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The purpose of this study is to investigate the two-dimensional unsteady inclined stagnation point flow and thermal transmission of Maxwell fluid on oscillating stretched/contracted plates. First, based on the momentum equation at infinity, pressure field is modified by solving first-order differential equation. Meanwhile, thermal relaxation characteristic of fluid is described by Cattaneo–Christov thermal diffusion model.

Highly coupled model equations are transformed into simpler partial differential equations (PDE) via appropriate dimensionless variables. The approximate analytical solutions of unsteady inclined stagnation point flow on oscillating stretched and contracted plates are acquired by homotopy analysis method for the first time, to the best of the authors’ knowledge.

Results indicate that because of tensile state of plate, streamline near stagnation point disperses to both sides with stagnation point as center, while in the case of shrinking plate, streamline near stagnation point is concentrated near stagnation point. The enhancement of velocity ratio parameter leads to increasing of pressure variation rate, which promotes flow of fluid. In tensile state, surface friction coefficient on both sides of stagnation point has opposite symbols; when the plate is in shrinkage state, there is reflux near the right side of the stagnation point. In addition, although the addition of unsteady parameters and thermal relaxation parameters reduce heat transfer efficiency of fluid, heat transfer of fluid near the plate can also be enhanced by considering thermal relaxation effect when plate shrinks.

First, approximate analytical solutions of unsteady inclined stagnation point flow on oscillating stretched and contracted plates are researched, respectively. Second, pressure field is further modified. Finally, based on this, thermal relaxation characteristic of fluid is described by Cattaneo–Christov thermal diffusion model.

The purpose of this paper is to investigate analytically the steady general three-dimensional stagnation-point flow of an aqueous titania-copper hybrid nanofluid past a circular cylinder that has a sinusoidal radius variation.

First, the analytic modeling of hybrid nanofluid is presented, and using appropriate similarity variables, the governing equations are transformed into nonlinear ordinary differential equations in the dimensionless stream function, which is solved by the well-known function bvp4c from MATLAB.

The current solution demonstrates good agreement with those of the previously published studies in the special cases of regular fluid and nanofluids. Graphical results are presented to investigate the influences of the titania and copper nanoparticle volume fractions and also the nodal/saddle indicative parameter on flow and heat transfer characteristics. Here, the thermal characteristics of hybrid nanofluid are found to be higher in comparison to the base fluid and fluid containing single nanoparticles. An important point to note is that the developed model can be used with great confidence to study the flow and heat transfer of hybrid nanofluids.

Analytic modeling of hybrid nanofluid is the important originality of present study. Hybrid nanofluids are potential fluids that offer better heat transfer performance and thermophysical properties than convectional heat transfer fluids (oil, water and ethylene glycol) and nanofluids with single nanoparticles. In this investigation, titania (TiO₂, 50 nm), copper (Cu, 20 nm) and the hybrid of these two are separately dispersed into the water as the base fluid and analyzed.

The purpose of this paper is to present an engineering inviscid‐boundary layer method for the calculation of convective heating rates on three‐dimensional non‐axisymmetric geometries at angle of attack.

Based on the axisymmetric analog, convective heating rates are calculated along the surface streamlines which are determined using the inviscid properties calculated on an unstructured grid.

Since the method is capable of using inviscid properties calculated on an unstructured grid, it is applicable to a variety of configurations and it requires much less computational effort than a Navier‐Stokes code. The results of the present method are evaluated on different wing body configurations in laminar and turbulent hypersonic equilibrium flows. In comparison to experimental data, the present results are found to be fairly accurate in the windward and leeward regions.

With this approach, heating rates can be predicted on general three‐dimensional configurations at hypersonic speeds in an accurate and fast scheme.

In order to calculate the heating rates at any specific point on the surface, a technique is developed to calculate the inviscid surface streamlines in a backward manner using the inviscid velocity components. The metric coefficients are also calculated using a new simple technique.

This paper seeks to conduct a numerical study to investigate heat transfer in turbulent, unconfined, submerged, and inclined impinging jet discharged from a slot nozzle, utilising finite volume code FLUENT.

Two re‐normalisation group k‐ε and the basic Reynolds stress models by using enhanced wall treatment for near wall turbulent modelling were applied and the local Nusselt numbers were compared with experiments. The enhanced wall treatment solves the fully turbulent region and viscous sublayer by considering a single blended function of both layers.

In inclined impinging jet by movement of stagnation point to the uphill side of the impinging plate, the location of the maximum Nusselt number moves to the uphill side of the plate. However, this movement increases by increasing of H/D and by decreasing of Reynolds number and inclination angle. For a flat plate impinging jet, the results were found to be less than 8 per cent different and for inclined impinging jet, more sensitive to H/D, 5‐20 per cent different in comparison with experiments. In addition, the flow streamlines were consistent with location of the heat transfer peak on the impinging surface.

Reynolds numbers in range of 4,000‐16,000, the ratio of nozzle height to hydraulic diameter of the nozzle (H/D) in range of 4‐10, and inclination angle of air jet and plate in range of 40‐90° were considered.

A unique achievement of this study in comparison with experimental data was locating the exact peak of the local Nusselt number on impinging plate by change of Reynolds number, H/D, and inclination angle.

The present critical analysis has been performed to explore the steady stagnation point flow of Jeffery fluid toward a stretching surface, in the presence of convective boundary conditions. It is assumed that the fluid strikes the wall obliquely. The governing non-linear partial differential equations for the flow field are converted to ordinary differential equations by using suitable similarity transformations. Optimal homotopy analysis method (OHAM) is operated to deal the resulting ordinary differential equations. OHAM is found to be extremely effective analytical technique to obtain convergent series solutions of highly non-linear differential equations. Graphically, non-dimensional velocities and temperature profile are expressed. Numerical values of skin friction coefficients and heat flux are computed. The comparison of results from this paper with the previous existing literature authorizes the precise accuracy of the OHAM for the limited case. The paper aims to discuss these issues.

The governing non-linear partial differential equations for the flow field are converted to ordinary differential equations by using suitable similarity transformations. OHAM is operated to deal the resulting ordinary differential equations.

OHAM is found to be extremely effective analytical technique to obtain convergent series solutions of highly non-linear differential equations. Graphically, non-dimensional velocities and temperature profile are expressed. Numerical values of skin friction coefficients and heat flux are computed.

The comparison of results from this paper with the previous existing literature authorizes the precise accuracy of the OHAM for the limited case.

This study aims to investigate the flow impinging on a stagnation point of a shrinking cylinder subjected to prescribed surface heat flux in Al₂O₃-Cu/water hybrid nanofluid.

Using similarity variables, the similarity equations are obtained and then solved using bvp4c in MATLAB. The effects of several physical parameters on the skin friction and heat transfer rate, as well as the velocity and temperature profiles are analysed and discussed.

The outcomes show that dual solutions are possible for the shrinking case, in the range λc<λ<−1, where λc is the bifurcation point of the solutions. Meanwhile, the solution is unique for λ≥−1. Besides, the boundary layer is detached on the surface at λc, where the value of λc is affected by the hybrid nanoparticle φhnf and the curvature parameter γ. Moreover, the friction and the heat transfer on the surface increase with the rising values φhnf and γ. Finally, the temporal stability analysis shows that the first solution is stable in the long run, whereas the second solution is not.

The present work considers the problem of stagnation point flow impinging on a shrinking cylinder containing Al₂O₃-Cu/water hybrid nanofluid, with prescribed surface heat flux. This paper shows that two solutions are obtained for the shrinking case. Further analysis shows that only one of the solutions is stable as time evolves.

This paper aims to assess the strengths and weaknesses of four thermodynamic models used in aircraft icing simulations to orient the development or the choice of an improved thermodynamic model.

Four models are compared to assess their capabilities: Messinger, iterative Messinger, extended Messinger and shallow water icing models. They have been implemented in the aero-icing framework, NSCODE-ICE, under development at Polytechnique Montreal since 2012. Comparison is performed over typical rime and glaze ice cases. Furthermore, a manufactured geometry with multiple recirculation zones is proposed as a benchmark test to assess the efficiency in runback water modeling and geometry evolution.

The comparison shows that one of the main differences is the runback water modeling. Runback modeling based on the location of the stagnation point fails to capture the water film behavior in the presence of recirculation zones on airfoils. However, runback modeling based on air shear stress is more suitable in this situation and can also handle water accumulation while the other models cannot. Also, accounting for the conduction through the ice layer is found to have a great impact on the final ice shape as it increases the overall freezing fraction.

This paper helps visualize the effect of different thermodynamic models implemented in the same aero-icing framework. Also, the use of a complex manufactured geometry highlights weaknesses not normally noticeable with classic ice accretion simulations. To help with the visualization, the ice shape is presented with the water layer, which is not shown on typical icing results.

This study considers the five factors of a car rotation system: angle (F1), arm length (F2), toe in and out (F3), width (F4) and length (F5). The purpose of this paper is to fine tune the design so it produces the smoothest response to various rotation angles.

In the case of Ackerman’s principle, the response surface methodology (RSM) was used to analyze data when encountering different quality characteristics at various rotation angles.

In this study, RSM was used to obtain the best factor and the best reaction value for the five factors of a car rotation system.

In this study, the four-wheel steering of a car is taken as an example. When the current wheel is turned, the intersection of the left and right wheels of the front axle falls on the extension line of the rear wheel. In this case, the steering will be the smoothest. In this example, we selected angle (F1), arm length (F2), toe in and out (F3), width (F4) and length (F5) as experimental factors, hoping to satisfy the Ackerman principle.

Traditionally, when dealing with four-wheel steering problems, solutions may be based on past experience or on new information used to formulate R&D plans. In this study, the combination of statistical factors and optimization is used to find the optimal combination of factors and the relationship between factors.

In the past, most literature relied on kinematics to study the car rotation system due to a lack of experimental design and analysis concepts. However, this study aims to achieve the above goals in finding the solution, which can be used to predict reaction values.

The problem of coupled heat and mass transfer by mixed convection in a linearly stratified stagnation flow (Hiemenz flow) in the presence of an externally applied magnetic field and internal heat generation or absorption effects is formulated. The plate surface is embedded in a uniform Darcian porous medium and is permeable in order to allow for possible fluid wall suction or blowing and has a power‐law variation of both the wall temperature and concentration. The resulting governing equations are transformed into similarity equations for the case of linearly varying wall temperature and concentration with the vertical distance using an appropriate similarity transformation. These ordinary differential equations are then solved numerically by an implicit, iterative, finite‐difference scheme. Comparisons with previously published work are performed and excellent agreement between the results is obtained. A parametric study of all involved parameters is conducted and a representative set of numerical results for the velocity and temperature profiles as well as the skin‐friction parameter, local Nusselt number, and the local Sherwood number is illustrated graphically to elucidate interesting features of the solutions.

The time development of the symmetrical standing zones of recirculation, which is formed in the early stages of the impulsively started laminar flow over the square cylinder, have been studied numerically. The Reynolds number considered ranges from 25 to 1,000. Main flow characteristics of the developing recirculation region aft of the square cylinder and its interaction with the separating shear layer from the leading edges are studied through the developing streamlines. Other flow characteristics are analysed in terms of pressure contours, surface pressure coefficient, wake length and drag coefficient. Four main‐flow types and three subflow types of regimes are identified through a detailed analysis of the evolution of the flow characteristics. Typically, for a given Reynolds number, it is noted that flow starts with no separation (type I main‐flow). As time advances, symmetrical standing zone of recirculation develops aft of the square cylinder (type II main‐flow). The rate of growth in width, length and structure of the aft end eddies (sub‐flow (a)) depends on the Reynolds number. In time, separated flow from the leading edges of the square cylinder also develops (type III main‐flow) and forms growing separation bubbles (sub‐flow (b)) on the upper and lower surfaces of the square cylinder. As time advances, the separation bubbles on the upper and lower surfaces of the cylinder grow towards downstream regions and eventually merge with the swelling symmetrical eddies aft of the cylinder. This merging of the type II and type III flows created a complex type IV main‐flow regime with a disturbed tertiary flow zone (sub‐flow (c)) near the merging junction. Eventually, depending on the Reynolds number, the flow develops into a particular category of symmetrical standing recirculatory flow of specific characteristics.