Stagnation Point Heat Transfer Research Articles

Stagnation Point Flow and Heat Transfer over an Exponentially Stretching/Shrinking Sheet in CNT with Homogeneous–Heterogeneous Reaction: Stability Analysis

This study focuses on the flow of stagnation region and heat transfer of carbon nanotubes (CNTs) over an exponentially stretching/shrinked sheet in the presence of homogeneous–heterogeneous reactions. Kerosene and water are considered base fluids in both single-wall and multi-wall carbon nanotubes. After employing the appropriate similarity variables, the system of partial differential equations is transformed to a system of nonlinear ordinary differential equations. Solution of the problems is obtained numerically using the bvp4c solver in MATLAB software. The impact of physical parameters, such as solid volume fraction, stretching/shrinking parameter, homogeneous and heterogeneous reaction rate, Schmidt number on the velocity, temperature and concentration profiles, skin friction, and heat transfer rate are discussed graphically and interpreted physically. The results indicate that for an exponentially shrinking sheet, dual solutions exist for a certain range. It is clear from figures that the concentration profile increases for increasing values of heterogeneous parameter and decreasing values of homogeneous parameter. Heat transfer and skin friction were observed to have a greater impact for single-wall carbon nanotubes (SWCNTs) compared to multi-wall carbon nanotubes (MWCNTs). A stability analysis has been performed to show which solutions are linearly stable.

Analysis of catalytic heat transfer for a multi-species gas mixture

Stagnation point catalytic heat transfer model for a multi-species gas mixture has been developed in this work. The analysis extends the existing tertiary gas mixture catalytic model that assumes thermochemical equilibrium at the edge of a chemically frozen boundary layer. The catalytic heat transfer is computed numerically by solving the governing equations with matrix diagonalization and shooting methods. The present model is applied to compute the heat transfer for both tertiary gas mixture O-O2-Ar and quinary gas mixture O-O2-N-N2-Ar. For the case of the tertiary gas mixture, the present model predicts in the finite-catalytic region, the stagnation-point heat transfer due to recombination is similar with that of the existing models of Goulard and Park. In the highly-catalytic region, however, noticeable differences are observed owing to how the species mass fraction at the wall is computed. Unlike the Goulard approach treating the oxygen and nitrogen as a single recombination efficiency, in the case of the quinary gas mixture, the oxygen recombination efficiency needs to be decoupled with that of nitrogen. The present global model for the tertiary gas mixture is also compared with the Computational Fluid Dynamics (CFD) approach. The results suggest that the present model predicts a similar diffusive stagnation heat transfer to that of the CFD approach, within some acceptable range, when a zero backward reaction rate constant is assumed in the chemical reaction modeling.

Stagnation point flow and heat transfer past a permeable stretching/shrinking Riga plate with velocity slip and radiation effects

This paper concerns the stagnation point flow and heat transfer of a viscous and incompressible fluid passing through a flat Riga plate with the effects of velocity slip and radiation. An appropriate similarity transformation is chosen to reduce the governing partial differential equations to a system of ordinary differential equations. The numerical results are verified by comparison with existing results from the literature for a special case of the present study. The computed results are analyzed and given in the form of tables and graphs. The behaviors of the skin friction coefficient and the heat transfer rate for various physical parameters are analyzed and discussed. Dual solutions exist for both stretching and shrinking cases. Stability analysis reveals that the solution with lower boundary layer thickness is stable while the other solution is unstable. It is also observed that for the stable solution, the skin friction coefficient and the local Nusselt number increase as the suction effect is increased. For the shrinking case, a solution exists only for a certain range of the shrinking strength and this range increases with increasing value of the suction effect.

Unsteady MHD Non-Newtonian Heat Transfer Nanofluids with Entropy Generation Analysis

AbstractA theoretical study of unsteady magnetohydrodynamic boundary layer stagnation point flow, heat and mass transfer of a second grade electrically-conducting nanofluid from a horizontal stretching sheet with thermal slip and second order slip velocity effects is presented. The Buongiorno formulation is employed for nanofluids and in addition the no-flux nanoparticle boundary condition is also considered. The appropriate similarity transformations are applied to convert the governing equations into the system of nonlinear partial differential equations, which is solved by using homotopy analysis method. Entropy generation and Bejan number have also been evaluated for the effects of magnetic parameter, Reynolds number and slip parameter in non-Newtonian (second-grade) time-dependent flow. The computations show that skin friction coefficient and entropy generation number increase with an increment in magnetic parameter whereas Bejan number decreases with it. Local Nusselt number decreases with an increase in the value of Eckert number (viscous dissipation) and thermal slip whereas the converse behaviour is captured for velocity parameter. The work is relevant to magnetohydrodynamic nanomaterials processing.

Unsteady magnetohydrodynamic stagnation point flow—closed-form analytical solutions

This paper investigates the unsteady stagnation point flow and heat transfer of magnetohydrodynamic (MHD) fluids over a moving permeable flat surface. The unsteady Navier-Stokes (NS) equations are transformed into a similarity nonlinear ordinary differential equation, and a closed form solution is obtained for the unsteadiness parameter of 2. The boundary layer energy equation is transformed into a similarity equation, and is solved for a constant wall temperature and a time-dependent uniform wall heat flux case. The solution domain, velocity, and temperature profiles are calculated for different combinations of parameters including the Prandtl number, mass transfer parameter, wall moving parameter, and magnetic parameter. Two solution branches are obtained for certain combinations of the controlling parameters, and a stability analysis demonstrates that the lower solution branch is not stable. The present solutions provide an exact solution to the entire unsteady MHD NS equations, which can be used for validating the numerical code of computational fluid dynamics.

Stability analysis of unsteady MHD stagnation point flow and heat transfer over a shrinking sheet in the presence of viscous dissipation

The unsteady MHD stagnation-point flow and heat transfer over a shrinking sheet was carried out. This study also was conducted in the existence of suction and viscous dissipation. In order to convert the governing partial differential equations to an ordinary differential equation, an appropriate similarity transformation was applied in this study. Then, the resulting equations are worked out by Bvp4c solver in Matlab. The impacts of the parameters involved in this study towards skin friction, Nusselt number, velocity and temperature profile are showed graphically and thoroughly discussed. Remarkably, there were dual solutions present in this study which made us continue deeper in performing the stability analysis. As expected, our study proves that the solution is stable only in the first one while not in the second solution.

Unsteady heat transfer in non-axisymmetric Homann stagnation-point flows towards a stretching /shrinking sheet

Abstract We have studied the unsteady non-axisymmetric Homann’s stagnation point flow and heat transfer of an incompressible viscous fluid over a stretching/shrinking sheet in the presence of time dependent free stream. In a very recent paper Mahapatra and Sidui (2017) show a modification of Homann’s stagnation point flow over a rigid plate. Now if the plate is not rigid but linearly stretched as well as shrunk with velocities in x and y -directions, then there is a new family of asymmetric viscous stagnation-point flows depending on the unsteadiness parameter δ ( = σ ∕ | c | ) and the ratios of shear to the rate of linear stretching/shrinking of the sheet γ ( = b ∕ | c | ) , the strain-rate to the rate of linear stretching/shrinking of the sheet λ ( = a ∕ | c | ) in the range − ∞ γ , λ ∞ . Here a and b are the strain rate and shear rate of the stagnation-point flow respectively, σ is a positive constant whose dimension is t i m e − 1 and c is the rate of linear stretching/shrinking of the sheet along x - and y -axes at unit distance from origin when time, t = 0 . We have also studied the heat transfer in the flow. The temperature of the sheet is assumed to be higher than the ambient fluid temperature. The governing momentum equations are solved numerically using fourth order Runge–Kutta method with shooting technique. The effect of the various parameters on wall shear stress parameters, dimensionless velocities, displacement thicknesses and temperature distributions are analysed. A good agreement is found when we compare our numerical results of wall shear stress, displacement thickness and temperature distributions with their corresponding asymptotic value behaviours. For the flow past a shrinking sheet dual solutions are found to exist. Here we have made a stability analysis in the case of non-unique solutions to identify the stable solution.

Heat transfer characteristics of impinging methane diffusion and partially premixed flames

Flame jet impingement heat transfer is a well-established technique for obtaining high heat transfer rates in many domestic and industrial applications. The flame structure and the heat transfer characteristics of the impinging methane diffusion flame and partially premixed flame are experimentally investigated. The heat transfer characteristics of the impinging methane flame are determined using the minimization technique wherein the target surface is impinged by a methane flame from the bottom and is simultaneously cooled from the top by air jets of different Reynolds number. At steady state, one-dimensional energy balance across the impingement surface provides an over-determined system of equations which when solved using the minimization technique give the heat transfer coefficient of the flame jet, the reference temperature and the emissivity of the gas/flame beneath the impingement surface.The stagnation point heat transfer coefficient and reference temperature are found to be maximum for the case of flame just touching the impingement surface. The radial variation of the non-dimensional heat transfer coefficient and reference temperature is found to have a Gaussian profile. For low H/d’s where the flame is impinging the target surface, the temperature at the stagnation zone is lower than in the radial position as the hot jet turns in the radial direction and impinges at a distance slightly away from the stagnation region.The separation of heat transfer components indicates that the heat transfer is convective dominant with radiation accounting to 10% of the total incident heat flux in the case of methane diffusion flame and 3.5% in the case of partially premixed flame. Re-radiation becomes a significant component of heat transfer, accounting to 25–30% of the incident heat flux, due to higher wall temperatures. The present study also investigates the effect of tube burner to plate spacing.

An effective conductivity model for jet ablation of a solid substrate

Jet impingement heat transfer is a specialized area of heat transfer having numerous industrial applications involving fast and localized heating or cooling. In the very rare case of a nuclear reactor core melt-down accident scenario, the molten corium (a mixture of nuclear fuel and structural material) jet with its large heat content is capable of breaching solid structures with which they come into contact. Simulation experiments have been conducted at SED, IGCAR to study the jet ablation of solid structures, using high temperature Wood’s metal jet directed towards solid wood’s metal plate. The objective of the present work is to predict the ablation or melt through time of the plate by numerical heat transfer analysis. The computational model is also used to carry out a parametric study by varying the jet velocity and plate thickness. Comprehensive CFD analysis of impinging jet with melting entails huge computational resources. Hence in this study, an effective conductivity model has been employed to predict the solid plate melt-through time by jet impingement. Available Nusselt number empirical correlations for stagnation point heat transfer in low Prandtl number fluids are collected from literature. For the experimental conditions, Nusselt number is evaluated using the relevant correlation. Effective conductivity (keff) is then computed from Nusselt number. Making use of this keff value, which accounts for the enhanced heat transfer due to the jet, transient heat conduction equation is solved numerically. Temperature profile across the plate is obtained as a function of time and melt-through time is estimated. The computed result is validated with the experimental result.

Direct numerical simulation of heat transfer from a cylinder immersed in the production and decay regions of grid-element turbulence

The present direct numerical simulation (DNS) study, the first of its kind, explores the effect that the location of a cylinder, immersed in the turbulent wake of a grid-element, has on heat transfer. An insulated single square grid-element is used to generate the turbulent wake upstream of the heated circular cylinder. Due to fine-scale resolution requirements, the simulations are carried out for a low Reynolds number. Three locations downstream of the grid-element, inside the production, peak and decay regions, respectively, are considered. The turbulent flow in the production and peak regions is highly intermittent, non-Gaussian and inhomogeneous, while it is Gaussian, homogeneous and fully turbulent in the decay region. The turbulence intensities at the location of the cylinder in the production and decay regions are almost equal at 11 %, while the peak location has the highest turbulence intensity of 15 %. A baseline simulation of heat transfer from the cylinder without oncoming turbulence was also performed. Although the oncoming turbulent intensities are similar, the production region increases the stagnation point heat transfer by 63 %, while in the decay region it is enhanced by only 28 %. This difference cannot be explained only by the increased approaching velocity in the production region. The existing correlations for the stagnation point heat transfer coefficient are found invalid for the production and peak locations, while they are satisfied in the decay region. It is established that the flow in the production and peak regions is dominated by shedding events, in which the predominant vorticity component is in the azimuthal direction. This leads to increased heat transfer from the cylinder, even before vorticity is stretched by the accelerating boundary layer. The frequency of oncoming turbulence in production and peak cases also lies close to the range of frequencies that can penetrate the boundary layer developing on the cylinder, and therefore the latter is very responsive to the impinging disturbances. The highest Nusselt number along the circumference of the cylinder is shifted 45 degrees from the front stagnation point. This shift is due to the turbulence-generating grid-element bars that result in the prevalence of intense events at the point of maximum Nusselt number compared to the stagnation point.

Melting heat transfer in stagnation point of Carreau fluid with nonlinear thermal radiation and heat source

Here melting heat and heat generation characteristics in radiated stagnant point flow of Carreau fluid are addressed. Heterogeneous–homogeneous chemical processes are utilized to elaborate the phenomenon of mass transfer. Nonlinear partial differential systems are reduced to the ordinary ones through transformation procedure. The modeled nonlinear systems are computed implementing bvp4c scheme. Residual errors are achieved through optimal homotopy technique. Optimal estimations of auxiliary variables are presented. Physics associated with the considered flow problem is described in detail graphically. The obtained results are compared with published literatures and reasonable agreement is found.

Heat Transfer in Nonequilibrium Flows with Homogeneous and Heterogeneous Recombination Reactions

The aeroheating performance of hypersonic vehicles is usually significantly influenced by the chemical reaction processes. For the new-generation hypersonic cruise vehicles, the boundary-layer flow is shown to be in chemical nonequilibrium due to rarefied gas effects. As a result, there will be a competition between the homogeneous recombination of atoms in the near-wall flowfield and the heterogeneous recombination on the catalytic wall surface, which, leading to a coupling of the heat diffusion and conduction, is beyond the application scope of the classical theories developed originally for the traditional blunt reentry vehicles. In this paper, the theoretical modeling and the direct simulation Monte Carlo method are employed to study the corresponding rarefied nonequilibrium flow and heat transfer phenomena near the sharp leading edges. A generalized model is proposed to evaluate the deviation of the actual aeroheating performance from the classical description. Based on this model, an integrated nonequilibrium criterion and a simple but effective bridging function are introduced to predict the stagnation-point heat transfer under the competitive effects between the homogeneous and heterogeneous recombination of atoms. The analytical formula is validated by the numerical results under various flow conditions.

Thermal Radiative MHD Stagnation Point Slip Flow and Heat Transfer Due to a Stretching Sheet

Thermal Radiative MHD Stagnation Point Slip Flow and Heat Transfer Due to a Stretching Sheet

Self-Similar Solution of Radial Stagnation Point Flow and Heat Transfer of a Viscous, Compressible Fluid Impinging on a Rotating Cylinder

In this study, the radial stagnation point flow of strain rate $$\bar{k}$$ impinging on a cylinder rotating at constant angular velocity ω and its heat transfer are investigated. Reduction in the Navier–Stokes equations and energy equation to primary nonlinear ordinary differential equation systems is obtained by use of appropriate transformations when the angular velocity and wall temperature or wall heat flux all are constant. The impinging free stream is steady and normal to the surface from all sides, and the range of Reynolds number variation ( $$Re = \bar{k}a^{2} /2\upsilon$$ ) is 0.1–1000 in which a and υ are cylinder radius and kinematic viscosity, respectively. Flow results are presented for selected values of compressibility factor and different values of Prandtl numbers along with shear stress and Nusselt number. For all values of Reynolds numbers and surface temperature or surface heat flux, as compressibility factor increases the radial velocity field, the heat transfer coefficient and the wall shear stress increase, whereas the angular velocity field decreases. The rotating movement of the cylinder does not have any effect on the radial component of the velocity, but its increase increases the angular component of the fluid velocity field and the surface shear stress.

Stagnation point transient heat flux measurement analysis from coaxial thermocouples

ABSTRACTThe transient heat flux measurement at stagnation point is a significant solicitation at highly compressed flow field environment. In aerodynamics surface heating point of view, the estimation of stagnation heat fluxes at the tip of a blunt body is very imperative. When the blunt body is exposed to high-speed flow field environments, at the stagnation point heat transfer would be maximum. The coaxial surface junction thermocouples (CSJTs) are convenient for short duration time scale due to the fast response in the range of millisecond or less (̴0.1 ms). These robust CSJTs have the tractability of intensifying them directly on any type of surface and can be used for routine measurement in ground-based impulse amenities as a temperature measuring devices where rapid heat loads are anticipated. In this work, three different types of coaxial thermocouples K-type, E-type, and J-type have been designed and contrived. The microstructural analysis of measuring surface property has been carried out to see the surface morphology using field emission scanning electron microscopy (FESME) and chemical characterization of these CSJTs materials using energy dispersive X-ray analysis (EDXA) technique is used to verify qualitatively appraise the CSJTs materials composition. The thermal coefficient of resistance (TCR) and sensitivity (S) of each coaxial thermocouple have been determined by using oil-bath calibration technique with the linear variation of resistance corresponding to the variation of temperature and found that these coaxial thermocouples are highly sensitive and suitable for highly transient heat transfer measurements. For this purpose, these three types of CSJTs have been tested under highly compressed heated air 310 K temperature for 100 ms at pressure 6.1 bar with Mach number unity (M = 1) using compressor test rig. Numerical simulation has also been carried out with these three RTDs to satisfy the experimental parameters using Ansys Fluent 15.0 and typical transient temperature recorded. Surface heat fluxes recovered from experimental and numerical transient temperatures histories using semi-infinite heat conduction modeling having good agreement with accuracy ±3% or less. This study divulges the expertise of these handmade coaxial thermocouples for transient surface heat flux measurement for short durations at highly compressed air facilities.

Dependence of submerged jet heat transfer on nozzle length

In this work the influence of nozzle length in submerged jet impingement heat transfer was studied by validated direct numerical simulations, in the laminar flow regime. With the purpose of examining the entire range of nozzle lengths and 500⩽Re⩽2000, other effects were reduced by setting a low nozzle-to-heater spacing (H/D = 3) and ideal, undisturbed inlet conditions. While developing pipe-flow is well-known, this parametric study characterized in detail short and intermediate nozzle flow regimes, affected by a separation bubble at the sharp-edged inlet. It is found that the maximal (centerline) jet velocity first decreases with increasing effective nozzle length, Z = L/(D ⋅ Re), to a minimum at Z∗≈0.0015, beyond which it increases as in developing pipe-flow. For Z<Z∗ two physical regimes are found: while the plane of the vena-contracta is outside the nozzle (L/D⩽0.6) the maximal centerline velocity occurs there, rather than at the nozzle exit-plane; whereas in the intermediate range, 0.6⩽L/D and Z⩽0.0015, the centerline velocity scales with the effective nozzle length, Z, and a predictive correlation could be developed for it. As a clear linear dependence of heat transfer on centerline velocity was observed, this predictive correlation could easily be converted into a new stagnation point heat transfer correlation, found to give good agreement over the entire range of nozzle lengths. This correlation provides a practical design tool, especially applicable to micro-jet cooling where constraints correspond with the new model’s validity range.

MHD mixed convective stagnation point flow and heat transfer of an incompressible nanofluid over an inclined stretching sheet with chemical reaction and radiation

The principal concern of the present work is to investigate the effects of thermally developed Brownian motion and thermophoresis diffusion in non-Newtonian nanofluid through an inclined stretching surface with effect of chemical reaction and thermal radiation. By using compatible similarity transformations the governing equations of momentum, energy and concentration profiles are converted to a set of nonlinear differential equations. A Mathematica package BVPh 2.0 is applied to examine the given system of equations. Influences of developing parameters such as magnetic parameter, radiation, Lewis number, Prandtl number, mixed convective parameter, Brownian motion and thermophoresis parameter on velocity, temperature and nanoparticles concentration are displayed through graphical experiment. A comparative study between OHAM and previously published results is made. It is noticed that OHAM can overcome the earlier restriction, assumptions and limitation of classical perturbation schemes. The implementation of OHAM is reasonably simple through Mathematica package need to define the governing equations, boundary conditions; suitable auxiliary linear operator and initial guess etc. The key advantage of the suggested technique is that it can be used direct way in highly nonlinear differential equations without using discretization, linearization and round-off errors.

Stagnation point flow and heat transfer for a viscoelastic fluid impinging on a quiescent fluid

A theoretical study is made in the region near the stagnation point when a lighter incompressible viscoelastic fluids impinges orthogonally on the surface of another quiescent heavier incompressible viscous fluid. Similarity solutions of the momentum balance equations for both fluids are equalized at the interface. It is noted that an exact boundary layer solution is obtained for the lower lighter fluid. The velocity of the lower fluid is independent of lateral interface velocity but the velocity of the upper viscoelastic fluid increases with increasing lateral interface velocity. It is observed that lateral interface velocity increases with increasing viscoelastic parameter for fixed values of density and viscosity ratio of the two fluids. The convective heat transfer is investigated base on the similarity solutions for the temperature distribution of the two fluids. The interface temperature increases with increasing viscoelastic parameter of the upper viscoelastic fluid.

Dual solutions of magnetohydrodynamic stagnation point flow and heat transfer of viscoelastic nanofluid over a permeable stretching/shrinking sheet with thermal radiation

The present study is intended to encompass the stagnation point flow and heat transfer of viscoelastic nanofluid with the presence of thermal radiation. The viscous incompressible electrically conducting and Jeffrey fluid model is taken into account. The governing partial differential equations are reduced to ordinary differential equations by using the appropriate similarity variables. The resulting differential equations are solved numerically using the built in bvp4c function in Matlab. Dual solutions are discovered for a certain range of the governing parameters. Numerical results for the velocity and temperature profiles as well as the skin friction coefficients and the local Nusselt number are elucidated through tables and graphs.

Second-order velocity slip with axisymmetric stagnation point flow and heat transfer due to a stretching vertical plate in a Copper-water nanofluid

The steady axisymmetric stagnation point flow with second-order velocity slip due to a stretching vertical plate with the existence of copper-water nanofluid was investigated. Similarity transformation has been applied to reduce the governing partial differential equations to ordinary differential equations. Then the self-similar equations are solved numerically using solver bvp4c available in Matlab with Prandtl number, Pr = 6.2. It is found that the dual solutions exist for the certain range of mixed convection parameter. The effects of the governing parameters on the velocity and temperature profile, skin friction coefficient and the local Nusselt number are observed. The results show that the inclusion of nanoparticle copper, will increase the shear stress on the stretching sheet and decrease the heat transfer rate for the slip parameters.