# Non-uniform mass transfer or wall enthalpy into a compressible flow over yawed cylinder

01 Aug 2001-International Journal of Heat and Mass Transfer (Pergamon)-Vol. 44, Iss: 16, pp 3017-3024

TL;DR: In this article, an analysis is performed to obtain the non-similar solution of a steady compressible laminar boundary layer flow over a yawed infinite circular cylinder with non-uniform slot injection (or suction) and nonuniform wall enthalpy, where the difficulties arising at the starting point of the streamwise coordinate, at the edges of the slot and at the point of separation are overcome by applying the method of quasilinear implicit finite difference scheme.

Abstract: An analysis is performed to obtain the non-similar solution of a steady compressible laminar boundary layer flow over a yawed infinite circular cylinder with non-uniform slot injection (or suction) and non-uniform wall enthalpy. The difficulties arising at the starting point of the streamwise coordinate, at the edges of the slot and at the point of separation are overcome by applying the method of quasilinear implicit finite-difference scheme. It is observed that the separation can be delayed by non-uniform slot suction and also by moving the slot downstream but the effect of non-uniform slot injection is just the reverse. An increase in Mach number and total enthalpy at wall causes the separation to occur earlier while cooling delays it. The non-uniform total enthalpy at the wall (i.e., the cooling or heating of the wall in a slot) has very little effect on the skin friction and hence on the point of separation.

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TL;DR: In this article, the spectral relaxation method (SRM) and the spectral quasilinearization method (SQLM) are extended for the first time to systems of nonlinear PDEs that model unsteady boundary layer flow.

Abstract: Nonlinear partial differential equations (PDEs) modelling unsteady boundary-layer flows are solved by the spectral relaxation method (SRM) and the spectral quasilinearization method (SQLM). The SRM and SQLM are Chebyshev pseudospectral based methods that have been successfully used to solve nonlinear boundary layer flow problems described by systems of ordinary differential equations. In this paper application of these methods is extended, for the first time, to systems of nonlinear PDEs that model unsteady boundary layer flow. The new extension is tested on two problems: boundary layer flow caused by an impulsively stretching plate and a coupled four-equation system that models the problem of unsteady MHD flow and mass transfer in a porous space. Numerous simulation experiments are conducted to determine the accuracy and compare the computational performance of the proposed methods against the popular Keller-box finite difference scheme which is widely accepted as being one of the ideal tools for solving nonlinear PDEs that model boundary layer flow problems. The results indicate that the methods are more efficient in terms of computational accuracy and speed compared with the Keller-box.

109Â citations

### Cites background from "Non-uniform mass transfer or wall e..."

...A sizeable body of literature now exists on the use of various finite difference based QLM schemes in boundary layer flows described by both nonlinear ODE and PDE-based systems [11â€“15]....

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TL;DR: In this paper, contact conduction and contact resistance were investigated. But contact conuction with convection, phase change, and phase change was not one of the main issues in this paper.

Abstract: 2. Conduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1892 2.1. Contact conduction and contact resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1892 2.2. Micro/nanoscale thermal effects, laser pulse heating, and hyperbolic heat transport . . 1892 2.3. Composites, heterogeneous media and complex geometries . . . . . . . . . . . . . . . . . . . 1893 2.4. Conduction with convection, phase change . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1893 2.5. Analytical, numerical and experimental studies . . . . . . . . . . . . . . . . . . . . . . . . . . . 1893 2.6. Thermomechanical problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1893 2.7. Miscellaneous and special applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1893

53Â citations

### Cites background from "Non-uniform mass transfer or wall e..."

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...The compressible flow past a yawed cylinder was studied for non-uniform mass transfer or wall enthalpy [334]....

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TL;DR: In this article, the influence of non-uniform slot injection (suction) into steady axi-symmetric laminar incompressible boundary layer flows with temperature dependent viscosity and Prandtl number has been examined from the origin of the streamwise coordinate to the exact point of separation.

Abstract: The influence of non-uniform slot injection (suction) into steady axi-symmetric laminar incompressible boundary layer flows with temperature dependent viscosity and Prandtl number has been examined from the origin of the streamwise coordinate to the exact point of separation. The difficulties in obtaining the non-similar solutions at the origin of the streamwise coordinate, at the edges of the slot and at the point of separation have been overcome by applying an implicit finite difference scheme with the quasilinearization technique and an appropriate selection of finer step size along the streamwise coordinate. The results indicate that the separation can be delayed by non-uniform slot suction and also by moving the slot downstream but the effect of non-uniform slot injection is just the opposite. Further, the effect of variable fluid properties is to move the point of separation downstream but rotation parameter has the reverse effect.

49Â citations

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TL;DR: In this article, an analysis is performed to obtain the non-similar solution of a steady laminar forced convection boundary layer flow over a horizontal slender cylinder including the effect of non-uniform slot injection (suction) including the effects of transverse curvature and viscous dissipation.

Abstract: An analysis is performed to obtain the non-similar solution of a steady laminar forced convection boundary layer flow over a horizontal slender cylinder including the effect of non-uniform slot injection (suction) The effects of transverse curvature and viscous dissipation are also included in the analysis The governing boundary layer equations along with the boundary conditions are first cast into a dimensionless form using suitable transformations and the resulting system of nonlinear coupled partial differential equations is then solved by an implicit finite difference scheme in combination with the quasilinearization technique Numerical results for the effect of non-uniform slot injection (suction) on skin friction coefficient and heat transfer rate are presented The effects of transverse curvature, viscous dissipation and Prandtl number on velocity and temperature profiles and skin friction and heat transfer coefficients are also reported

47Â citations

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TL;DR: In this article, the non-uniform slot injection (suction) into water boundary layer flow over a yawed infinite circular cylinder is analyzed including the temperature-dependent viscosity and Prandtl number.

Abstract: The non-uniform slot injection (suction) into water boundary layer flow over a yawed infinite circular cylinder is analyzed including the temperature-dependent viscosity and Prandtl number. The difficulties arising at the starting point of the streamwise coordinate, at the edges of the slot and at the point of separation are overcome by applying the implicit finite difference scheme in combination with the quasilinearization technique. The results indicate that the separation can be delayed by non-uniform slot suction and also by moving the slot downstream but effect of non-uniform slot injection is just the opposite. Further, the effect of variable fluid properties is to move the point of separation downstream but yaw angle has very little affect on the location of the point of separation.

31Â citations

##### References

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01 Jan 1955

TL;DR: The flow laws of the actual flows at high Reynolds numbers differ considerably from those of the laminar flows treated in the preceding part, denoted as turbulence as discussed by the authors, and the actual flow is very different from that of the Poiseuille flow.

Abstract: The flow laws of the actual flows at high Reynolds numbers differ considerably from those of the laminar flows treated in the preceding part. These actual flows show a special characteristic, denoted as turbulence. The character of a turbulent flow is most easily understood the case of the pipe flow. Consider the flow through a straight pipe of circular cross section and with a smooth wall. For laminar flow each fluid particle moves with uniform velocity along a rectilinear path. Because of viscosity, the velocity of the particles near the wall is smaller than that of the particles at the center. i% order to maintain the motion, a pressure decrease is required which, for laminar flow, is proportional to the first power of the mean flow velocity. Actually, however, one ob~erves that, for larger Reynolds numbers, the pressure drop increases almost with the square of the velocity and is very much larger then that given by the Hagen Poiseuille law. One may conclude that the actual flow is very different from that of the Poiseuille flow.

17,321Â citations

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30 Nov 1961

TL;DR: In this article, the authors propose Matrix Methods for Parabolic Partial Differential Equations (PPDE) and estimate of Acceleration Parameters, and derive the solution of Elliptic Difference Equations.

Abstract: Matrix Properties and Concepts.- Nonnegative Matrices.- Basic Iterative Methods and Comparison Theorems.- Successive Overrelaxation Iterative Methods.- Semi-Iterative Methods.- Derivation and Solution of Elliptic Difference Equations.- Alternating-Direction Implicit Iterative Methods.- Matrix Methods for Parabolic Partial Differential Equations.- Estimation of Acceleration Parameters.

5,317Â citations

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28 Mar 1988TL;DR: In this article, a comprehensive presentation of numerical methods suitable for the analysis of various heat transverse and fluid flow problems that occur in research, practice, and university instruction is given.

Abstract: A comprehensive presentation is given of virtually all numerical methods that are suitable for the analysis of the various heat transverse and fluid flow problems that occur in research, practice, and university instruction. After reviewing basic methodologies, the following topics are covered: finite difference and finite element methods for parabolic, elliptic, and hyperbolic systems; a comparative appraisal of finite difference versus finite element methods; integral and integrodifferential systems; perturbation methods; Monte Carlo methods; finite analytic methods; moving boundary problems; inverse problems; graphical display methods; grid generation methods; and programing methods for supercomputers.

718Â citations

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01 Jan 1976

TL;DR: The Diffusion Equation as discussed by the authors is a generalization of the Wave Equation, which is used in the Laplace Transform Methods (LTLM) and Green's Functions.

Abstract: The Diffusion Equation. Laplace Transform Methods. The Wave Equation. The Potential Equation. Classification of Second Order Equations. First Order Equations. Extensions. Perturbations. Green's Functions. Variational Methods. Eigenvalue Problems. More on First Order Equations. More on Characteristics. Finite-Difference Equations and Numerical Methods. More on Transforms. Singular Perturbation Methods. Index.

154Â citations