Effect of variable viscosity on boundary layer flow along a continuously moving plate with variable surface temperature

Flow of an incompressible viscous fluid past a continuously moving semi-infinite plate is studied by taking into account variable viscosity and variable temperature. Velocity and temperature profiles are shown graphically whereas the numerical values of the skin-friction and the rate of heat transfer are listed in a table. The effect of different parameters on the flow field is discussed.     

A time marching method for unsteady two-dimensional flow in a blade passage

A time marching method for calculating non-uniform unsteady two-dimensional flow through a blade passage is presented. The various problems encountered in extending time marching techniques into this field are examined, and the method is applied to analyse unsteady wake flows through a compressor and turbine blade row.     

Boiling on a straight pin fin with variable thermal conductivity

This work theoretically investigated the thermal performance and stability characteristics of a straight pin fin subject to boiling considering a temperature-dependent thermal conductivity of fin, k=k _sat(1+b(T−T _sat)). Steady-state temperature distribution and the associated fin base heat flow were for the first time analytically found, whose stability characteristics were evaluated by linear stability analysis. A positive temperature coefficient b will raise both the fin's temperature and base heat flow. The corresponding stability for stable fin boiling was enhanced. A negative b results in an opposite trend. The use of a mean thermal conductivity in fin boiling calculations is discussed. Received on 3 November 1997     

Heat transfer in flow past a continuous moving plate with variable temperature

A study of thermal boundary layer on a continuously moving semi-infinite flat plate, whose temperature varies as Axⁿ, where A is a constant and x is measured from the leading edge of the plate, has been presented. Similarity solutions have been derived and the resulting equations are integrated numerically. It has been observed that the value of the Nusselt number increases with increasing n.

---

Wärmeübertragung in einer Strömung längs einer kontinuierlich bewegten Platte mit variabler Temperatur

Zusammenfassung Es wird die thermische Grenzschicht an einer gleichförmig bewegten halbunendlichen Platte, deren Temperatur sich nach der Gleichung Axⁿ ändert, betrachtet. A ist eine Konstante und x ist der Abstand von der Vorderkante. Ähnlichkeitslösungen wurden abgeleitet und die entstehenden Gleichungen numerisch integriert. Aus den Ergebnissen ergibt sich ein Anstieg der Nusselt-Zahlen mit steigendem Exponenten n.

     

Mass transfer effects on flow past a vertical oscillating plate with variable temperature

An exact solution to the flow of a viscous incompressible fluid past an infinite vertical oscillating plate, in the presence of a foreign mass has been derived by the Laplace-transform technique when the plate temperature is linearly varying as time. The velocity profiles are shown on graphs and the numerical values of the skin-friction are listed in a table. It is observed that the skin-friction increases with increasingSc, t orGr but decreases with increasingGm ort, whereSc (the Schmidt number), (frequency),t (time),Gr (the Grashof number) andGm is (the modified Grashof number) andt.

---

Einfluß von Stoffübergang auf die Strömung entlang einer senkrechten oszillierenden Platte veränderlicher Temperaturen

Zusammenfassung Mit Hilfe der Laplace-Transformation wird eine exakte Lösung für die Strömung einer zähen, inkompressiblen Flüssigkeit entlang einer unendlich ausgedehnten, senkrechten, oszillierenden Platte gewonnen, wobei die Einwirkung eines Feststoffs Berücksichtigung findet und die Plattentemperatur linear mit der Zeit veränderlich sein soll. Die Geschwindigkeitsprofile sind in Diagrammen dargestellt und die numerischen Werte der Reibungsschubspannung in einer Tabelle. Letztere wächst mit der Schmidt-ZahlSc, der Grashof-ZahlGr und dem Produkt aus Frequenz und Zeitt; sie nimmt ab, wennGm (die modifizierte Grashof-Zahl) undt zunehmen.

---

Nomenclature C species concentration in the fluid near the plate - C ^– species concentration in the fluid away from the plate - C _W species concentration at the plate - C _p specific heat at constant pressure - D chemical molecular diffusivity - Gm modified Grashof number - Gr Grashof number - g acceleration due to gravity - K thermal conductivity - P Prandtl number - Sc Schmidt number - T Temperature of the fluid near the plate - T _W temperature of the plate - T temperature of the fluid far away from the plate - t time - u velocity of the fluid in the upward direction - U ₀ amplitude of oscillation - x coordinate axis along the plate in the vertically upward direction - y coordinate axis normal to the plate Greek symbols skin-friction - viscosity - coefficient of volume expansion - ^* coefficient of species expansion - density - frequency     

Effects of magnetohydrodynamic flow past a vertical plate with variable surface temperature

An analysis is performed to study the magnetohydrodynamic flow of an electrically conducting, viscous incompressible fluid past a semi-infinite vertical plate with variable surface temperature under the action of transversely applied magnetic field. The heat due to viscous dissipation and the induced magnetic field are assumed to be negligible. The dimensionless governing equations are unsteady, two-dimensional, coupled and non-linear governing equations. It is found that the magnetic field parameter has a retarding effect on the velocities of air and water.     

Unsteady-state temperature distribution in a convecting fin of constant area

A solution for the unsteady-state temperature distribution in a fin of constant area dissipating heat only by convection to an environment of constant temperature, is obtained. The partial differential equation is separated into an ordinary differential equation with position as the independent variable, and a partial differential equation with position and time as the independent variables. The problem is solved for either a step function in temperature or a step function in heat flow rate, for zero time, at one boundary while the other boundary is insulated. The initial condition is taken as an arbitrary constant. The unspecified boundary values (temperature or heat flow rate) are presented for both cases by utilizing dimensionless plots. Experimental verification is presented for the case of constant heat flow rate boundary condition.     

Steady nonlinear hydromagnetic flow and heat transfer over a stretching surface of variable temperature

The steady nonlinear hydromagnetic flow of an incompressible, viscous and electrically conducting fluid with heat transfer over a surface of variable temperature stretching with a power-law velocity in the presence of variable transverse magnetic field is analysed. Utilizing similarity transformation, governing nonlinear partial differential equations are transformed to nonlinear ordinary differential equations and they are numerically solved using fourth-order Runge–Kutta shooting method. Numerical solutions are illustrated graphically by means of graphs. The effects of magnetic field, stretching parameter and Prandtl number on velocity, skin friction, temperature distribution and rate of heat transfer are discussed.     

Analytic study on non-Newtonian natural convection boundary layer flow with variable wall temperature on a horizontal plate

The similarity transform for the steady free convection boundary layer flow of a non-Newtonian fluid (Casson model) with variable wall temperature on a horizontal plate gives a system of nonlinear ordinary differential equations which is solved analytically by applying a newly developed method namely the homotopy analysis method (HAM). The velocity and temperature profiles are obtained and the influence of Prandtl number and various physical parameters of the problem on these distributions are discussed in detail and are illustrated graphically through a set of graphs. The validity of our solutions is verified by the numerical results.     

Viscoelastic flow in a two-dimensional collapsible channel

We compute the flow of three viscoelastic fluids (Oldroyd-B, FENE-P, and Owens blood model) in a two-dimensional channel partly bounded by a tensioned membrane, a benchmark geometry for fluid–structure interactions. The predicted flow patterns are compared to those of a Newtonian liquid. We find that computations fail beyond a limiting Weissenberg number. Flow fields and membrane shape differ significantly because of the different degree of shear thinning and molecular extensibility underlying the three different microstructural models.     

Radiation effect on optimum design analysis of a constructal T-shaped fin with variable thermal conductivity

A constructal T-shaped fin with temperature dependent thermal conductivity of fin the material exposed to both convective and radiative environments is analyzed by Adomian decomposition method. This method provides a closed form of analytical solution for analyzing the temperature distribution, performance and optimum design. A comparative study has been executed among the present and published works. Unlike the published work, dependent parameters on the performance and optimization analysis are highlighted.     

Variable permeability effect on buoyancy-induced inclined boundary layer flow in a saturated porous medium with variable wall temperature

The analysis is carried out for buoyancy-induced boundary layer flow adjacent to an inclined heated surface in a saturated porous medium incorporating the variation of permeability and thermal conductivity due to paking particles with non-uniform temperature. The surface temperature is assumed to vary as a power function of the axial coordinate measured from the leading edge of the surface. Both the streamwise and normal component of the buoyancy force are retained in the momentum equations. Numerical solutions are obtained in the cases of uniform and nonuniform permeability and various values of the inclination parameter ξ (x) = (Ra _x cos ϕ)^1/3 tan ϕ by using finite difference method. The problem is solved using nonsimilarity solutions for the case of variable wall temperature. Results for the details of the velocity and temperature fields as well as local Nusselt number have been presented.     

Transient multiboiling in a pin fin with temperature dependent thermal conductivity

Transient heat conduction in fins undergoing different kinds of convective processes (film, transition, nucleated boiling and natural convection) as in multiboiling processes take place, is a strongly non-linear problem because of the abrupt changes in the heat transfer coefficient that occur at certain temperatures. Transient equations for the thermal fields and fluxes are solved simultaneously, giving the time constant of the process; the stationary solution is compared with the numerical or experimental values of other authors. Temperature dependencies of the heat transfer coefficient and the thermal conductivity is assumed due to the large interval of temperatures occurring. Network Simulation Method is used for the numerical solution, which gives simultaneously thermal field of temperatures and heat fluxes.     

Transonic flow around bodies of revolution with a passage in the presence of a jet issuing from the passage

Similarity laws are obtained for the transonic flow around axisymmetric bodies with a passage of the nacelle type air-breathing engine (or its root section) in the presence of a jet issuing from a nozzle. The validity of the laws established is verified by the results of a numerical solution of the problem of the transonic flow around the bodies investigated, executed by integrating the complete nonlinear system of flow equations.     

Separation of flow over a diaphragm in a two-dimensional channel

A study is made of the hydrodynamic problem of the flow with separation over a diaphragm with sharp edges. The vorticity of the fluid in The separation region is determined by means of the Zhukovskii—Chaplygin condition of finiteness of the velocity at the sharp edge, and the extension of the separation region is found from the condition of vanishing of the velocity of the fluid at the point of closure of the separation region.Translated from Izvestiya Akademii Nauk SSSE, Mekhanika Zhidkosti i Gaza, No. 4, pp. 134–137, July–August, 1981.I thank L. I. Sedov and N. A. Slezkin, and also the participants of the seminars run by them for helpful discussion of the work.     

Supersonic two-dimensional flow in a forward separation zone

Supersonic separated flow past a spiked body with a plane cap on the end of the spike (a flat plate or a wedge) is studied. The cases of both symmetric and nonsymmetric flow, with a rotating or nonrotating spike, are considered. The flow pattern, visualized by means of a Toepler instrument and a laser knife, and the limiting streamline patterns are analyzed. The reasons for the initiation of self-oscillations in the flow between the cap and the body are determined. The flow patterns for a rotating and nonrotating spike are compared.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 152–162, January–February, 1995.