Stagnation Point Heat Research Articles

MHD stagnation point flow and heat transfer impinging on stretching sheet with chemical reaction and transpiration

This work is focused on the study of combined heat and mass transfer by MHD stagnation point flow toward a permeable stretching surface in the presence of a first order chemical reaction. The governing equations for the flow, heat and mass transfer are formulated and solved analytically using the homotopy analysis method (HAM). Graphical and numerical demonstrations of the convergence of the HAM solutions are provided. A detailed study illustrating the influences of the magnetic, velocity ratio, suction/injection and chemical reaction parameters, the Schmidt and Prandtl numbers on the dimensionless velocity, temperature as well as the skin-friction and the Nusselt and Sherwood numbers is conducted. The results obtained show that the flow field is substantially influenced by the presence of chemical reaction, transpiration, and magnetic field.

Stagnation-point heat transfer of nanofluids toward stretching sheets with variable thermo-physical properties

The objective of this study is to investigate stagnation-point flow of nanofluids over an isothermal stretching sheet. The volume fraction of nanoparticles at the sheet is assumed to be passively controlled. Furthermore, due to low volume fraction of nanoparticles and dilute nanofluid, the thermal conductivity and dynamic viscosity of the nanofluid are assumed to be linear functions of the volume fraction of nanoparticles. In order to study the effects of a plethora of parameters on the boundary layer flow and heat and mass transfer, a practical range of these parameters have been utilized. An accurate numerical solution of the governing equations based on the finite difference method is obtained and the effect of various physical parameters such as the Prandtl number, Lewis number, thermophoresis parameter, and the Brownian motion parameter on the thermal, hydrodynamic, and concentration boundary layers is evaluated. In order to examine the alteration of the thermal convective coefficient, a dimensionless heat transfer enhancement ratio parameter is introduced. The results show that the variation of different thermodynamic parameters induces substantial impression on the behavior of the nanoparticles distribution. For example, it is found that an increase in the value of the Lewis number leads to a decrease in the value of the non-dimensional nanoparticles volume fraction at the sheet, but it does not have any influence on the thermal and hydrodynamic boundary layers. Increasing the Prandtl number is predicted to decrease the thermal boundary layer thickness and the volume fraction of nanoparticles at the surface. In most instances, the heat transfer augments in the presence of nanoparticles.

The Effect of Induced Magnetic Field and Convective Boundary Condition on MHD Stagnation Point Flow and Heat Transfer of Nanofluid Past a Stretching Sheet

This study examines the effect of induced magnetic field and convective boundary condition on MHD stagnation point flow and heat transfer due to nanofluid over a stretching sheet. It takes into account the effect of Brownian motion and thermophoresis parameters. The nonlinear governing equations and their associated boundary conditions are reduced into dimensionless form by similarity variables. The resulting systems of equations are then solved numerically using fourth-order Runge-Kutta method along with shooting technique. The solution for the problem depends on parameters: magnetic M, velocity ratio B, Biot number Bi, Prandtl number Pr, Lewis number Le, Brownian motion Nb, thermophoresis Nt, and reciprocal of magnetic Prandtl number A. Numerical results of the study are obtained for velocity, temperature, induced magnetic field, and concentration profiles as well as skin friction coefficient, the local Nusselt number, and Sherwood number. It is found that the skin friction coefficient, the local Nusselt number, and Sherwood number decrease with an increase in B and M parameters. However, the local Nusselt number -θ'(0) increases with an increase in Bi, and local Sherwood number -φ'(0) decreases with an increase in convective parameter Bi. The study indicated that the flow velocity and the skin friction coefficient on stretching sheet are strongly influenced by velocity ratio (B <; 1) and magnetic parameters. It is also observed that the skin friction coefficient -f"(0) is an increasing function of magnetic parameter and a decreasing function of velocity ratio parameter B. The study also shows that the local heat transfer rate -θ'(0) is an increasing function of the convective parameter Bi, but it is a decreasing function of magnetic parameter M, velocity ratio parameter B, and thermophoresis parameter Nt. The obtained results are displayed both in graphical and tabular form to show the effect of the governing parameters on the dimensionless velocity, induced magnetic field, temperature and concentration. The numerical results are compared and found to be in good agreement with the previously published results on special cases of the problem.

НЕСТАЦИОНАРНОЕ ТРЕХМЕРНОЕ ТЕЧЕНИЕ И ТЕПЛООБМЕН В НАНОЖИДКОСТИ В ТОЧКЕ ОСТАНОВКИ ПОТОКА С УЧЕТОМ ТЕРМОФОРЕЗА И БРОУНОВСКОГО ДВИЖЕНИЯ

НЕСТАЦИОНАРНОЕ ТРЕХМЕРНОЕ ТЕЧЕНИЕ И ТЕПЛООБМЕН В НАНОЖИДКОСТИ В ТОЧКЕ ОСТАНОВКИ ПОТОКА С УЧЕТОМ ТЕРМОФОРЕЗА И БРОУНОВСКОГО ДВИЖЕНИЯ

Mixed Convection Boundary Layer Stagnation-Point Flow of a Jeffery Fluid Past a Permeable Vertical Flat Plate

Abstract This paper analyzes the combined effects of buoyancy force, mass flux, and variable surface temperature on the stagnation point flow and heat transfer due to a Jeffery fluid over a vertical surface. The governing nonlinear partial differential equations are transformed into a system of coupled nonlinear ordinary differential equations using similarity transformations and then solved numerically using the function bvp4c from computer algebra software Matlab. Numerical results are obtained for skin friction coefficient, Nusselt number as well as dimensionless velocity and temperature profiles for various values of the controlling parameters namely mixed convection parameter λ, mass flux parameter s, elastic parameter (Deborah number) γ, and the ratio of relaxation and retardation time parameter λ1. The results indicate that dual solutions exist in a certain range of the mixed convection and mass flux parameters. In order to establish the physically realizable of these solutions, a stability analysis has also been performed. The results indicate that mixed convection and mass flux significantly affects the nature of the solutions, skin friction, and Nusselt number of a Jeffery fluid.

Temperature and Heat Flux Measurement on Hot Models in Short-Duration Facilities

An electrical preheating technique applied to a carbon-based model in an impulse facility has previously demonstrated surface temperatures around 2500 K, but the measurement of heat flux at such elevated surface temperatures was not previously achieved. A technique for fast-response surface temperature measurement of an electrically preheated carbon-phenolic model using an indium gallium arsenide detector with in situ calibration via a visible/near-infrared spectrometer is assessed through application in a short-duration cold-flow hypersonic wind tunnel. The method is reliable: the scatter in temperatures determined from successive acquisitions of the spectrometer data had a standard deviation of 3 K at a mean temperature of about 1500 K; the standard deviation of the Indium gallium arsenide detector results from the visible/near-infrared spectrometer data was 11 K at a temperature of about 1100 K after the termination of the hypersonic flow. The surface temperature history from the Indium gallium arsenide detector was analyzed using a one-dimensional transient heat conduction model to deduce the surface heat flux. Good agreement with an engineering correlation for stagnation point heat flux is demonstrated; however, uncertainties are large (), as the thermal properties of the particular carbon-phenolic material were not available. The method is suitable for application in impulse facilities, but the effusivity () for the heat shield material will need to be accurately defined for reliable deduction of surface heat flux.

Steady Stagnation Point Flow and Heat Transfer Over a Shrinking Sheet with Induced Magnetic Field

The problem of the steady magnetohydrodynamic (MHD) stagnation-point flow of an incompressible, viscous and electrically conducting fluid over a shrinking sheet is studied. The effects of an induced magnetic field and thermal radiation are taken into account. Velocity and thermal slip conditions have also been incorporated in the study. The nonlinear partial differential equations are transformed into ordinary differential equations via the similarity transformation. The transformed boundary layer equations are solved numerically using Newton’s linearization method. Computational results for the variation in velocity, temperature, skin-friction co-efficient and Nusselt number are presented graphically and in tabular form. Study reveals that the surface velocity gradient and heat transfer are enhanced by decreasing magnetic parameter.

Conjugate Heat Transfer Analysis for a Finite Thickness Cylinder in a Hypersonic Flow

Prediction of surface heating rates is of prime importance for the hypersonic flow regime. Experimental and conventional computational efforts overlook the heat transfer phenomenon in the solid due to the rigid assumptions involved in the solution methodologies. In order to address this fact, conjugate heat transfer (CHT) studies are carried out using various coupling techniques to examine their implementation abilities. Three types of solution methodologies are adopted, namely, decoupled, strongly coupled, and loosely coupled analysis. This study is also focused on looking into the effect of a hypersonic flow field on wall heat flux for a finite thickness insulating cylinder at moderately large time scales. Increase in wall temperature and decrease in surface heat flux have been noticed using strong and loose coupling techniques with an increase in simulation time. Decoupled fluid and solid domain analysis is found to be useful for typical shock tunnel test durations (∼1 ms) while investigations with loose coupling techniques are advisable for time scales corresponding to flight testing (∼1 s). Efforts are also made to reason the discrimination in prediction of stagnation point heat flux using conventional computational and experimental analysis.

Effect of Induced Magnetic Field on Magnetohydrodynamic Stagnation Point Flow and Heat Transfer on a Stretching Sheet

In this paper, the steady magnetohydrodynamic (MHD) stagnation point flow of an incompressible viscous electrically conducting fluid over a stretching sheet has been investigated. Velocity and thermal slip conditions have been incorporated in the study. The effects of induced magnetic field and thermal radiation have also been duly taken into account. The nonlinear partial differential equations arising out of the mathematical analysis of the problem are transformed into a system of nonlinear ordinary differential equations by using similarity transformation and boundary layer approximation. These equations are solved by developing an appropriate numerical method. Considering an illustrative example, numerical results are obtained for velocity, temperature, skin friction, and Nusselt number by considering a chosen set of values of various parameters involved in the study. The results are presented graphically/in tabular form.

MHD stagnation flow towards a porous stretching sheet with suction or injection and prescribed surface heat flux

The objective of the present study is to analyze the effect of heat generation/absorption on magnetohydrodynamic stagnation point flow and heat transfer over a porous stretching surface, with prescribed surface heat flux. The governing coupled partial differential equations are non-dimensionalized and solved analytically by homotopy perturbation method employing Pade technique. The effects of involved parameters (stretching velocity, magnetic parameter, porosity parameter, suction or injection parameter, heat flux index, heat source or sink parameter, Prandtl number) on velocity, temperature profiles are presented graphically and analyzed. The obtained results are compared with the numerical solution and with other results obtained in previous works so that the high accuracy of present results is clear.

Dual Solutions in Magnetohydrodynamic Stagnation-Point Flow and Heat Transfer Over a Shrinking Surface With Partial Slip

In this paper, the problem of steady two-dimensional magnetohydrodynamic (MHD) stagnation-point flow and heat transfer of an incompressible viscous fluid over a stretching/shrinking sheet is investigated in the presence of velocity and thermal slips. With the help of similarity transformations, the governing Navier–Stokes and the energy equations are reduced to ordinary differential equations, which are then solved numerically using a shooting technique. Interesting solution behavior is observed for the similarity equations with multiple solution branches for certain parameter domain. Fluid velocity increases due to the increasing value of the velocity slip parameter resulting in a decrease in the temperature field. Temperature at a point increases with increase in the thermal slip parameter. The effects of the slips, stretching/shrinking, and the magnetic parameters on the skin friction or the wall shear stress, heat flux from the surface of the sheet, velocity, and temperature profiles are computed and discussed.

Effect of time-dependent chemical reaction on stagnation point flow and heat transfer over a stretching sheet in a nanofluid

The unsteady two-dimensional boundary layer stagnation-point flow of a nanofluid over a heated stretching sheet is investigated numerically. The unsteadiness in the flow, temperature and nanoparticle concentration fields is caused by the time-dependence of the stretching velocity, the free stream velocity and the surface temperature and concentration. The transport model employed includes the effects of Brownian motion, thermophoresis and time-dependent chemical reaction. The resulting non-linear governing equations with the associated boundary conditions are solved numerically using the shooting technique with the aid of similarity transformation. The velocity, temperature and nanoparticle volume fraction profiles, as well as the local Nusselt and Sherwood numbers, are analyzed due to the effect of the involved parameters of interest, namely the Brownian motion paramter Nb, thermophoresis parameter Nt, unsteadiness parameter S, velocity ratio parameter , chemical reaction parameter , Prandtl number and Lewis number Le. It is found that the mass transfer process at the solid-fluid interface is stopped for some values of Le, Nb, and Nt despite of the continuity of the heat transfer process for the same parameter values.

Flow and heat transfer of nanofluids at a stagnation point flow over a stretching/shrinking surface in a porous medium with thermal radiation

In this paper, the effects of thermal radiation and viscous dissipation on a stagnation point flow and heat transfer over a flat stretching/shrinking surface in nanofluids are analyzed. The effects of suction/injection are also considered. Using a similarity transformation, the governing equations are transformed into a system of nonlinear ordinary differential equations. The resulting system is then solved numerically by Runge–Kutta–Fehlberg method with shooting technique. It is observed that the local Nusselt number increases with increment in the suction/injection parameter for stretching sheet whereas reverse effect is observed for shrinking sheet. It is found that skin-friction coefficient increases for both stretching/shrinking sheet with increase in volume fraction of the nanoparticles.

Approximate Analytical Solution of Stagnation Point Flow and Heat Transfer over an Exponential Stretching Sheet with Convective Boundary Condition

This study is concerned with the stagnation point flow and heat transfer over an exponential stretching sheet via an approximate analytical method known as optimal homotopy asymptotic method (OHAM). The governing partial differential equations are converted into ordinary nonlinear differential equations using similarity transformations available in the literature. The heat transfer problem is modeled using two‐point convective boundary condition. These equations are then solved using the OHAM approach. The effects of controlling parameters on the dimensionless velocity, temperature, friction factor, and heat transfer rate are analyzed and discussed through graphs and tables. It is found that the OHAM results match well with numerical results obtained by Runge–Kutta Fehlberg fourth‐fifth order method for different assigned values of parameters. The rate of heat transfer increases with the stretching parameter. It is also found that the stretching parameter reduces the hydrodynamic boundary layer thickness whereas the Prandtl number reduces the thermal boundary layer thickness.

Aerodynamic Heating of a Hypersonic Projectile with Forward-Facing Ellipsoid Cavity at Nose

Numerical experiments are carried out using a commercially available computational-fluid-dynamics code to investigate the aerodynamic heating of a hemisphere–cylinder with a forward-facing ellipsoid cavity at nose in atmosphere. A wide range ellipsoid cavity of depths varying between 3 to 30 mm placed axisymmetrically at the nose of the blunt body with base diameter 40 mm and overall length 70 mm have been investigated. The ratios of semimajor axis to semiminor axis of these cavities () are 3, 2, or 1.5, where semimajor axis a is equal to the depth of cavity and the semiminor axis is close to the lip radius of the cavity. All computations have been done at a freestream Mach number of 10.1 and static pressure and temperature of 16,066 Pa and 216.65 K respectively. The steady-state solutions of axisymmetric Navier–Stokes equations are obtained using a time marching approach in order to study the aerodynamic heating of a hypersonic projectile with a forward-facing ellipsoid cavity at a nose. The simulation results suggest that, though the stagnation-point heat flux and the total heat-transfer rates to the blunt body can be favorably reduced by the introduction of ellipsoid cavity, the local heating at lip can become drastically high.

Slip effects on steady and transient stagnation-point heat transfer in axisymmetric geometries

Steady and transient heat convection in axisymmetric stagnation point flow with momentum and thermal slip effects are studied numerically for different flow parameters. The thermal response to time-dependent wall temperature variations in surface cooling and heating processes is analyzed in terms of temporal variations in the heat transfer coefficient, thermal jump, and fluid temperature at the surface. The transition time from an initial to a final steady state is also investigated over a range of slip factor and decay/growth rate of the wall temperature. A criterion in the form of a relation between Prandtl number and the specific heat ratio that characterizes the variation of the convective heat transfer coefficient with the slip factor is established. The results presented show that the convective heat transfer coefficient is less influenced by transient conditions as rarefaction increases. Higher Prandtl number flows are more influenced by transients. The transition time is found to increase with slip and decrease with the decay/growth rate of the wall temperature and is most influenced at relatively low values of both slip and decay/growth rate of the wall temperature.

Axisymmetric stagnation point flow and heat transfer towards a permeable moving flat plate with surface slip condition

The steady axisymmetric stagnation point flow and heat transfer of a viscous and incompressible fluid due to a permeable moving flat plate with partial slip is considered. The partial slip is controlled by a dimensionless slip factor, which varies between zero (total adhesion) and infinity (full slip). Suitable similarity transformations are used to reduce the partial differential Navier–Stokes and energy equations to ordinary (similarity) differential equations, which are then solved numerically. Analytical solutions for the energy similarity equation have been also obtained for some particular values of the governing parameters. The important finding in this paper is the combined effect of the partial slip with the moving and the suction parameters on the skin friction coefficients, heat transfer, and the velocity and temperature profiles. Dual solutions are found for suction and opposing flow cases.

Unsteady MHD flow and heat transfer near stagnation point over a stretching/shrinking sheet in porous medium filled with a nanofluid

In this article, the unsteady magnetohydrodynamic (MHD) stagnation point flow and heat transfer of a nanofluid over a stretching/shrinking sheet is investigated numerically. The similarity solution 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 ambient fluid velocity, stretching/shrinking velocity of sheet, and the wall temperature are assumed to vary linearly with the distance from the stagnation point. To investigate the influence of various pertinent parameters, graphical results for the local Nusselt number, the skin friction coefficient, velocity profile, and temperature profile are presented for different values of the governing parameters for three types of nanoparticles, namely copper, alumina, and titania in the water-based fluid. It is found that the dual solution exists for the decelerating flow. Numerical results show that the extent of the dual solution domain increases with the increases of velocity ratio, magnetic parameter, and permeability parameter whereas it remains constant as the value of solid volume fraction of nanoparticles changes. Also, it is found that permeability parameter has a greater effect on the flow and heat transfer of a nanofluid than the magnetic parameter.

Integrated Analysis of Reusable Thermal Protection Systems Based on Variable-Transpiration Cooling

Reusable thermal protection systems are one of the key technologies that have to be improved to use hypersonic vehicles as practical, long-range, transportation systems. The proposed concept of variable-transpiration cooling is investigated in this work by coupling the hypersonic boundary-layer solution with the thermal response of a porous material. The simulations of the hypersonic boundary layers are obtained using an in-house-developed reduced-order model capable of handling generic injection velocity profiles at the porous wall and the high-fidelity computational-fluid-dynamics code Langley Aerothermodynamic Upwind Relaxation Algorithm. The material thermal response is included adopting a one-dimensional model for the porous medium. The integrated analysis is performed for a flat plate and a two-dimensional blunt-body configuration. A sawtooth wall velocity profile was chosen to represent the variable-transpiration strategy. The uniform transpiration on the blunt body allows for a reduction of the stagnation point heat flux by 48% in comparison with the case without transpiration. The variable transpiration reduces the stagnation point heat flux by an additional 8%. The integrated analysis highlights the coolant blockage effects, the potential offered by the variable-transpiration cooling, and the necessity of performing a coupled flow-material analysis, at the design stage, to define realizable combinations of porosity, thermal conductivity, and material thickness capable to guarantee the thermostructural integrity of the thermal protection system.

Unsteady Two-Dimensional Stagnation-Point Flow and Heat Transfer of a Viscous, Compressible Fluid on an Accelerated Flat Plate

The general formulation and exact solution of the Navier–Stokes and energy equations regarding the problem of steady and unsteady two-dimensional stagnation-point flow and heat transfer is investigated in the vicinity of a flat plate. The plate is moving at time-dependent or constant velocity towards the main low Mach number free stream or away from it. The main stream impinges along z-direction on the flat plate with strain rate a and produces two-dimensional flow. The fluid is assumed to be viscous and compressible. The density of the fluid is affected by the existing temperature difference between the plate and potential far field flow. Suitably introduced similarity transformations are used to reduce the governing equations to a coupled system of ordinary differential equations. Finite Difference Scheme is used to solve these non-linear ordinary differential equations. The obtained results are presented over a wide range of parameters characterizing the problem. It is revealed that the significance of the increase of thermal expansion coefficient, β, and wall temperature on velocity and temperature distributions is much more noticeable for a plate moving away from impinging flow. Moreover, negligible shear stress and heat transfer is reported between the plate and fluid viscous layer close to the plate for a wide range of β coefficient when the plate moves away from incoming far field flow.