Effect of non-uniform slot injection (suction) on a forced flow over a slender cylinder

An analysis is performed to obtain the non-similar solution of a steady laminar forced convection boundary layer flow over a horizontal slender cylinder including the effect of non-uniform slot injection (suction). The effects of transverse curvature and viscous dissipation are also included in the analysis. The governing boundary layer equations along with the boundary conditions are first cast into a dimensionless form using suitable transformations and the resulting system of nonlinear coupled partial differential equations is then solved by an implicit finite difference scheme in combination with the quasilinearization technique. Numerical results for the effect of non-uniform slot injection (suction) on skin friction coefficient and heat transfer rate are presented. The effects of transverse curvature, viscous dissipation and Prandtl number on velocity and temperature profiles and skin friction and heat transfer coefficients are also reported.     

Free convection boundary layer flow over a horizontal cylinder of elliptic cross section in porous media saturated by a nanofluid

This work studies the free convection boundary layer flow over a horizontal cylinder of elliptic cross section in porous media saturated by a nanofluid with constant wall temperature and constant wall nanoparticle volume fraction. The effects of Brownian motion and thermophoresis are incorporated into the model for nanofluids. A coordinate transformation is performed, and the obtained nonsimilar governing equations are then solved by the cubic spline collocation method. The effects of the Brownian motion parameter and thermophoresis parameter on the profiles of the temperature, nanoparticle volume fraction and velocity profiles are presented. The local Nusselt number is presented as a function of the thermophoresis parameter, Brownian parameter, Lewis number and the aspect ratio when the major axis of the elliptical cylinder is vertical (slender orientation) and horizontal (blunt orientation). Results show that the local Nusselt number is increased as the thermophoresis parameter or the Brownian parameter is decreased. The local Nusselt number increases as the buoyancy ratio or the Lewis number is decreased. Moreover, the local Nusselt number of the elliptical cylinder with slender orientation is higher than those of the elliptical cylinder with blunt orientation over the lower half cylinder.     

Non-uniform double slot injection (suction) on a forced flow over a slender cylinder

A general analysis has been developed to investigate the influence of non-uniform double slot injection (suction) on the steady non-similar incompressible laminar boundary layer flow over a slender cylinder, where the slender cylinder is inline with the flow. Non-similar solutions are obtained starting from the origin of the stream-wise coordinate along the stream-wise direction by using an implicit finite difference scheme in combination with the quasilinearization technique. Numerical results are reported to display the effects of non-uniform double slot injection/suction on skin friction coefficient and heat transfer rate at the wall. Further, the effects of viscous dissipation and Prandtl number on velocity and temperature profile, and skin friction and heat transfer co-efficients are also presented in this paper.     

Effects of surface roughness on mixed convection nanoliquid flow over slender cylinder with liquid hydrogen diffusion

The influence of surface roughness on boundary layer flow characteristics over moving surfaces is of considerable research interest in recent times. In the present study, the effects of surface roughness on flow over moving slender cylinder are analyzed in presence of mixed convection nanoliquid boundary layer flow. The problem is modelled in terms of highly nonlinear dimensional partial differential equations, which are written in non-dimensional form with the help of non-similar transformations. The resulting equations are reduced to linear partial differential equations by utilizing Quasilinearization technique, which are discretized using implicit finite difference scheme. The results obtained during the numerical simulation are then depicted through graphs in terms of various profiles and gradients and are analyzed with proper physical explanations. The roughness of slender cylinder surface is represented in a deterministic model as a sine wave form and yields sinusoidal variations in the values of skin-friction coefficient, wall heat and mass transfer rates. It is observed that the surface roughness effects are more prominent away from the orifice. The local frequency of gradients increases (i.e. wavelength decreases) with the increase in the frequency of surface roughness (n). The addition of nanoparticles into the ordinary fluid enhances the skin-friction coefficient and wall mass transfer rate. However, due to its effects, significant reduction is observed in the wall heat transfer rate. The phase difference of gradient oscillations arising in presence of nanoparticles is suppressed further away from the origin due to surface roughness. Interestingly, the amplitude of gradient oscillations remain higher in case of nanoliquid in comparison with that in case of ordinary fluid. Furthermore, the magnitude of wall mass transfer rate of liquid hydrogen is higher than that of nanoparticle wall mass transfer rate, which signifies the higher diffusivity of nanoparticles. The results of present study are of practical relevance to industrial applications such as polymer fibre coating and coating of wires.     

Natural convection heat transfer from a horizontal isothermal elliptical cylinder with internal heat generation

This work examines the natural convection heat transfer from a horizontal isothermal cylinder of elliptic cross section in a Newtonian fluid with temperature dependent internal heat generation. The governing boundary layer equations are transformed into a non-dimensional form and the resulting nonlinear systems of partial differential equations are solved numerically applying cubic spline collocation method. Results for the local Nusselt number and the local skin-friction coefficient are presented as functions of eccentric angle for various values of heat generation parameters, Prandtl numbers and aspect ratios. Results show that both the heat transfer rate and skin friction of the elliptical cylinder with slender orientation are higher than the elliptical cylinder with blunt orientation. Moreover, an increase in the heat generation parameter for natural convection flow over an isothermal horizontal elliptic cylinder leads to a decrease in the heat transfer rate from the elliptical cylinder and an increase in the skin friction of the elliptical cylinder.     

Natural convection boundary layer on a horizontal elliptical cylinder with constant heat flux and internal heat generation

In this paper the natural convection boundary layer on a horizontal elliptical cylinder with constant heat flux and temperature dependent internal heat generation is investigated. The mathematical problem is reduced to a pair of coupled partial differential equations for the temperature and the stream function, and the resulting nonlinear equations are solved numerically by cubic spline collocation method. Results for the local Nusselt number and the local skin-friction coefficient are presented as functions of eccentric angle for various values of heat generation parameters, Prandtl numbers and aspect ratios. An increase in the aspect ratio of the elliptical cylinder decreases the average surface temperature of the elliptical cylinder with blunt orientation, while it increases the average surface temperature of the elliptical cylinder with slender orientation. Moreover, an increase in the heat generation parameter for natural convection flow over a horizontal elliptic cylinder with constant heat flux leads to an increase in the average surface temperature of the elliptical cylinder.     

A boundary layer analysis of heat transfer by free convection from permeable horizontal cylinders of elliptic cross-section in porous media using a thermal non-equilibrium model

This work uses a thermal non-equilibrium model to study the free convection boundary layer flow driven by temperature gradients near a permeable horizontal cylinder of elliptic cross-section with constant wall temperature in a fluid-saturated porous medium. A coordinate transformation is used to obtain the nonsimilar boundary layer equations. The transformed boundary layer equations are then solved by the cubic spline collocation method. Results for the local Nusselt numbers are presented as functions of the porosity scaled thermal conductivity ratio, the heat transfer coefficient between solid and fluid phases, the transpiration parameter, and the aspect ratio when the major axis of the elliptical cylinder is vertical (slender orientation) and horizontal (blunt orientation). An increase in the porosity scaled thermal conductivity ratio or the heat transfer coefficient between the solid and fluid phases increases the heat transfer rates. Moreover, the use of suction (positive transpiration parameter) tends to increase the heat transfer rates between the porous medium and the surface.     

Magnetohydrodynamic Slip Flow and Heat Transfer in a Porous Medium over a Stretching Cylinder: Homotopy Analysis Method

This study considers magnetohydrodynamic flow and heat transfer outside a hollow stretching cylinder immersed in a fluid saturated porous medium of sparse distribution of particles with high permeability. Partial slip boundary conditions for the velocity and temperature fields are assumed at the stretching surface of the cylinder. Using similarity transformations, the nonlinear partial differential equations governing the flow and heat transfer are converted into nonlinear ordinary differential equations which are then solved by the homotopy analysis method. The effects of the pertinent parameters on the velocity and temperature profiles are investigated and discussed graphically.     

Darcian mixed convection along slender vertical cylinders with variable surface heat flux embedded in a porous medium

The problem of mixed convection flow along a vertical slender circular cylinder with variable surface heat flux embedded ina fluid-porous medium has been studied. The effects of mixed convection, surface curvature and buoyancy parameters are analyzed for the case of power-law variation in surface heat flux. The numerical solution of the transformed governing equations has been obtained using the Keller box method to demonstrate the important influence of these parameters on the flow and heat transfer characteristics     

Buoyancy and wall conduction effects on forced convection of micropolar fluid flow along a vertical slender hollow circular cylinder

This paper presents a numerical analysis of the flow and heat transfer characteristics of forced convection in a micropolar fluid flowing along a vertical slender hollow circular cylinder with wall conduction and buoyancy effects. The non-linear formulation governing equations and their associated boundary conditions are solved using the cubic spline collocation method and the finite difference scheme with a local non-similar transformation. This study investigates the effects of the conjugate heat transfer parameter, the Richardson number, the micropolar parameter, and the Prandtl number on the flow and the thermal fields. The effect of wall conduction on the thermal and the flow fields are found to be more pronounced in a system with a greater buoyancy effect or Prandtl number but is less sensitive with a greater micropolar material parameter. Compared to the case of pure forced convection, buoyancy effect is found to result in a lower interfacial temperature but higher the local heat transfer rate and the skin friction factor. Finally, compared to Newtonian fluid, an increase in the interfacial temperature, a reduction in the skin friction factor, and a reduction in the local heat transfer rate are identified in the current micropolar fluid case.     

Stokes flow and heat transfer past a circular cylinder in a square cavity with suction/injection on sidewalls

The laminar viscous fluid flow past a circular cylinder placed in a square cavity of a uniform cross‐section is generated by applying injection/suction at the adjacent sidewalls. The temperature on the side walls without suction and on the boundary of the cylinder is kept constant, and constant heat flux is maintained on the walls with suction. The streamline flow pattern and isothermal lines are drawn. The flow is assumed to be Stokesian. Hence, the resulting biharmonic equation is solved for stream function by expressing it in two coupled equations, and a 5‐point formula is used to solve these equations. Fictitious nodes are introduced for derivative boundary conditions for stream function by using a central difference scheme, and a 3‐point backward difference formula is used for derivative boundary conditions on temperature.     

CONJUGATE NATURAL CONVECTION FROM A HORIZONTAL CIRCULAR CYLINDER

ABSTRACT

Steady, laminar natural convection flow from a horizontal circular cylinder with a heated core region has been theoretically analyzed by taking account of the thermal conduction of the core region. The problem is conjugate, and the main focus of the study is to examine the effect of conduction in the core region on the natural convection flow from the cylinder. The governing equations were solved numerically using a finite difference technique. The effects of various parameters are presented in graphical form. Approximate solutions for the average boundary temperature at the surface of the cylinder and for the average Nusselt number are also found. In the parametric range investigated, both the theoretical and numerical results predict nearly the same values for the average boundary temperature at the surface of the cylinder and the same values for the average Nusselt number, showing the validity of the present analysis.     

Double diffusion from a horizontal cylinder of elliptic cross section with uniform wall heat and mass fluxes in a porous medium

This work studies the double diffusion near a horizontal cylinder of elliptic cross section with uniform wall heat and mass fluxes in a fluid-saturated porous medium. A coordinate transformation is used to obtain the non-similar governing boundary layer equations. The transformed equations are solved numerically by an efficient cubic spline collocation method. Results for the local surface temperature and the local surface concentration are presented as functions of the Lewis number, the buoyancy ratio, and the aspect ratio when the major axis of the elliptical cylinder is vertical (slender orientation) and horizontal (blunt orientation). As the Lewis number is increased, the local surface concentration decreases while the local surface temperature increases. Moreover, an increase in the buoyancy ratio tends to decrease both the local surface temperature and the local surface concentration.     

Natural convection boundary layer flow of water at 4°C past slender cones

This paper is concerned with an analysis of the transverse curvature effects on axisymmetric free convection boundary layer flow of water at 4°C past a slender, vertical cone. Numerical solutions are provided for the governing equations for momentum and energy. Missing values of the velocity and thermal functions which are proportional to the surface friction factor and the dimensionless heat transfer rate, have been tabulated for a Prandtl number of 11.4. The results indicate that the heat transfer rate increases with increasing transverse curvature.     

Free Convection Heat Transfer from Vertical Slender Cylinders: A Review

The effect of transversal curvature of a vertical cylinder becomes important where the thermal boundary layer thickness is comparable or thicker then the radius of cylinder. The cylinder slenderness criterion for laminar free convection for fluids of Prandtl numbers from 0.01 to 100 is presented. The classical analysis of the laminar free convection heat transfer from vertical cylinders is shown. Some results of numerical calculations of the turbulent boundary layer on a vertical cylinder using modified integral method are given. Experimental data concerning the laminar-turbulent transition suggest that the critical Grashof number for a vertical flat plate is Gr _cr ≈ 10⁹ and for a vertical cylinder is Gr _cr ≈ 4 × 10⁹. Theoretical, numerical, and experimental data for free convection heat transfer from vertical slender circular cylinders are surveyed. A separate section of the paper is devoted to the presentation of the list of selected correlation equations. Some of them are compared graphically. In the laminar region, the correlation equation based on the numerical calculations is validated with the recent experimental results for Prandtl number of 0.71 and for the cylinder height to diameter ratio from 1 to 60. In the turbulent region, few experimental data are available, and some results indicate that the effect of transversal curvature on the average convective heat transfer is very weak.     

The hypersonic boundary layer on a wedge with uniform mass addition and viscous interaction

The effects of uniform surface blowing on the hypersonic boundary layer with viscous interaction are investigated analytically and experimentally. For strong and moderate viscous interaction, the heat transfer on a flat plate and a slender wedge is calculated by use of the local similarity technique to solve the boundary layer equations and the tangent wedge approximation to determine the inviscid pressure. The experiments are conducted at Mach numbers of 16 and 20, at unit Reynolds numbers of 2.3 and 1.3 × 10⁵ ft⁻¹, and at the cold wall condition. The analytical and experimental results are in good agreement. For moderate blowing, it is found that the effects of viscous interaction dominate the flow when the interaction is strong and that the effects of blowing become more important as the strength of the viscous interaction decreases.     

Unsteady mixed convection heat transfer from a solid sphere: The conjugate problem

Heat transfer associated with a spherical particle under simultaneous free and forced convection is numerically investigated using a combined Chebyshev Legendre spectral method. Both internal and external thermal resistances are taken into consideration by means of a conjugate model consisting of the full Navier -Stokes equations for external flow and the energy equations for both inside and outside the sphere. An influence matrix technique is employed to resolve the difficulties created by the lack of vorticity boundary conditions and to decouple the energy equations from interfacial couplings. Simulation results reveal that effects due to natural convection are most remarkable in the wake where the flow structure is changed. The overall Nusselt number and the drag coefficient show an increase or decrease in magnitude depending on whether gravity-induced flow aids or opposes the main flow. However, the change does not exceed 17% for the cases Gr/Re2 40. When the buoyancy and the free stream are in the same direction, the effects are less pronounced than when they are in the opposite direction.     

Homogeneous–heterogeneous reactions in flow past a horizontal circular cylinder with an induced magnetic field and nonlinear thermal radiation

In this study, we investigate the steady, two‐dimensional, incompressible viscous boundary layer flow of an electrically conducting Casson fluid over a horizontal circular cylinder. The cylinder is impermeable and the flow is assumed to be subject to homogeneous–heterogeneous reactions. The homogeneous–heterogeneous reactions are also assumed to have unequal diffusion coefficients. The novelty in this study is in the consideration of a nonlinear radiative flux together with Joule heating and an induced magnetic field. The magnetodynamic pressure gradient in induced magnetic flows is important as it gives insights into the boundary layer characteristics. The flow velocity and the magnetic field in the free stream are assumed to be uniform and directed vertically over the cylinder. The partial differential equations are solved using the bivariate spectral quasi‐linearization method. An analysis and comparison of results with existing literature are provided. Among the findings, we show, inter alia, that the reactants dominate while the autocatalysts have a negligible impact on the flow progression. The skin friction coefficient decreases with an increase in the Casson parameter and increases when the Joule heating parameter is increased. The rate of heat transfer increases with increasing the Casson parameter and decreases when the Joule heating parameter is increased.