sheet with non-uniform heat source. The non-linear boundary layer equation for momentum is converted into ordinary differential equation by means of similarity transformation and is solved exactly. Heat transfer differential equation is also solved analytically. The effect of magnetic field on velocity, skin friction and temperature profiles are presented graphically and discussed.     

Visco-elastic boundary layer flow past a stretching plate and heat transfer

In the present paper, we study the temperature profile in the case of a linear stretching plate for large Prandtl numberP by an asymptotic approach. Also, we evaluate the Nusselt number and the order of magnitude of Prandtl number for variable Nusselt numbers.     

Mixed convection boundary layer flow over a permeable vertical surface with prescribed wall heat flux

The effects of suction/injection on the laminar mixed convection boundary-layer flow on a vertical wall with a prescribed heat flux are considered. The conditions which allow the equations to be reduced to similarity form are derived and numerical solutions of the resulting equations are obtained for a range of values of the suction/injection and buoyancy parameters. Two specific cases, corresponding to a stagnation point flow and uniform wall heat flux, are treated in detail. Results are presented in terms of the skin friction and wall temperature with a selection of velocity and temperature profiles also being given. Dual solutions are found to exist for assisting flow, these are an addition to what has been reported previously for opposing flows. Solutions for some limiting values of the parameters are also derived.      

Mixed convection boundary layer flow over a permeable vertical surface with prescribed wall heat flux

The effects of suction/injection on the laminar mixed convection boundary-layer flow on a vertical wall with a prescribed heat flux are considered. The conditions which allow the equations to be reduced to similarity form are derived and numerical solutions of the resulting equations are obtained for a range of values of the suction/injection and buoyancy parameters. Two specific cases, corresponding to a stagnation point flow and uniform wall heat flux, are treated in detail. Results are presented in terms of the skin friction and wall temperature with a selection of velocity and temperature profiles also being given. Dual solutions are found to exist for assisting flow, these are an addition to what has been reported previously for opposing flows. Solutions for some limiting values of the parameters are also derived.     

Heat transfer in MHD viscoelastic boundary layer flow over a stretching sheet with thermal radiation and non-uniform heat source/sink

An analysis has been carried out to study the flow and heat transfer characteristics for MHD viscoelastic boundary layer flow over an impermeable stretching sheet with space and temperature dependent internal heat generation/absorption (non-uniform heat source/sink), viscous dissipation, thermal radiation and magnetic field due to frictional heating. The flow is generated due to linear stretching of the sheet and influenced by uniform magnetic field, which is applied vertically in the flow region. The governing partial differential equations for the flow and heat transfer are transformed into ordinary differential equations by a suitable similarity transformation. The governing equations with the appropriate conditions are solved exactly. The effects of viscoelastic parameter and magnetic parameter on skin friction and the effects of viscous dissipation, non-uniform heat source/sink and the thermal radiation on heat transfer characteristics for two general cases namely, the prescribed surface temperature (PST) case and the prescribed wall heat flux (PHF) case are presented graphically and discussed. The numerical results for the wall temperature gradient (the Nusselt number) are presented in tables and are discussed.     

Mechanics of transition in an axisymmetric laminar boundary layer on a circular cylinder

Measurements of the growth of artificially generated turbulent spots and intermittency distribution in the transition region on a circular cylinder in axial flow show that the instability Reynolds number of 11,000 has a marked effect on the properties. In particular, it is found that the spot production in the initial region when a single turbulent spot has not yet wrapped around the cylinder and the propagation is essentially two-dimensional, is significantly altered. But the transition in the downstream or latter region, where most of the turbulent spots propagate onedimensionally (like the turbulent plugs in a pipe), is not affected. When the radius Reynolds number is more than 11,000, the intermittency law in the initial region is essentially the same as in twodimensional flow on a flat plate and in the latter region it is the one-dimensional flow in a pipe, the demarcation between the two regions being quite sharp.     

A quasilinearization approach to heat transfer in MHD visco-elastic fluid flow

The paper deals with the study of the flow of an incompressible electrically conducting visco-elastic fluid referred to as Walter’s liquid B over a porous non-isothermal stretching sheet using quasilinearization technique adopting a numerical approach. The sheet is assumed to stretch uni-directionally and the fluid above the sheet is at rest if there were no stretching. The temperature profiles are obtained numerically and these are displayed through graphs for diverse values of Prandtl number, visco-elastic parameter, magnetic parameter, source/sink parameter, wall temperature parameter and wall heat flux parameter. The results are compared with those available in literature obtained through analytical procedures and are seen to be in good agreement.     

Similarity solutions for flow and heat transfer over a permeable surface with convective boundary condition

The steady laminar boundary layer flow over a permeable flat plate in a uniform free stream, with the bottom surface of the plate is heated by convection from a hot fluid is considered. Similarity solutions for the flow and thermal fields are possible if the mass transpiration rate at the surface and the convective heat transfer from the hot fluid on the lower surface of the plate vary like x^−1/2, where x is the distance from the leading edge of the solid surface. The governing partial differential equations are first transformed into ordinary differential equations, before being solved numerically. The effects of the governing parameters on the flow and thermal fields are thoroughly examined and discussed.     

A similarity solution for laminar thermal boundary layer over a flat plate with a convective surface boundary condition

This paper considers the classical problem of hydrodynamic and thermal boundary layers over a flat plate in a uniform stream of fluid. It is well known that similarity solutions of the energy equation are possible for the boundary conditions of constant surface temperature and constant heat flux. However, no such solution has been attempted for the convective surface boundary condition. The paper demonstrates that a similarity solution is possible if the convective heat transfer associated with the hot fluid on the lower surface of the plate is proportional to x^?1/2. Numerical solutions of the resulting similarity energy equation are provided for representative Prandtl numbers of 0.1, 0.72, and 10 and a range of values of the parameter characterizing the hot fluid convection process. For the case of constant heat transfer coefficient, the same data provide local similarity solutions.     

Natural convection boundary layer flow of fluid with temperature-dependent viscosity from a horizontal elliptical cylinder with constant surface heat flux

This study deals with the temperature-dependent viscosity effects on the natural convection boundary layer on a horizontal elliptical cylinder with constant surface heat flux. The mathematical problem is reduced to a pair of coupled partial differential equations for the temperature and the stream function, and the resulting nonlinear equations are solved numerically by cubic spline collocation method. Results for the heat transfer characteristics are presented as functions of eccentric angle for various values of viscosity variation parameters, Prandtl numbers and aspect ratios. Results show that an increase in the viscosity variation parameter tends to accelerate the fluid flow near the surface and increase the maximum velocity, thus decreasing the velocity boundary layer thickness. As the viscosity variation parameter is increased, the surface temperature tends to decrease, thus increasing the local Nusselt number. Moreover, the local Nusselt number of the elliptical cylinder increases as the Prandtl number of the fluid is increased.     

Optimization technique in solving laminar boundary layer problems with temperature dependent viscosity

In this paper, a novel numerical method is proposed to solve specific third order ODE on semi-infinite interval. These kinds of problems often occur in laminar boundary layer with temperature dependent viscosity. Runge-Kutta method incorporating with optimization techniques is used to solve the problem. First, the semi-infinite interval is transformed into a finite interval. Second, by converting the boundary value problem, with some initial and distributed unknowns, into an optimization problem, solving the original problem is limited to solving a multiobjective optimization problem. Third, we use shooting-Newton’s method for solving this optimization problem. It is shown that the Falkner-Skan problem with constant surface temperature, that arise during the solution for the laminar forced convection heat transfer from wedges to flow, can be solved accurately and simultaneously by this strategy. Numerical results for different values of wedge angle and Prandtl number are presented, which are in good agreement with some of the successful provided solutions in the literature.     

Investigation of secondary flow on an infinite yawed cylinder with 15 per cent. Thick Joukowski profile as section

This paper contains a theoretical investigation of the secondary flow in the laminar incompressible boundary layer on an infinite yawed cylinder with chordwise section as Joukowski profile of 15 per cent. thickness at zero incidence and with homogeneous suction, the suction mass flow coefficient being equal to 0·2085. The secondary flow profiles are obtained at different points of the wing section and for various angles of sweepback. It is found that in favourable pressure gradients and at pressure minimum, the secondary flow profiles have negative values. In regions of adverse pressure gradients after the pressure minimum the secondary flow changes sign from negative to positive values and have points of inflexion. The change of sign starts from the surface and extends to the edge of the boundary layer downstream. At some points in adverse pressure gradients the secondary flow profiles have double points of inflexion and values of both signs simultaneously. It is also found that an adverse pressure gradient produces more powerful secondary flow than a favourable pressure gradient of the same strength.     

On the heat transfer in a two-phase hollow cylinder with piecewise continuous boundary conditions

This consideration concern heat transfer in two-component composite with a deterministic microstructure, which is Δ-periodic along the angular axis and has slowly varying effective properties in the radial direction (Fig.1). Therefore, we deal here with a special case of functionally graded materials, FGM, c.f. Suresh, Mortensen (1998). The main aim of this consideration is to capture effect of the discontinuous boundary conditions on the thermal field. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)