Compressible second-order boundary layers for three-dimensional stagnation point flows with mass transfer

All the second-order boundary-layer effects have been studied for the steady laminar compressible 3-dimensional stagnation-point flows with variable properties and mass transfer for both saddle and nodal point regions. The governing equations have been solved numerically using an implicit finite-difference scheme. Results for the heat transfer and skin friction have been obtained for several values of the mass-transfer rate, wall temperature, and also for several values of parameters characterizing the nature of stagnation point and variable gas properties. The second-order effects on the heat transfer and skin friction at the wall are found to be significant and at large injection rates, they dominate over the results of the first-order boundary layer, but the effect of large suction is just the opposite. In general, the second-order effects are more pronounced in the saddle-point region than in the nodal-point region. The overall heat-transfer rate for the 3-dimensional flows is found to be more than that of the 2-dimensional flows.     

Unsteady incompressible boundary layer flow of a micropolar fluid at a stagnation point

The flow, heat and mass transfer on the unsteady laminar incompressible boundary layer in micropolar fluid at the stagnation point of a 2-dimensional and an axisymmetric body have been studied when the free stream velocity and the wall temperature vary arbitrarily with time. The partial defferential equations governing the flow have been solved numerically using a quasilinear finite-difference scheme. The skin friction, microrotation gradient and heat transfer parameters are found to be strongly dependent on the coupling parameter, mass transfer and time, whereas the effect of the microrotation parameter on the skin friction and heat transfer is rather weak, but microrotation gradient is strongly affected by it. The Prandtl number and the variation of the wall temperature with time affect the heat-transfer very significantly but the skin friction and micrortation gradient are unaffected by them.     

Nonsimilar mixed convection flow of a non-Newtonian fluid past a vertical wedge

Summary The flow and heat transfer characteristics of a second-order fluid over a vertical wedge with buoyancy forces have been analysed. The coupled nonlinear partial differential equations governing the nonsimilar mixed convection flow have been solved numerically using Keller box method. The effects of the buoyancy parameter, viscoelastic parameter, mass transfer parameter, pressure gradient parameter, Prandtl number and viscous dissipation parameter on the skin friction and heat transfer have been examined in detail. Particular cases of the present results match exactly with those available in the literature.     

Unsteady compressible 3-dimensional boundary-layer flow near an asymmetric stagnation point with mass transfer

The heat and mass transfer for unsteady laminar compressible boundary-layer flow, which is asymmetric with respect to a 3-dimensional stagnation point (i.e. for a jet incident at an angle on the body), have been studied. It is assumed that the free-stream velocity, wall temperature, and surface mass transfer vary arbitrarily with time and also that the gas has variable properties. The solution in the neighbourhood of the stagnation point has been obtained by series expansion in the longitudinal distance. The resulting partial differential equations have been solved numerically using an implicit finite-difference scheme. The results show that, in contrast with the symmetric flow, the maximum heat transfer does not occur at the stagnation point. The skin-friction and heat-transfer components due to asymmetric flow are only weakly affected by the mass transfer as compared to those components associated with symmetric flow. The variation of the wall temperature with time has a strong effect on the heat transfer component associated with the symmetric part of the flow. The skin friction and heat transfer are strongly affected by the variation of the density-viscosity product across the boundary layer. The skin friction responds more to the fluctuations of the free stream oscillating velocities than the heat transfer. The results have been compared with the available results and they are found to be in excellent agreement.     

Unsteady attachment line flow on a flat plate with attached cylinder

The unsteady laminar incompressible boundary-layer attachment-line flow on a flat plate with attached cylinder with heat and mass transfer has been studied when the free stream velocity, mass transfer and surface wall temperature vary arbitrarily with time. The governing partial differential equations with three independent variables have been solved numerically using an implicit finite-difference scheme. The heat transfer was found to be strongly dependent on the Prandtl number, variation of wall temperature with time and dissipation parameter (for large times). However, the free stream velocity distribution and mass transfer affect both the heat transfer and skin friction.     

Unsteady mixed convection flow of a thermomicropolar fluid on a long thin vertical cylinder

The unsteady laminar mixed convection boundary layer flow of a thermomicropolar fluid over a long thin vertical cylinder has been studied when the free stream velocity varies with time. The coupled nonlinear partial differential equations with three independent variables governing the flow have been solved numerically using an implicit finite difference scheme in combination with the quasilinearization technique. The results show that the buoyancy, curvature and suction parameters, in general, enhance the skin friction, heat transfer and gradient of microrotation, but the effect of injection is just opposite. The skin friction and heat transfer for the micropolar fluid are considerably less than those for the Newtonian fluids. The effect of microrotation parameter is appreciable only on the microrotation gradient. The effect of the Prandtl number is appreciable on the skin friction, heat transfer and gradient of microtation.     

Hydromagnetic stagnation point flow by a perturbation technique

An analysis is performed to study the momentum, heat and mass transfer characteristics of MHD natural convection flow and heat generating/absorbing fluid at the stagnation point of an isothermal two-dimensional porous body immersed in a fluid saturated porous medium. The results are obtained by solving the coupled non-linear partial differential equations describing the conservation of mass, momentum and energy by a perturbation technique [A. Aziz, T.Y. Na, Perturbation Methods in Heat Transfer, Springer-Verlag, Berlin, 1984 (pp. 1–184), R. Kenneth Cramer, Shih-I Pai, Magnetofluid Dynamics for Engineers and Applied Physicists, McGraw-Hill Book Company, New York, 1973 (pp. 164–171).]. These results are presented to illustrate the influence of the Hartmann number, Prandtl number, and dimensionless heat generation/absorption coefficient and suction injection parameter. Numerical results for the dimensionless velocity profiles, the temperature profiles, the local friction coefficient and the local Nusselt number are presented for various parameters. These effects of the different parameters on the velocity and temperature as well as the skin friction and wall heat transfer are presented graphically.     

Analysis of forced convection micropolar boundary layer about a permeable sphere

The heat transfer characteristics and local skin friction for forced convection flow of micropolar fluid over an isothermal or a constant-heat-flux surface of sphere with surface mass transfer have been studied. The problem was formulated by applying a suitable variables transformation and the solutions were obtained by an implicit finite difference method. Numerical results were carried out for a wide range of mass transfer parameters as the Prandtl number at 0.7 or 7 with several values of material parameters of the micropolar fluid. The variations of the local friction factor and local Nusselt number are plotted and discussed.     

Natural convection on a thin vertical cylinder moving in a high-porosity ambient medium

An analysis has been performed to study the natural convection flow over a thin vertical cylinder which is moving with a constant velocity in a non-Darcy high-porosity ambient medium. Both constant wall temperature and constant heat flux conditions have been considered. The coupled non-linear parabolic partial differential equations have been solved numerically by using an implicit finite-difference scheme. The heat transfer is found to be significantly affected by the inertia and porosity parameters, and the Prandtl number, whereas the skin friction is weakly affected. The heat transfer for the constant heat flux case is more than that of the constant wall temperature case and this difference increases with the Prandtl number. The heat transfer increases with the buoyancy force, but the skin friction is slightly reduced.     

Unsteady two-dimensional and axisymmetric MHD boundary-layer flows

Summary Nonsimilar solution of the unsteady laminar incompressible magneto-hydrodynamic boundary layer flow and heat transfer for an electrically conducting fluid over two-dimensional and axisymmetric bodies in the presence of an applied magnetic field has been obtained. The effects of surface mass transfer, Joule heating and viscous dissipation are included in the analysis. Numerical computation have been carried out for the flow over a circular cylinder and a sphere using an implicit finite difference scheme in combination with a quasi-linearization technique. It is observed that magnetic field and suction cause the location of vanishing skin friction to move downstream while, the effect of injection is just the opposite. The effect of magnetic field on the skin friction is more pronounced as compared to its effect on the heat transfer. On the other hand, the heat transfer is strongly affected by the viscous dissipation and the effect is more for larte times. However, heat transfer responds comparatively less to the fluctuations of the free stream than the skin friction.     

Heat transfer in a second order viscoelastic boundary layer flow at a stagnation point

The steady and transient heat transfer characteristics of a second order viscoelastic boundary layer flow at a stagnation point have been studied in this paper. The implicit cubic spline numerical procedure is used to solve the governing boundary layer equations. The details of the temperature profiles and wall heat flux rates have been graphically illustrated. The range of values of the Prandtl number was from 5 to 1000 while the Weissenberg number was varied from 0.1 to 0.3.     

Non-uniform slot injection (suction) into water boundary layers over (i) a cylinder and (ii) a sphere

An analysis is performed to study the effect of non-uniform slot injection (suction) into steady two-dimensional and axi-symmetric laminar boundary layers with variable viscosity and Prandtl number. Non-similar solutions have been obtained from the starting point of the streamwise co-ordinate to the exact point of separation. The difficulties arising at the starting point of the streamwise co-ordinate, at the edges of the slot and at the point of separation have been overcome by applying an implicit finite difference scheme with the quasi-linearization technique and an appropriate selection of finer step size along the streamwise direction. 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. The heat transfer rate is found to depend strongly on viscous dissipation but the skin friction is little affected by it.     

Unsteady MHD forced flow due to a point sink

Summary An analysis is performed to study the unsteady laminar incompressible boundary-layer flow of an electrically conducting fluid in a cone due to a point sink with an applied magnetic field. The unsteadiness in the flow is considered for two types of motion, viz. the motion arising due to the free stream velocity varying continuously with time and the transient motion occurring due to an impulsive change either in the strength of the point sink or in the wall temperature. The partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme in combination with the quasilinearization technique. The magnetic field increases the skin friction but reduces heat transfer. The heat transfer and temperature field are strongly influenced by the viscous dissipation and Prandtl number. The velocity field is more affected at the early stage of the transient motion, caused by an impulsive change in the strength of the point sink, as compared to the temperature field. When the transient motion is caused by a sudden change in the wall temperature, both skin friction and heat transfer take more time to reach a new steady state. The transient nature of the flow and heat transfer is active for a short time in the case of suction and for a long time in the case of injection. The viscous dissipation prolongs the transient behavior of the flow.     

Mixed convection on a vertical surface with a prescribed heat flux: the solution for small and large Prandtl numbers

The mixed convection boundary-layer flow over a vertical surface with a prescribed surface heat flux is considered for both large and small values of the Prandtl number. The similarity equations are treated first. It is shown that, for large values of the Prandtl number, the solution approaches the forced convection limit with the free convection effects having only a small perturbation on this. The opposite is seen to be the case for small values of the Prandtl number, now free convection becomes the dominant heat transfer mechanism. A consequence of this is seen to be that the range of negative buoyancy parameter (opposed flow) over which a solution can exist decreases to zero as the Prandtl number is decreased.The scalings worked out for the similarity equations are then applied to the general boundary-layer flow, with the particular example of a uniform stream over a flat plate with uniform surface heat flux being treated in detail. Again it is seen that, for large Prandtl numbers, the solution approaches the forced convection limit whereas, for small Prandtl numbers, free convection dominates the flow. The effect of this is seen, for opposed flow, to delay the onset of separation for large Prandtl numbers, and to bring the separation point closer to the leading edge as the Prandtl number is decreased. An estimate for this effect is obtained.     

Thermal convection of micropolar fluids past two-dimensional or axisymmetric bodies with suction/injection

Steady laminar forced convection of micropolar fluids past two-dimensional or axisymmetric bodies with porous walls and different thermal boundary conditions has been analyzed. New coordinate transformations are employed to reduce the streamwise-dependence in the coupled nonlinear boundary-layer equations. The analysis is applied to cylinders and spheres with fluid injection/suction at the surface. Of interest are the effects of material parameters, wall mass transfer, the Prandtl number and the distinct thermal boundary conditions on the local skin friction coefficient and heat transfer coefficient.     

Unsteady mixed convection flow at the stagnation point

The unsteady mixed convection flow of an electrically conducting fluid at the stagnation point of a two-dimensional body and an axisymmetric body in the presence of an applied magnetic field has been studied. The effect of induced magnetic field has been included in the analysis. Both prescribed wall temperature and prescribed heat flux conditions have been considered. It is found that if the free stream velocity, applied magnetic field and square root of the wall temperature vary inversely as a linear function of time, i.e. as (1 − λt′)⁻¹, the governing boundary layer equations admit a locally self-similar solution. If surface heat flux is prescribed, it should vary as (1 − λt^*)^−5/2 for the existence of a local self-similar solution. The resulting ordinary differential equations have been solved using a finite element method as well as a shooting method with Newton's corrections for missing initial conditions. The skin friction and heat transfer coefficients and x-component of the induced magnetic field on the surface increase with the applied magnetic field or buoyancy force. Also they are found to change more for decelerating free stream velocity than for accelerating free stream velocity. Furthermore, they change little with the reciprocal of the magnetic Prandtl number. The buoyancy parameter causes overshoot in the velocity profile. For a given Prandtl number, beyond a certain critical value of the dissipation parameter, the hot wall ceases to be cooled due to the “heat cushion” provided by frictional heat.     

Compressible magnetohydrodynamic boundary layer swirling nozzle and diffuser flows with a magnetic field

The flow, heat and mass transfer problem for boundary layer swirling flow of a laminar steady compressible electrically conducting gas with variable properties through a conical nozzle and a diffuser with an applied magnetic field has been studied. The partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme after they have been transformed into dimensionless form using the modified Lees transformation. The results indicate that the skin friction and heat transfer strongly depend on the magnetic field, mass transfer and variation of the density-viscosity product across the boundary layer. However, the effect of the variation of the density-viscosity product is more pronounced in the case of a nozzle than in the case of a diffuser. It has been found that large swirl is required to produce strong effect on the skin friction and heat transfer. Separationless flow along the entire length of the diffuser can be obtained by applying appropriate amount of suction. The results are found to be in good agreement with those of the local nonsimilarity method, but they differ quite significantly from those of the local similarity method.     

An investigation of the Prandtl number effect on turbulent heat transfer in channel flows by large eddy simulation

Summary Fully developed turbulent channel flow with passive heat transfer has been calculated to investigate the turbulent heat transfer by use of the large eddy simulation (LES) approach coupled with dynamic subgrid-scale (SGS) models. The objectives of this study are to examine the effectiveness of the LES technique for predicting the turbulent heat transfer at high Prandtl numbers and the effects of the Prandtl number on the turbulent heat transfer in a fully developed turbulent channel flow. In the present study, the Prandtl number is chosen as 0.1 to 200, and the Reynolds number, based on the central mean velocity and the half-width of the channel, is 10⁴. Some typical cases are computed and compared with available data obtained by direct numerical simulation (DNS), theoretical analysis and experimental measurement, respectively, which confirm that the present approach can be used to predict the heat transfer satisfactorily, even at high Prandtl numbers. To depict the effect of the Prandtl number on turbulent heat transfer, the distributions of mean value and fluctuation of resolved flow temperatures, the heat transfer coefficient, turbulent heat fluxes, and some instantaneous iso-thermal sketches are analyzed.     

超临界CO2在管内流动换热特性的实验研究

以超临界二氧化碳为研究对象,对其在水平管内与水成垂直交叉流动的换热特性进行了实验研究。实验结果表明,超临界二氧化碳在外部水垂直交叉流动冷却下的入口压力、质量流量、冷却水流量的变化都对换热性能产生一定的影响。并且比较了两种不同冷却方式,即在逆流和垂直交叉流形式下,Re和Pr数的变化规律;最后,利用实验数据对四个考虑不同影响因素的常用经验关联式进行了验证,指出了适合实验条件的关联式。     

Flow and heat transfer in the boundary layer due to rotating spheres,spheroids and paraboloids

The effects of rotating spheres, spheroids and paraboloids on the flow and heat transfer in the boundary layers have been investigated. The field functions corresponding to the polynomial profiles have been determined numerically. The nonlinear boundary value problem for the flow near the poles has been solved through quasilinearization whereupon the higher order equations were also integrated. Detailed results have been presented for flow and temperature profiles and the relevant parameters. The steady increase in the heat transfer parameter with Prandtl number has also been shown for different geometries.