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.     

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 compressible boundary layer swirling flow in a nozzle and a diffuser

This paper presents the results of the study of unsteady swirling boundary-layer flow of compressible fluid in a nozzle and a diffuser when the free stream velocity, mass transfer and wall temperature vary arbitrarily with time. The set of coupled nonlinear partial differential equations governing the flow which involves three independent variables has been solved numerically using an implicit finite-difference scheme. Both the heat transfer and skin friction are strongly affected by the free stream velocity, variation of the density-viscosity product across the boundary layer, mass transfer and swirl parameter. However, the variation of the wall temperature with time strongly affects only the heat transfer. Also, separationless flow along the entire length of the diffuser can be obtained by applying appropriate amount of suction.     

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.     

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     

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.     

Non-Darcy mixed convection flow with thermal dispersion on a vertical cylinder in a saturated porous medium

Summary The non-Darcy mixed convection flow on a vertical cylinder embedded in a saturated porous medium has been studied taking into account the effect of thermal dispersion. Both forced flow and buoyancy force dominated cases with constant wall temperature condition have been considered. The governing partial differential equations have been solved numerically using the Keller box method. The results are presented for the buoyancy parameter which cover the entire regime of mixed convection flow ranging from pure forced convection to pure free convection. The effect of thermal dispersion is found to be more pronounced on the heat transfer than on the skin friction and it enhances the heat transfer but reduces the skin friction.     

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.     

Nonsimilar laminar incompressible boundary layers with vectored mass transfer

The effect of vectored mass transfer on the flow and heat transfer of the steady laminar incompressible nonsimilar boundary layer with viscous dissipation for two-dimensional and axisymmetric porous bodies with pressure gradient has been studied. The partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme. The computations have been carried out for a cylinder and a sphere. The skin friction is strongly influenced by the vectored mass transfer, and the heat transfer both by the vectored mass transfer and dissipation parameter. It is observed that the vectored suction tends to delay the separation whereas the effect of the vectored injection is just the reverse. Our results agree with those of the local nonsimilarity, difference-differential and asymptotic methods but not with those of the local similarity method.     

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.     

Unsteady laminar incompressible second-order boundary-layer flow at a three-dimensional stagnation point

Summary The unsteadely laminar incompressible second-order boundary-layer flow at the stagnation point of a three-dimensional body has been studied for both nodal and saddle point regions. The effects of mass transfer and Prandtl number have been taken into account. The equations governing the flow have been solved numerically using an implicit finite-difference scheme. It has been found that the parameter characterizing the unsteadiness in the velocity of the free stream, the nature of the stagnation point, the mass transfer and Prandtl number strongly affect the second-order skin friction and heat transfer. The overall skin friction becomes less due to second-order effects but the heat transfer has the opposite behaviour. For large injection, the second-order skin-friction and heat-transfer results prevail over the first-order boundary layer results whereas for the case of large suction the behaviour is just the opposite.With 14 Figures     

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.     

Finite element analysis of combined heat and mass transfer in hydromagnetic micropolar flow along a stretching sheet

This paper presents a finite element solution of the problem of heat and mass transfer in a hydromagnetic flow of a micropolar fluid past a stretching sheet. The transformed equations for the flow regime are solved numerically by using finite element method. The effect of important parameters namely magnetic field parameter, material parameter, Eckert number and Schmidt number over velocity, microrotation, temperature and concentration functions has been studied. It has been observed that the magnetic field parameter has the effect of reducing the velocity and increasing the microrotation, temperature and concentration while the micropolar parameter has the opposite effect on these functions except temperature function. Temperature increases with the increase in Eckert number and concentration decreases with the increase in Schmidt number.     

Similarity solutions for laminar free convection flow of a thermomicropolar fluid past a non-isothermal vertical flat plate

Laminar free convection boundary layer flow of a thermomicropolar fluid past a non-isothermal vertical flat plate has been studied in detail. It has been established that the flow problem has similarity solutions when the variation in the temperature of the plate is a linear function of the distance from the leading edge measured along the plate. The resulting system of the nonlinear ordinary differential equations has been solved numerically by “Shooting Method” for various values of the material parameters. The effects of these parameters has been studied on the velocity and microrotation fields graphically. Also “Tables” have been given for the values of temperature, skin-friction parameter, microrotation gradient on the wall and Nusselt number. Two types of boundary conditions are prescribed for the microrotation on the wall.     

MHD boundary-layer flow of a non-Newtonian fluid over a continuously moving surface with a parallel free stream

Summary The MHD flow and heat transfer of a non-Newtonian power-law fluid over a continuously moving surface with a parallel free stream have been investigated. The partial differential equations governing the non-similar flow have been solved numerically using an implicit finite-difference scheme. The skin friction and heat-transfer coefficients increase with the magnetic parameter, and they are more for the pseudoplastic fluid than for the dilatant fluid. The heat-transfer coefficient increases significantly with the Prandtl number. The gradient of the velocity at the surface is negative when the wall velocity is greater than the free stream velocity, and it is positive when the wall velocity is less than the free stream velocity.     

Unsteady compressible flow in the stagnation region of two-dimensional and axi-symmetric bodies

Summary This paper deals with a new similarity solution of unsteady laminar compressible two-dimensional and axi-symmetric boundary layers. It has been shown that a self-similar solution is possible when the free stream velocity varies inversely with time. The two-point boundary value problems governed by self-similar equations have been solved numerically using an implicit finite difference scheme in combination with the quasi-linearization technique. It is observed that the effect of the acceleration parameter (A) in the free stream velocity on the skin friction is more pronounced compared to the heat transfer. For certain values of the acceleration parameter and the total enthalpy at the wall, the surface shear stress (skin friction) vanishes. The skin friction and heat transfer increase due to suction, and the effect of injection is found to be just opposite. Velocity profiles are presented with reverse flow and without reverse flow depending on the values of toal enthalpy at the wall and the acceleration parameter.     

Unsteady compressible boundary layer flow on the stagnation line of an infinite swept cylinder

Summary Numerical solutions of flow and heat transfer process on the unsteady flow of a compressible viscous fluid with variable gas properties in the vicinity of the stagnation line of an infinite swept cylinder are presented. Results are given for the case where the unsteady temperature field is produced by (i) a sudden change in the wall temperature (enthalpy) as the impulsive motion is started and (ii) a sudden change in the free-stream velocity. Solutions for the simultaneous development of the thermal and momentum boundary layers are obtained by using quasilinearization technique with an implicit finite difference scheme. Attention is given to the transient phenomenon from the initial flow to the final steady-state distribution. Results are presented for the skin friction and heat transfer coefficients as well as for the velocity and enthalpy profiles. The effects of wall enthalpy parameter, sweep parameter, fluid properties and transpiration cooling on the heat transfer and skin friction are considered.     

Three-dimensional flow with heat transfer of a viscoelastic fluid over a stretching surface with a magnetic field

The present research study deals with the steady flow and heat transfer of a viscoelastic fluid over a stretching surface in two lateral directions with a magnetic field applied normal to the surface. The fluid far away from the surface is ambient and the motion in the flow field is caused by stretching surface in two directions. This result is a three-dimensional flow instead of two-dimensional as considered by many authors. Self-similar solutions are obtained numerically. For some particular cases, closed form analytical solutions are also obtained. The numerical calculations show that the skin friction coefficients in x- and y-directions and the heat transfer coefficient decrease with the increasing elastic parameter, but they increase with the stretching parameter. The heat transfer coefficient for the constant heat flux case is higher than that of the constant wall temperature case.     

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.     

Heat transfer in MHD flow with pressure gradient,suction and injection

Summary Numerical solutions to the MHD Falkner-Skan equation and the corresponding heat transfer equation have been obtained on taking into consideration the effects of suction and injection and the pressure gradient parameter . Velocity and temperature profiles are shown on graphs and the numerical values of the skin friction and the rate of heat transfer are given in the form of tables. It has been observed that an increase inN _m (magnetic field parameter) leads to an increase in velocity, skin friction, rate of heat transfer and a fall in temperature. Also an increase in suction leads to a fall in the value of the skin friction and the rate of heat transfer, opposite to the case of injection.