Stagnation Point Heat Research Articles

MHD Stagnation Point Ferrofluid Flow and Heat Transfer Toward a Stretching Sheet

This paper investigates stagnation point flow and heat transfer of a ferrofluid toward a stretching sheet in the presence of viscous dissipation. Three types of ferroparticles: magnetite (Fe 3O 4 ), cobalt ferrite (CoFe 2O 4), and Mn-Zn ferrite (Mn-ZnFe 2O 4) are considered with water and kerosene as conventional base fluids. Numerical solutions to the resulting ordinary differential equations are obtained by using an implicit finite-difference method with quasi-linearization technique. The effects of controlling parameters on the dimensionless velocity, temperature, skin friction, and Nusselt numbers are investigated. It is found that kerosene-based ferrofluids have higher skin friction and Nusselt numbers than water-based ferrofluids. The numerical results of skin friction are compared with the available data for special cases and are found to be in good agreement.

Stagnation-point Flow and Heat Transfer of a Nanofluid Adjacent to Linearly Stretching/Shrinking Sheet: A Numerical Study

In this study, the steady stagnation point flow and heat transfer of three different types of nanofluid over a linearly shrinking/stretching sheet is investigated numerically. A similarity transformation is used to reduce the governing system of partial differential equations to a set of nonlinear ordinary differential equations which are then solved numerically using the fourth-order Runge-Kutta method with shooting technique. The effects of the governing parameters on the nanofluid flow and heat transfer characteristics are analyzed and discussed. Numerical results for the local Nusselt number, skin friction coefficient, velocity profiles and temperature profiles are presented for different values of the solid volume fraction (&phi) and for three different types of nanoparticles (Cu, Al₂O₃ and TiO₂) in stretching or shrinking cases. It is found that the skin friction coefficient and the heat transfer rate at the surface are highest for Cu-water nanofluid compared to the Al₂O₃-water and TiO₂-water nanofluids. Furthermore, it was seen that the effect of the solid volume fraction of nanoparticles on the heat transfer and fluid flow characteristics is more important compared to the type of the nanoparticles.

An HAM Analysis of Stagnation-Point Flow of a Nanofluid over a Porous Stretching Sheet with Heat Generation

Steady two-dimensional stagnation point flow and heat transfer of a nanofluid over a porous stretching sheet is investigated analytically using the Homotopy Analysis Method (HAM). The employed model for nanofluid includes two-component four-equation non-homogeneous equilibrium model that incorporates the effects of Brownian diffusion and thermophoresis simultaneously. The basic partial boundary layer equations have been reduced to a twopoint boundary value problem via similarity variables. The effects of thermophoresis number (

Effects of Thermal Radiation and Viscous Dissipation on Magnetohydrodynamic Stagnation Point Flow and Heat Transfer of Nanofluid Towards a Stretching Sheet

Effects of Thermal Radiation and Viscous Dissipation on Magnetohydrodynamic Stagnation Point Flow and Heat Transfer of Nanofluid Towards a Stretching Sheet

Stagnation point flow and heat transfer over a non-linearly moving flat plate in a parallel free stream with slip

An analysis is presented for the steady boundary layer flow and heat transfer of a viscous and incompressible fluid in the stagnation point towards a non-linearly moving flat plate in a parallel free stream with a partial slip velocity. The governing partial differential equations are converted into nonlinear ordinary differential equations by a similarity transformation, which are then solved numerically using the function bvp4c from Matlab for different values of the governing parameters. Dual (upper and lower branch) solutions are found to exist for certain parameters. Particular attention is given to deriving numerical results for the critical/turning points which determine the range of existence of the dual solutions. A stability analysis has been also performed to show that the upper branch solutions are stable and physically realizable, while the lower branch solutions are not stable and, therefore, not physically possible.

Effects of Magnetic Field and Thermal Radiation on Stagnation Flow and Heat Transfer of a Power-Law Fluid over a Shrinking Sheet

An analysis is made on the steady two-dimensional boundary layer magnetohydrodynamic (MHD) stagnation-point flow and radiative heat transfer of an electrically conducting power-law fluid over a shrinking sheet which is shrunk in its own plane with a velocity proportional to the distance from a fixed point. The similarity transformations are used to transform the boundary layer equations into a system of nonlinear ordinary differential equations which are then solved numerically using shooting technique. It is found that multiple solutions exist for a certain range of the ratio of the shrinking velocity to the free stream velocity (i.e., α) which again depends on the magnetic parameter (M) and the power-law index parameter (n). The results pertaining to the present study indicate that as the strength of the magnetic parameter increases, the range of α where similarity solutions exist gradually increases. It is also observed that the temperature at a point decreases with increase in M for the first solution branch, whereas it increases with increase in M for the second solution branch. The reported results are in good agreement with the available published work in the literature.

The MHD Mixed Convection Stagnation Point Flow and Heat Transfer in a Porous Medium

The steady two dimensional laminar MHD mixed convection stagnation point flow and heat transfer past a heated semi-infinite permeable surface embedded in a porous medium have been discussed using the mixed convection effects on the flow. The results are obtained by solving the coupled nonlinear partial differential equations describing the conservation of mass, momentum and energy by a perturbation technique. The present study concludes that when local Grashof number and Reynolds number are of the same order, instability in the flow and heat transfer phenomena occur. Further, the fluid with low thermal diffusivity gives rise to constant velocity and temperature gradients.

Stagnation point properties for non-continuum gaseous jet impinging at a flat plate surface from a planar exit

In this paper, we investigate highly rarefied gaseous jet flows out of a planar exit and impinging at a normally set flat plate. Especially, we concentrate on the plate center stagnation point pressure and heat flux coefficients. For a specular reflective plate, the stagnation point pressure coefficient can be represented using two non-dimensional factors: the characteristic gas exit speed ratio S0 and the geometry ratio of H/L, where H is the planar exit semi-height and L is the center-to-center distance from the exit to the plate. For a diffuse reflective plate, the stagnation point pressure and heat flux coefficients involve an extra factor of T0/Tw, i.e., the ratio of exit gas temperature to the plate wall temperature. These results allow us to develop four diagrams, from which we can conveniently obtain the pressure and heat flux coefficients for the stagnation impingement point, at the collisionless flow limit. After normalization with these maximum coefficients, the pressure and heat flux coefficient distributions along the surface essentially degenerate to almost identical curves. As a result, with known plate surface pressure coefficient distributions and these diagrams, we can conveniently construct the heat flux coefficient distributions along the plate surface, and vice versa.

Magnetohydrodynamic stagnation point flow toward stretching/shrinking permeable plate in porous medium filled with a nanofluid

In this article, the magnetohydrodynamic stagnation point flow and heat transfer of an incompressible viscous nanofluid over a shrinking/stretching permeable sheet is investigated theoretically and analytically. The ambient fluid velocity, stretching/shrinking velocity of sheet and the wall temperature are assumed to vary linearly with the distance from the stagnation point. The similarity solution is used to reduce the governing system of partial differential equations to a set of highly non-linear ordinary differential equations which are then solved analytically using a very efficient technique, namely homotopy analysis method. Expressions for velocity and temperature fields are developed in series form and graphical results are presented to investigate the influence of various pertinent parameters. Here, three different types of nanoparticles, namely copper [Formula: see text], alumina [Formula: see text] and titania [Formula: see text] with water as the base fluid are considered. It is observed that, for all three nanoparticles, the magnitude of the skin friction coefficient and local Nusselt number increases with the nanoparticle volume fraction Φ. The highest values of the skin friction coefficient and the local Nusselt number were obtained for the [Formula: see text] nanoparticles compared to [Formula: see text] and [Formula: see text].

Direct Numerical Simulation of Stagnation Point Heat Transfer Affected by Varying Wake-Induced Turbulence

In the present study the flow and heat transfer in a tandem cylinder setup are simulated by means of embedded direct numerical simulation (DNS). The influence of wake turbulence on the heat transfer in the stagnation region of the rear cylinder is investigated. The oncoming flow is varied by increasing the distance between the two cylinders, causing a change of the turbulent wake characteristics and the heat transfer. The data of both simulations show good agreement with an existing experimental correlation in the literature. For the small wake generator distance, a clear shift of the maximum heat transfer away from the stagnation line is observed. This shift is less pronounced for the larger distance.

Scaling of Convective Heat Transfer Enhancement Due to Flow Pulsation in an Axisymmetric Impinging Jet

Impinging jets are widely used to achieve a high local convective heat flux, with applications in high power density electronics and various other industrial fields. The heat transfer to steady impinging jets has been extensively researched, yet the understanding of pulsating impinging jets remains incomplete. Although some studies have shown a significant enhancement compared to steady jets, others have shown reductions in heat transfer rate, without consensus on the heat transfer mechanisms that determine this behavior. This study investigates the local convective heat transfer to a pulsating air jet from a long straight circular pipe nozzle impinging onto a smooth planar surface (nozzle-to-surface spacing 1 ≤ H/D ≤ 6, Reynolds numbers 6000 ≤ Re ≤ 14,000, pulsation frequency 9 Hz ≤ f ≤ 55Hz, Strouhal number 0.007 ≤ Sr = fD/Um ≤ 0.1). A different behavior is observed for the heat transfer enhancement in (i) the stagnation zone, (ii) the wall jet region and overall area average. Two different modified Strouhal numbers have been identified to scale the heat transfer enhancement in both regions: (i) Sr(H/D) and (ii) SrRe0.5. The average heat transfer rate increases by up to 75–85% for SrRe0.5 ≅ 8 (Sr = 0.1, Re = 6000), independent of nozzle-to-surface spacing. The stagnation heat transfer rate increases with nozzle-to-surface distance H/D. For H/D = 1 and low pulsation frequency (Sr < 0.025), a reduction in stagnation point heat transfer rate by 13% is observed, increasing to positive enhancements for Sr(H/D) > 0.1 up to a maximum enhancement of 48% at Sr(H/D) = 0.6.

Boundary layer stagnation-point flow of a third grade fluid over an exponentially stretching sheet

In this paper, the mixed convection steady boundary layer stagnation point flow and heat transfer of a third grade fluid over an exponentially stretching sheet is investigated. Both the analytical and numerical solutions are carried out. The analytical solutions are obtained through the homotopy analysis method (HAM) while the numerical solutions are computed by using the Keller box method (K-b). Comparison of the HAM and Keller-box methods is also given. The effects of important physical parameters are presented through graphs and the salient features are discussed.

Numerical Analysis of Jet Impingement Heat Transfer at High Jet Reynolds Number and Large Temperature Difference

Jet impingement heat transfer from a round gas jet to a flat wall was investigated numerically for a ratio of 2 between the jet inlet to wall distance and the jet inlet diameter. The influence of turbulence intensity at the jet inlet and choice of turbulence model on the wall heat transfer was investigated at a jet Reynolds number of 1.66 × 105 and a temperature difference between jet inlet and wall of 1600 K. The focus was on the convective heat transfer contribution as thermal radiation was not included in the investigation. A considerable influence of the turbulence intensity at the jet inlet was observed in the stagnation region, where the wall heat flux increased by a factor of almost 3 when increasing the turbulence intensity from 1.5% to 10%. The choice of turbulence model also influenced the heat transfer predictions significantly, especially in the stagnation region, where differences of up to about 100% were observed. Furthermore, the variation in stagnation point heat transfer was examined for jet Reynolds numbers in the range from 1.10 × 105 to 6.64 × 105. Based on the investigations, a correlation is suggested between the stagnation point Nusselt number, the jet Reynolds number, and the turbulence intensity at the jet inlet for impinging jet flows at high jet Reynolds numbers.

Nanofluid flow over a shrinking sheet with surface slip

In the present study, the effects of partial slip on mixed convection stagnation point flow and heat transfer of nanofluid impinging normally toward a shrinking sheet are investigated numerically. In particular, focus is on Cu–water and Al2O3–water nanofluids. Similarity transformation technique is adopted to obtain the self-similar ordinary differential equations and then solved numerically using Runge–Kutta–Fehlberg method with shooting technique. A parametric study is performed to explore the effects of various governing parameters on the fluid flow and heat transfer characteristics. Both the cases of assisting and opposing flows are considered. The physical aspects of the problem are highlighted and discussed.

On a Seemingly New Three-Dimensional Stagnation-Point Flow

In a recent paper by Abbassi and Rahimi (2009, “Nonaxisymmetric Three-Dimensional Stagnation-Point Flow and Heat Transfer on a Flat Plate,’’ ASME J. Fluids Eng, 131(7), p. 074501) the existence of a new nonaxisymmetric 3D stagnation-point flow has been reported. The present paper shows, however, that the model of Abbassis and Rahimi is fully equivalent to the classical 3D stagnation-point flow of Howarth (1951, “The Boundary Layer in Three-Dimensional Flow—Part II: The Flow Near a Stagnation Point,’’ Philos. Mag., 42, pp. 1433–1440) published more than sixty years ago. Thus their “new’’ solution can be recovered from Howarth's known solution by simple transformations, without any additional research effort. Once this flow problem is solved, the solution of the heat transfer problem of Abbassi and Rahimi (2009, “Nonaxisymmetric Three-Dimensional Stagnation-Point Flow and Heat Transfer on a Flat Plate,’’ ASME J. Fluids Eng, 131(7), p. 074501) can be calculated by a semi-analytical or by a usual numerical procedure.

Effects of hydrogen addition on the characteristics of a biogas diffusion flame

This work describes an experimental study of the effect of hydrogen addition on the stability and impingement heat transfer behaviors of a biogas diffusion flame. The amount of hydrogen added was varied from 5% to 10% of the biogas by volume. The results show that upon hydrogen addition in the biogas flame, there is a corresponding change in the appearance, stability and heat transfer characteristics of the flame.Addition of hydrogen significantly enhances the stability of the biogas flame, and the initial 5% hydrogen addition is found to be more efficient in the stability enhancement than the other 5% hydrogen addition. As the component CO2 in the biogas is replaced by N2, the stability limit can be further enhanced, indicative of a more adverse effect of CO2 than N2 on flame stabilization. Compared to the CH4–N2 flame, the biogas flame (CH4–CO2) has lower flame temperature and lesser soot emission. For both flames, the effect of hydrogen addition is to increase the flame temperature and reduce the flame height. The heat transfer data show that the stagnation point heat flux is enhanced by hydrogen addition due to the fact that there is higher flame temperature at higher level of hydrogen addition. While the total heat transfer rate is lowered because hydrogen has lower energy content per unit volume than the biogas substituted.

Buoyancy effects on MHD stagnation point flow and heat transfer of a nanofluid past a convectively heated stretching/shrinking sheet

This paper analyzes the combined effects of buoyancy force, convective heating, Brownian motion, thermophoresis and magnetic field on stagnation point flow and heat transfer due to nanofluid flow towards a stretching sheet. The governing nonlinear partial differential equations are transformed into a system of coupled nonlinear ordinary differential equations using similarity transformations and then tackled numerically using the Runge–Kutta fourth order method with shooting technique. Numerical results are obtained for dimensionless velocity, temperature, nanoparticle volume fraction, as well as the skin friction, local Nusselt and Sherwood numbers. The results indicate that dual solutions exist for shrinking case. The effects of various controlling parameters on these quantities are investigated. It is found that both the skin friction coefficient and the local Sherwood number decrease while the local Nusselt number increases with increasing intensity of buoyancy force.

Numerical Study of Stagnation Point Flow and Heat Transfer of Micropolar Fluid towards a Surface with Viscous Dissipation Effects

In this paper, we present numerical investigation of the problem of steady laminar two dimensional boundary layer stagnation point flow and heat transfer of a Micropolar fluid towards a heated surface in the presence of viscous dissipation. The governing boundary layer partial differential equations are reduced to a set of ordinary ones using similarity transformations. The solutions for different values of Eckert number, Micropolar parameters and Prandtl number are computed, analyzed and discussed. The study reveals that the reverse flow of heat near the surface may occur due to viscous dissipation which may further be enhanced by the increasing values of the Prandtl number. It may be recommended that the viscous dissipation should not be simply ignored while studying the boundary layer stagnation point flows.

Mixed convection stagnation point flow and heat transfer of Cu‐water nanofluids towards a shrinking sheet

AbstractThis work is focused on numerical simulations of mixed convection stagnation point flow and heat transfer of Cu‐water nanofluids impinging normally towards a shrinking sheet. Similarity transformation technique is adopted to obtain the self‐ similar ordinary differential equations and then solved numerically using symbolic software MATHEMATICA. The features of the flow and heat transfer characteristics for different values of the governing parameters are analyzed and discussed through graphs and tables. Both cases of assisting and opposing flows are considered. The physical aspects of the problem are highlighted and discussed. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.210372000 Mathematics Subject Classification: 76M20, 76W05

Flow regime characterisation of an impinging axisymmetric synthetic jet

Impinging synthetic jets have excellent potential for energy-efficient local cooling in confined geometries. For a given geometry, synthetic jet flows are mainly characterised by the Reynolds number and the ratio of stroke length to a geometric length scale. The flow field of an impinging synthetic jet and the corresponding surface heat transfer distribution are strongly dependent on the dimensionless stroke length, yet few studies have investigated the flow field dependence for a wide range of stroke lengths. Therefore, the aim of this paper is to identify the various flow regimes as a function of stroke length. The experimental approach combines high speed particle image velocimetry and single point hot wire anemometry, and investigates an axisymmetric synthetic air jet impinging onto a smooth planar surface for a wide range of stroke length (3<L0/D<32) and nozzle-to-surface spacing (2<H/D<16). Since the Reynolds number effect is better understood, most of the presented results are for a single Reynolds number (Re=1500). Four free synthetic jet flow morphology regimes are identified based on threshold values for the stroke length L0/D, which are in good agreement with previously published findings for an impulsively started jet flow. Furthermore, four impinging synthetic jet flow regimes are identified based on threshold values for the ratio of normalised stroke length to nozzle-to-surface spacing (L0−2D)/H, which are in good agreement with previously published thresholds for stagnation point heat transfer regimes.