Flow and heat transfer of a micropolar fluid past a continuously moving porous plate

The boundary layer flow and heat transfer of a micropolar fluid past a semi-infinite porous plate moving continuously is studied. Similarity solutions for the velocity, the temperature, and the microrotation equations are derived. These are shown graphically. The numerical values of the skin-friction coefficient C_f and the rate of heat transfer [?θ'(0)] are entered in tables for different values of suction and injection parameters. The effects of suction and injection, K (the coupling parameter) and G (the microrotation parameter) are discussed.     

Flow of micropolar fluid past a continuously moving plate

A similarity analysis of the flow and heat transfer past a continuously moving semi-infinite plate in a micropolar fluid is presented. The velocity, micro-rotation distribution and the temperature profiles are shown on graphs and the numerical values of the skin friction and the rate of heat transfer are entered in tables. The effects of $\text{K}$ (coupling parameter) and $\text{G}$ (micro-rotation parameter) are discussed.     

Moving wedge and flat plate in a micropolar fluid

Similarity solutions for a moving wedge and flat plate in a micropolar fluid may be obtained when the fluid and boundary velocities are proportional to the same power-law of the downstream coordinate. The governing partial differential equations are transformed to the ordinary differential equations using similarity variables, and then solve numerically using a finite-difference scheme known as the Keller-box method. Numerical results are given for the dimensionless velocity and microrotation profiles, as well as the skin friction coefficient for several values of the Falkner–Skan power-law parameter (m), the ratio of the boundary velocity to the free stream velocity parameter (λ) and the material parameter (K). Important features of these flow characteristics are plotted and discussed. It is found that multiple solutions exist when the boundary is moving in the opposite direction to the free stream, and the micropolar fluids display a drag reduction compared to Newtonian fluids.     

Heat transfer in boundary layer flow of a micropolar fluid past a curved surface with suction and injection

Van Dyke's singular perturbation technique has been used to study the heat transfer in the flow of a micropolar fluid past a curved surface with suction and injection. The conditions for similar solutions of the thermal boundary layer equations have been obtained. In addition to the usual “no slip” condition for velocity, the two types of boundary conditions used for microrotation are: (i) no relative spin on the boundary; (ii) the anti-symmetric part of the stress tensor vanishes at the boundary. The effect of suction or injection on velocity, microrotation, temperature, skin friction coefficient, wall couple stress coefficient, displacement and momentum thicknesses, rate of heat transfer and adiabatic wall temperature have been studied. It is observed that with the increase of injection velocity, the thickness of the boundary layer is increased and the local drag is reduced. A comparison with the results obtained for a Newtonian fluid reveals that the microelements present in the fluid reduce the velocity and frictional drag, and cool the boundary.     

Flow and heat transfer of a micropolar fluid in an axisymmetric stagnation flow on a cylinder with variable properties and suction (numerical study)

Summary. In this paper, an analysis is presented to study the effects of variable properties, density, viscosity and thermal conductivity of a micropolar fluid flow and heat transfer in an axisymmetric stagnation flow on a horizontal cylinder with suction, numerically. The fluid density and the thermal conductivity are assumed to vary linearly with temperature. However, the fluid viscosity is assumed to vary as a reciprocal of a linear function of temperature. The similarity solution is used to transform the problem under consideration into a boundary value problem of nonlinear coupled ordinary differential equations which are solved numerically by using the Chebyshev finite difference method (ChFD). Numerical results are carried out for various values of the dimensionless parameters of the problem. The numerical results show variable density, variable viscosity, variable thermal conductivity and micropolar parameters, which have significant influences on the azimuthal and the angular velocities and temperature profiles, shear stress, couple stress and the Nusselt number. The numerical results have demonstrated that with increasing temperature ratio parameter the azimuthal velocity decreases. With increasing variable viscosity parameter the temperature increases, whereas the azimuthal and the angular velocities decrease. Also, the azimuthal and the angular velocities increase and the temperature decreases as the variable conductivity parameter increases. Finally, the pressure increases as the suction parameter increases.     

Heat transfer in micropolar boundary layer flow over a flat plate

Boundary layer solutions are presented to study the steady state heat transfer from a semi-infinite flat plate to a micropolar fluid. The boundary conditions of isothermal wall, constant surface heat flux and insulated wall with viscous dissipation effects have been treated in this paper. Numerical results for the temperature distribution and the missing wall values of the thermal functions have been given. The range of Prandtl numbers investigated was from 10 to 1000 while the dimensionless grouping of the material properties was allowed to vary over a wide range.     

Flow and heat transfer from a continuous surface in a parallel free stream of micropolar fluid

Boundary layer solutions are presented to investigate the steady now and heat transfer characteristics from a continuous flat surface moving in a parallel free stream of micropolar fluid. Numerical results are presented for the distribution of velocity, micro-rotation and temperature profiles within the boundary layer. The groupings of the material properties of the fluid were allowed to vary over a wide range.     

Free convection in the laminar boundary layer flow of a thermomicropolar fluid past a vertical flat plate with suction/injection

Summary The effect of suction/injection in the laminar free convection flow of a thermomicropolar fluid past a nonuniformly heated vertical flat plate has been considered. The conditions under which similarity exists have been examined. The resulting system of non-linear ordinary differential equations has been solved numerically after transforming the infinite domain of boundary layer coordinate into a finite domain. The effects of variation of the boundary condition parameter and suction/injection parameter on the velocity, microrotation and temperature fields and the heat transfer coefficient have been studied graphically. The skin-friction parameter and the gradient of microrotation on the wall have been tabulated. It is found that there is significant increase in velocity, skin-friction and the heat transfer coefficient with the decreasing concentration of microelements.With 4 Figures     

Unsteady heat transfer in a micropolar fluid flowing in a plane channel

Heat transfer in a micropolar fluid flowing in a plane channel following an abrupt change in the wall temperature is investigated. The obtained results indicate that in several cases the fluid microstructure has a considerable effect on the main heat-transfer characteristics.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 37, No. 6, pp. 994–999, December, 1979.     

Mixed convection in micropolar fluid flow over a horizontal plate with surface mass transfer

Combined free and forced convection in the boundary layer flow of a micropolar fluid over a horizontal surface is studied. Buoyancy effects on the flow and temperature fields are discussed. The influence of uniform mass transfer from the surface is also considered. Wall friction and heat transfer results are presented for various cases representing the relative effects of blowing or suction as compared to the combined effects of buoyancy and mass transfer.     

Thermal boundary layer of a micropolar fluid jet impinging normally on a flat plate

Summary The heat transfer is studied in the boundary layer formed on a flat plate by the impingement of an incompressible micropolar fluid jet. The thermal boundary layer equations are obtained after writing the governing equations for the steady two-dimensional flow of an incompressible micropolar fluid in cartesian co-ordinate system. The solution for the energy equation inside the boundary layer is obtained as a polynomial in terms of the distance from the stagnation point. The temperature of the plate and the temperature outside the boundary layer are assumed to be constant. The temperature distribution and the dimensionless heat transfer coefficient are presented graphically for various values of the material parameters which arise due to the micropolar property of the fluid. These results have been compared with the corresponding results for a Newtonian fluid.

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Thermische Grenzschicht eines mikropolaren Flüssigkeitsstrahles, der senkrecht auf eine ebene Platte auftrifft

Zusammenfassung Der Wärmeübergang in der Grenzschicht einer ebenen Platte, zufolge des Auftreffens eines inkompressiblen, mikropolaren Flüssigkeitsstrahles wird untersucht. Die thermischen Grenzschichtgleichungen werden aus den Grundgleichungen für die stationäre zweidimensionale Strömung einer inkompressiblen, mikropolaren Flüssigkeit in kartesischen Koordinaten erhalten. Die Lösung der Energiegleichung innerhalb der Grenzschicht wird als Polynom in Termen des Abstandes zum Staupunkt angegeben. Die Temperatur der Platte, sowie die Temperatur außerhalb der Grenzschicht werden als konstant vorausgesetzt. Die Temperaturverteilung und der dimensionslose Wärmeübergangskoeffizient sind graphisch für verschiedene Werte der Materialparameter, zufolge der mikropolaren Eigenschaften der Flüssigkeit, dargestellt. Diese Ergebnisse wurden mit den entsprechenden Ergebnissen für Newtonsche Flüssigkeiten verglichen.

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With 6 Figures     

Flat plate drag in a micropolar fluid

Summary The drag experienced in a micropolar fluid is investigated by considering uniform streaming past a flat plate. Some recent results on the fundamental solution of the Oseenlinearization of the micropolar flow equations are used to reduce the problem to that of solving a scalar integral equation. The integral equation is analyzed by the application of both asymptotic and variational methods. Results indicate that the drag experienced in a micropolar fluid always exceeds that found in the absence of any micropolarity; however one of the parameters which characterizes a micropolar fluid can be used to minimize the drag.With 2 Figures     

Flow past an accelerated horizontal plate in a rotating fluid

Summary A semi-infinite mass of an incompressible viscous fluid bounded by an infinite flat plate is initially rotating with uniform angular velocity about an axis normal to the plate. An analysis is presented for the subsequent flow when the plate started impulsively from rest relative to the rotating fluid moves with uniform acceleration in its own plane. It is found that when 0, the velocity profiles for varying times are nonsimilar in contrast to the velocity profiles which are similar in the absence of rotation (=0). At a given instant, the velocity component along the direction of motion of the plate decreases with an increase in rotation but the transverse velocity component (induced by the Coriolis force) increases with increasing rotation. Due to the gradual thinning of the boundary layer with rotation, both the skin-friction components along and transverse to the direction of motion of the plate increase with increasing rotation. A study of the asymptotic behavior of the velocity field for large time reveals a novel feature of the flow; it develops inertial oscillations with frequency 2, which grow with time. This behavior has not been reported in the absence of rotation.     

Numerical solution of heat transfer in micropolar fluid flow in a channel with porous walls

Using the basic equations of heat conducting micropolar fluid, heat transfer through a channel of porous walls has been studied. The temperature distribution is obtained for different values of suction parameter $\text{S}$, convective parameter $\text{E}$ and micropolar parameter $\text{R}$.     

Shear flow past a flat plate

Summary The controversy over the induced pressure gradient in shear flow is re-examined in the context of general bounding. It is shown that the results reported by Ludford and this author in two earlier papers are indeed typical near the leading edge. However far downstream they are only valid in the presence of walls. In particular two new effects arise; for weak bounding logarithmic terms appear in the inviscid pressure and a resonance with the first eigensolution occurs. For the symmetric case Toomre and Rott's result is recovered.     

Mixed convection of micropolar fluid about a sphere with blowing and suction

An analysis is performed to study the skin friction characteristics of laminar mixed forced and free convection flow of micropolar fluid about a permeable sphere with various prescribed thermal conditions on the surface. The problem was formulated by applying a suitable variables transformation and solutions were obtained by an efficient difference method. Numerical results were carried out for a wide range of mass transfer parameter as the Prandtl number at 0.7 or 7 with several values of material parameters and buoyancy force parameter of the micropolar fluid. The variations of the local friction factor and local Nusselt number are plotted and discussed. A comparison between the present solution and finite-difference solution from T.S. Chen, etc. is also shown.