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.     

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.     

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 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.     

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 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.     

Unsteady flow and heat transfer of a viscous fluid in the stagnation region of a three-dimensional body with a magnetic field

The unsteady incompressible flow and heat transfer of a viscous electrically conducting fluid in the vicinity of a stagnation point of a general three-dimensional body have been studied when the velocity in the potential flow varies arbitrary with time. The magnetic field is applied normal to the surface. The effects of viscous dissipation and Ohmic heating are included in the analysis. Both nodal-point region (0?c?1, where c=b/a is the ratio of the velocity gradients in y and x directions in the potential flow) and saddle-point region (−1?c<0) are considered. The semi-similar solution of the Navier-Stokes equations and the energy equation are obtained numerically using an implicit finite difference scheme. Also a self-similar solution is found when the velocity in the potential flow, the magnetic field and the wall temperature vary with time in a particular manner. The asymptotic behaviour of the self-similar equations for large η is obtained which enables us to find the upper limit of the unsteady parameter λ. One interesting result is that the magnetic field tends to delay or prevent flow reversal in y-component of the velocity. The surface shear stresses in x and y directions and the surface heat transfer increase with the magnetic field as well as with the accelerating free stream velocity.     

Heat and mass transfer in MHD flow by natural convection from a permeable, inclined surface with variable wall temperature and concentration

Summary. An analysis is performed to study the momentum, heat and mass transfer characteristics of MHD natural convection flow over a permeable, inclined surface with variable wall temperature and concentration, taking into consideration the effects of ohmic heating and viscous dissipation. Power-law temperature and concentration variations are assumed at the inclined surface. The resulting governing equations are transformed using suitable transformations and then solved numerically by an implicit finite-difference method. The solution is found to be dependent on several governing parameters, including the magnetic field strength parameter, Eckert number, the buoyancy ratio between species and thermal diffusion, Prandtl number, Schmidt number, wall temperature and concentration exponent, the inclination angle from the vertical direction, and the injection parameter. A parametric study of all the governing parameters is carried out and representative results are illustrated to reveal a typical tendency of the solutions. Representative results are presented for the velocity, temperature, and concentration distributions as well as the local friction coefficient, local Nusselt number, and the local Sherwood number.     

Thermal boundary layers over a shrinking sheet: an analytical solution

In this paper, the heat transfer over a shrinking sheet with mass transfer is studied. The flow is induced by a sheet shrinking with a linear velocity distribution from the slot. The fluid flow solution given by previous researchers is an exact solution of the whole Navier–Stokes equations. By ignoring the viscous dissipation terms, exact analytical solutions of the boundary layer energy equation were obtained for two cases including a prescribed power-law wall temperature case and a prescribed power-law wall heat flux case. The solutions were expressed by Kummer’s function. Closed-form solutions were found and presented for some special parameters. The effects of the Prandtl number, the wall mass transfer parameter, the power index on the wall heat flux, the wall temperature, and the temperature distribution in the fluids were investigated. The heat transfer problem for the algebraically decaying flow over a shrinking sheet was also studied and compared with the exponentially decaying flow profiles. It was found that the heat transfer over a shrinking sheet was significantly different from that of a stretching surface. Interesting and complicated heat transfer characteristics were observed for a positive power index value for both power-law wall temperature and power-law wall heat flux cases. Some solutions involving negative temperature values were observed and these solutions may not physically exist in a real word.     

Laminar heat transfer to power law fluids in flat gaps with various thermal wall conditions

Summary This paper deals with laminar, steady heat transfer in flat gaps formed by two wide parallel plates to power law fluids with temperature dependent rheological properties. Basic equations governing the problem to be discussed here are derived including the effects of viscous dissipation but neglecting the internal heat generation. The derived equations of motion, energy and continuity (the last in integral form) have been solved numerically by means of Dufort-Frankel scheme for various thermal wall conditions (constant and variable wall temperature as well as constant and variable wall heat flux). The results of numerical computations are presented in form of graphs illustrating the changes in temperature and velocity profiles as well as in local and mean Nusselt numbers and pressure drops with increasing distance from the inlet cross section. A special attention has been paid to the effects of viscous dissipation and temperature dependent rheological fluid properties on the changes mentioned above. The present work is intended to be an extension of the classical Graetz-Nusselt problem on non-Newtonian power law fluids with temperature dependent rheological properties flowing through a narrow gap formed by two wide parallel plates.With 8 Figures     

Magnetohydrodynamic (MHD) stratified bioconvective flow of nanofluid due to gyrotactic microorganisms

The aim of present paper is to investigate the heat/mass and motile microorganisms transfer rates in the convective stretched flow of nanofluid consisting of nanoparticles and gyrotactic microorganisms. Magneto nanofluid in presence of an inclined magnetic field is adopted. Idea of microorganisms is employed just to stabilize the suspended nanoparticles through bioconvection which has been induced by combined effects of buoyancy forces and magnetic field. Further interesting aspects of Brownian motion, thermophoresis, viscous dissipation, Joule heating and stratification are examined. Convergent solutions for the obtained nonlinear differential systems are derived. Main attention through plots is given to the influences of sundry variables on the velocity, temperature, concentration and motile microorganisms density. Numerical values for the skin friction coefficient, local Nusselt number, Sherwood number and local density number of motile microorganisms are computed and analyzed. Comparison is also made with limiting published results from open literature and an excellent agreement is noticed.     

Analysis of slip flow heat transfer between two unsymmetrically heated parallel plates with viscous dissipation

This paper presents an analytical investigation to study the heat transfer and fluid flow characteristics in the slip flow region for hydrodynamically and thermally fully developed flow between parallel plates. Both upper and lower plates are subjected to asymmetric heat flux boundary conditions. The effect of first order velocity slip, temperature jump, asymmetric heat flux ratio and viscous dissipation on the heat transfer performance is analyzed. Closed form expressions are obtained for the temperature distribution and Nusselt number. Present predictions are verified for the cases that neglect the viscous heating and microscale effects. The effect of asymmetric heat flux ratio with and without viscous dissipation on Nusselt number for both macroscale and microscale is highlighted. The heat transfer characteristics are found to depend on various modeling parameters, namely, modified Brinkman number, Knudsen number and heat flux ratio.     

Steady nonsimilar axisymmetric water boundary layers with variable viscosity and Prandtl number

Summary An analysis is performed to study the influence of temperature-dependent viscosity and Prandtl number on the steady nonsimilar laminar forced convection flow over a rotating sphere up to the point of separation. The difficulties arising at the starting point of the streamwise coordinate and at the point of separation are overcome by applying the method of quasilinear implicit finite difference scheme with an appropriate selection of finer step size along the streamwise direction. The results indicate that the effect of variable viscosity and Prandtl number is to move the point of separation downstream, but the rotation parameter has the reverse effect. For higher wall temperature than the free stream temperature, beyond a certain critical value of the dissipation parameter, the cooler free stream is unable to cool the hot wall due to the heat cushion provided by the frictional heating. The heat transfer rate is found to depend strongly on viscous dissipation but the skin frictions are little affected by it. In general, the results pertaining to variable fluid properties differ significantly from those of constant fluid properties.     

Luminaries-level structure improvement of LEDs for heat dissipation enhancement under natural convection

Heat dissipation enhancement of LED luminaries is of great significance to the large-scale application of LED. Luminaries-level structure improvement by the method of boring through-hole is adopted to intensify heat dissipation. Furthermore, the natural convection heat transfer process of LED luminaries is simulated by computational fluid dynamics (CFD) model before and after the structural modification. As shown by computational results, boring through-hole is beneficial to develop bottom-to-top natural convection, eliminate local circumfluence, and finally form better flow pattern. Analysis based on field synergy principle shows that boring through-hole across LED luminaries improves the synergy between flow field and temperature field, and effectively decreases the thermal resistance of luminaries-level heat dissipation structure. Under the same computational conditions, by luminaries-level structure improvement the highest temperature of heat sink is decreased by about 8°C and the average heat transfer coefficient is increased by 45.8%.     

Thermal boundary layers in magnetohydrodynamic flow over a flat plate in the presence of a transverse magnetic field

Summary A boundary layer solution for the heat transfer of an electrically conducting fluid over a semi-infinite flat plate in the presence of a transverse magnetic field has been studied. The heat due to viscous dissipation and stress work were also included into the energy equation. The governing nonsimilar partial differential equations are transformed into ordinary differential ones by means of difference-differential method. The temperature profiles and heat transfer coefficient are obtained for various values of the parameters entering the problem.     

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.     

Experimental Investigation of Changes in the Wall Temperature in Different Regimes of Motion of Supercritical-Pressure Liquids

Results of an investigation of the temperature regime of a wall for the laminar, transient, and turbulent regimes of motion of an ascending flow and different temperatures of toluene are given. Conditions for the occurrence of improved and impaired regimes of heat transfer with different characters of changes in the wall temperature are revealed.     

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.     

Numerical study of an unsteady free convective magnetohydrodynamic flow of a dissipative fluid along a vertical plate subject to a constant heat flux

A new method is presented to solve the transient free convection MHD flow of a dissipative fluid along a semi-infinite vertical plate with mass transfer, the surface of which is exposed to a constant heat flux. The non-linear system of partial differential equations is numerically solved by means of the network simulation method, based on the thermo–electric analogy. This method permits the direct visualisation and evolution of the local and/or integrated transport variables (temperatures, velocities, concentrations and fluxes) at any point or section of the medium. At the same time, the solution for both transient and steady-state problems is obtained, the only requirement being finite-difference schemes for the spatial variable, while its programming does not involve manipulation of the sophisticated mathematical software that is inherent in other numerical methods. The technique is always stable and convergent. Velocity, temperature and concentration profiles, local skin-friction, local Nusselt and local Sherwood numbers are plotted for air. The influence of the viscous dissipation, buoyancy ratio parameter, Schmidt number and magnetic parameter on heat and mass transfer and on the time needed to reach the steady-state are discussed.