Heat Transfer in a Laminar Channel Flow Generated by Injection Through Porous Walls

2007 ◽  
Vol 129 (8) ◽  
pp. 1048-1057 ◽  
Author(s):  
Clarisse Fournier ◽  
Marc Michard ◽  
Françoise Bataille
Keyword(s):  
Channel Flow ◽  
Numerical Solutions ◽  
Scaling Law ◽  
Similarity Solutions ◽  
Temperature Profiles ◽  
Governing Equations ◽  
Temperature Boundary ◽  
Laminar Channel Flow ◽  
Porous Walls ◽  
Uniform Fluid

Steady state similarity solutions are computed to determine the temperature profiles in a laminar channel flow driven by uniform fluid injection at one or two porous walls. The temperature boundary conditions are non-symmetric. The numerical solution of the governing equations permit to analyze the influence of the governing parameters, the Reynolds and Péclet numbers. For both geometries, we deduce a scaling law for the boundary layer thickness as a function of the Péclet number. We also compare the numerical solutions with asymptotic expansions in the limit of large Péclet numbers. Finally, for non-symmetric injection, we derive from the computed temperature profile a relationship between the Nusselt and Péclet numbers.

Laminar Free Convection on a Curved Wall

1971 ◽  
Vol 38 (4) ◽  
pp. 1081-1083
Author(s):  
K. W. McAlister
Keyword(s):  
Heat Transfer ◽  
Free Convection ◽  
Temperature Variation ◽  
Newtonian Fluid ◽  
Numerical Solutions ◽  
Similarity Solutions ◽  
Governing Equations ◽  
Transfer Rates ◽  
Arbitrary Temperature ◽  
Free Parameters

Laminar free convection of a Newtonian fluid passing over a curved wall having arbitrary temperature variation is considered. The governing equations are presented and the method of free parameters is used to investigate the existence of similarity solutions. It is found that similarity solutions do exist when the wall inclination and temperature are required to be certain functions of the coordinate parallel to the wall. Numerical solutions to several example cases are presented which indicate that higher heat-transfer rates are possible on a wall which is concave with respect to the fluid.

scholarly journals Second law analysis for MHD permeable channel flow with variable electrical conductivity and asymmetric Navier slips

Open Physics ◽  
2014 ◽  
Vol 13 (1) ◽  
Author(s):  
Adetayo S. Eegunjobi ◽  
Oluwole D. Makinde
Keyword(s):  
Electrical Conductivity ◽  
Channel Flow ◽  
Second Law ◽  
Bejan Number ◽  
Temperature Profiles ◽  
Governing Equations ◽  
Permeable Channel ◽  
Entropy Generation Number ◽  
Navier Slip ◽  
Second Law Analysis

AbstractThe inherent irreversibility in a steady hydromagnetic permeable channel flow of a conducting fluid with variable electrical conductivity and asymmetric Navier slip at the channel walls in the presence of induced electric field is theoretically investigated. The model nonlinear governing equations are obtained and numerically solved using shooting quadrature. Numerical results for velocity and temperature profiles are utilised to compute the entropy generation number and the Bejan number. Pertinent results are displayed graphically and discussed quantitatively.

Non-similarity solutions to the corner boundary-layer equations (and the effects of wall transpiration)

1999 ◽  
Vol 400 ◽  
pp. 125-162 ◽  
Author(s):  
PETER W. DUCK ◽  
SIMON R. STOW ◽  
MANHAR R. DHANAK
Keyword(s):  
Boundary Layer ◽  
Numerical Solutions ◽  
A Priori ◽  
Leading Edge ◽  
Flow Region ◽  
Similarity Solutions ◽  
Leading Order ◽  
Governing Equations ◽  
Boundary Layer Equations ◽  
Pressure Term

The incompressible boundary layer in the corner formed by two intersecting, semi-infinite planes is investigated, when the free-stream flow, aligned with the corner, is taken to be of the form U∞F(x), x representing the non-dimensional streamwise distance from the leading edge. In Dhanak & Duck (1997) similarity solutions for F(x) = xn were considered, and it was found that solutions exist for only a range of values of n, whilst for ∞ > n > −0.018, approximately, two solutions exist. In this paper, we extend the work of Dhanak & Duck to the case of non-90° corner angles and allow for streamwise development of solutions. In addition, the effect of transpiration at the walls of the corner is investigated. The governing equations are of boundary-layer type and as such are parabolic in nature. Crucially, although the leading-order pressure term is known a priori, the third-order pressure term is not, but this is nonetheless present in the leading-order governing equations, together with the transverse and crossflow viscous terms.Particular attention is paid to flows which develop spatially from similarity solutions. It turns out that two scenarios are possible. In some cases the problem may be treated in the usual parabolic sense, with standard numerical marching procedures being entirely appropriate. In other cases standard marching procedures lead to numerically inconsistent solutions. The source of this difficulty is linked to the existence of eigensolutions emanating from the leading edge (which are not present in flows appropriate to the first scenario), analogous to those found in the computation of some two-dimensional hypersonic boundary layers (Neiland 1970; Mikhailov et al. 1971; Brown & Stewartson 1975). In order to circumvent this difficulty, a different numerical solution strategy is adopted, based on a global Newton iteration procedure.A number of numerical solutions for the entire corner flow region are presented.

Laminar Free Convection from a Rotating Radial Plate

1972 ◽  
Vol 94 (4) ◽  
pp. 419-424 ◽  
Author(s):  
G. S. H. Lock ◽  
R. S. Ko
Keyword(s):  
Heat Transfer ◽  
Free Convection ◽  
High Speed ◽  
Numerical Solutions ◽  
Temperature Profiles ◽  
Governing Equations ◽  
High Speed Rotation ◽  
Convection Problem ◽  
Speed Rotation ◽  
Radial Plate

The paper presents a theoretical analysis of conduction through, and free convection from, a radial plate rotating in a synchronous environment of air. The plate resembles a tapered, radially protruding fin heated at the root. Ordering of the governing equations reveals three controlling parameters, under the condition of steady high-speed rotation. Numerical solutions to the combined conduction–convection problem reveal the effect of the parameters on the velocity and temperature profiles, the overall heat-transfer relation, and the fin effectiveness.

Symmetrical Laminar Channel Flow With Wall Suction

1976 ◽  
Vol 98 (3) ◽  
pp. 469-474 ◽  
Author(s):  
B. K. Gupta ◽  
E. K. Levy
Keyword(s):  
Velocity Profile ◽  
Channel Flow ◽  
Similarity Solutions ◽  
Inlet Velocity ◽  
Boundary Layer Equations ◽  
Wide Range ◽  
Laminar Channel Flow ◽  
Dimensional Boundary ◽  
Steady Laminar ◽  
Good Agreement

Entrance region solutions of the two-dimensional boundary layer equations are presented in terms of a convergent power series for steady, laminar, incompressible channel flow with uniform mass suction at the walls. The entrance solutions obtained using both uniform and parabolic velocity profiles at the inlet to the channel are compared to the solutions obtained from the similarity equations for a wide range of non-dimensional suction velocities (0 ≤ Rew ≤ 30). With a parabolic inlet velocity profile, the flow does not become fully developed for Rew > 7, except right at the downstream end of the channel (x = L). The similarity solutions are in good agreement with the entrance solutions over a reasonable length of the channel only for very small values of Rew. With a uniform inlet velocity profile, the flow does not become fully developed in the range 7 < Rew < 13, except right at x = L. In this case, the similarity equations should not be used to predict overall axial pressure variations except for very large values of Rew.

scholarly journals Unsteady turbulent line plumes

2018 ◽  
Vol 856 ◽  
pp. 103-134
Author(s):  
Andrew J. Hogg ◽  
Edward J. Goldsmith ◽  
Mark J. Woodhouse
Keyword(s):  
Numerical Solutions ◽  
Similarity Solutions ◽  
Stable Model ◽  
Governing Equations ◽  
Shape Factors ◽  
Piecewise Constant ◽  
Horizontal Variation ◽  
Model Account ◽  
Ill Posed ◽  
Well Posed

The unsteady ascent of a buoyant, turbulent line plume through a quiescent, uniform environment is modelled in terms of the width-averaged vertical velocity and density deficit. It is demonstrated that for a well-posed, linearly stable model, account must be made for the horizontal variation of the velocity and the density deficit; in particular the variance of the velocity field and the covariance of the density deficit and velocity fields, represented through shape factors, must exceed threshold values, and that models based upon ‘top-hat’ distributions in which the dependent fields are piecewise constant are ill-posed. Numerical solutions of the nonlinear governing equations are computed to reveal that the transient response of the system to an instantaneous change in buoyancy flux at the source may be captured through new similarity solutions, the form of which depend upon both the ratio of the old to new buoyancy fluxes and the shape factors.

MHD Mixed Convection of Viscoelastic Fluid Over a Stretching Sheet with Ohmic Dissipation

2008 ◽  
Vol 24 (3) ◽  
pp. N29-N34 ◽  
Author(s):  
K.-L. Hsiao
Keyword(s):  
Mixed Convection ◽  
Viscoelastic Fluid ◽  
Stretching Sheet ◽  
Magnetic Parameter ◽  
Numerical Solutions ◽  
Similarity Transformation ◽  
Temperature Profiles ◽  
Governing Equations ◽  
Ohmic Dissipation ◽  
Finitedifference Method

AbstractA magnetic hydrodynamic (MHD) mixed convection of an incompressible viscoelastic fluid over a stretching sheet with ohmic dissipation is studied. The buoyant effect and the electric number E1 couple with magnetic parameter M to represent the dominance of the ohmic effect are presented in governing equations which is the main contribution by this study. The similarity transformation, the finitedifference method have been used to analyze the present problem. The numerical solutions of the flow velocity distributions, temperature profiles and the important wall unknown values of f″(0) and θ′(0) are carried out.

On the Interaction and Reflection of Shocks in Hyperelastic Strings

1991 ◽  
Vol 58 (2) ◽  
pp. 554-558 ◽  
Author(s):  
J. L. Wegner ◽  
L. Jiang ◽  
J. B. Haddow
Keyword(s):  
Method Of Characteristics ◽  
Numerical Solutions ◽  
Similarity Solutions ◽  
Finite Amplitude ◽  
Governing Equations ◽  
Wave Interactions ◽  
Amplitude Wave ◽  
Multiple Wave ◽  
The Method Of Characteristics ◽  
Interaction Problem

Governing equations for finite amplitude wave propagation in stretched hyperelastic strings are given in recent papers, (Beatty and Haddow, 1985), along with similarity solutions for symmetrically plucked and impacted strings. The similarity solutions are valid until the first reflections at the fixed ends and in this paper we consider symmetrically plucked Mooney-Rivlin strings and investigate the response after reflections. The method of characteristics is applied to extend the results of the similarity solutions and to obtain solutions for the interaction of a reflected longitudinal shock and incident transverse shock and the reflection of an incident transverse shock. A deformed shape, which is not intuitively obvious, is predicted by the solution of the interaction problem and is confirmed by an experimental study. A finite difference scheme is used to obtain numerical solutions, which are valid after multiple wave interactions and reflections occur. Solutions obtained by the method of characteristics are used as a partial check on the numerical results.

Thermal Post-Buckling Analysis of Functionally Graded Composite Plates with Nonlinear Aerodynamic Forces

2010 ◽  
Vol 123-125 ◽  
pp. 280-283
Author(s):  
Chang Yull Lee ◽  
Ji Hwan Kim
Keyword(s):  
Material Properties ◽  
Numerical Solutions ◽  
Virtual Work ◽  
Shear Deformation Theory ◽  
Composite Plates ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Governing Equations ◽  
Functionally Graded Composite ◽  
Post Buckling

The post-buckling of the functionally graded composite plate under thermal environment with aerodynamic loading is studied. The structural model has three layers with ceramic, FGM and metal, respectively. The outer layers of the sandwich plate are different homogeneous and isotropic material properties for ceramic and metal. Whereas the core is FGM layer, material properties vary continuously from one interface to the other in the thickness direction according to a simple power law distribution in terms of the volume fractions. Governing equations are derived by using the principle of virtual work and numerical solutions are solved through a finite element method. The first-order shear deformation theory and von-Karman strain-displacement relations are based to derive governing equations of the plate. Aerodynamic effects are dealt by adopting nonlinear third-order piston theory for structural and aerodynamic nonlinearity. The Newton-Raphson iterative method applied for solving the nonlinear equations of the thermal post-buckling analysis

Integral Solutions of Phase Change With Internal Heat Generation

2004 ◽  
Author(s):  
Ali Siahpush ◽  
John Crepeau
Keyword(s):  
Differential Equation ◽  
Phase Change ◽  
Heat Generation ◽  
Numerical Solutions ◽  
Internal Heat ◽  
Melting Rate ◽  
Internal Heat Generation ◽  
Stefan Number ◽  
Temperature Boundary ◽  
Solid Liquid

This paper presents solutions to a one-dimensional solid-liquid phase change problem using the integral method for a semi-infinite material that generates internal heat. The analysis assumed a quadratic temperature profile and a constant temperature boundary condition on the exposed surface. We derived a differential equation for the solidification thickness as a function of the internal heat generation (IHG) and the Stefan number, which includes the temperature of the boundary. Plots of the numerical solutions for various values of the IHG and Stefan number show the time-dependant behavior of both the melting and solidification distances and rates. The IHG of the material opposes solidification and enhances melting. The differential equation shows that in steady-state, the thickness of the solidification band is inversely related to the square root of the IHG. The model also shows that the melting rate initially decreases and reaches a local minimum, then increases to an asymptotic value.

Sign in / Sign up

Export Citation Format

Share Document