Pressure Gradient Parameter Research Articles

Design and characterisation of an open-jet pressure gradient test rig for an aeroacoustic wind tunnel

This paper summarises an approach to generating controllable pressure gradients within an open-jet configuration for aeroacoustics research. A novel open-jet pressure gradient test rig has been designed for the UNSW Anechoic Wind Tunnel with the help of RANS simulations. A range of pressure gradients is created by adjusting the inclination angle of the top plate to change the cross-sectional area along the streamwise direction gradually. The test model mounting point is located on the bottom plate adjacent to partially opened side walls to allow far-field noise measurements. A comprehensive characterisation of flow quality, pressure gradient parameters and acoustic data quality has been carried out using Particle Imaging Velocimetry (PIV), surface pressure taps, and a microphone array. The test rig produces near-uniform pressure gradient flows at the model mounting point, with momentum Reynolds numbers (Reθ) ranging from 3014 to 11853 and Clauser's pressure gradient parameters (β) from -0.24 to 1.66. The pressure gradients generated by this facility are approximately linear, approaching the model mounting point, and the boundary layer profiles compare favourably with those from conventional hard-walled enclosed pressure gradient wind tunnel facilities. Measurements of airfoil trailing-edge noise from this test rig compare well with classical semi-empirical model predictions. Simultaneous acoustic and flow measurements on a square finite wall-mounted cylinder showcase the capability of this facility for coupled acoustic-flow diagnosis.

Computational micropolar model of hybrid nanofluid flow across a wedge

Non-Newtonian flow from wedges is a vital problem in coatings, polymer processing etc. Hence the main aim is to investigate the convective boundary layer flow of micropolar hybrid nanofluid (MHN)from a wedge. It is assumed that the wedge surface is isothermal. The Eringen model is employed to define micropolar fluid. Nanoscale Tiwari–Das formulations are used to study the specific effects of nanoparticles and volume fractions. The dimensionless boundary value problem arises by suitable coordinate transformations as a system of nonlinearly coupled ordinary differential equations. The so-called Falkner Skan flow case is resolved. Dimensionless, transformed, coupled momentum, microrotation, boundary layer equations are resolved using the numerical scheme MATLAB bvp4c. The parameteric investigations are performed on hybrid nanofluids using water as the basis liquid and varying volume fractions from 0 to 8%. Affirmation with previous work is done. The consequence of Eringen micropolar parameter, Hartree pressure gradient parameter, nanoparticle volume fraction, Eckert number, heat absorption (sink) parameter, on the flow and physical characteristics are visualized graphically and in tables. With rising material factor and volume fraction of nanoparticle, temperature is markedly enhanced. Increases in volume fraction dampen angular velocity close to the wedge surface, while farther from the wall, the opposite effect is seen. Temperature and thermal boundary layer thickness are both greatly enhanced by increasing Eckert number. With an increase in the volume proportion of nanoparticles, velocity decreases. Heat generation raises temperatures while a heat sink lowers them. The pressure gradient parameter increases skin friction while decreasing Nusselt number. Nusselt number for hybrid nanofluid is higher than for nanofluid.

On the thermal performance of radiative stagnation-point hybrid nanofluid flow across a wedge with heat source/sink effects and sensitivity analysis

The present article aims to examine the thermal performance and the sensitivity analysis of a GO−TiO2/water hybrid nanofluid in the presence of different nanoparticle shapes along with heat absorption and thermal radiation effects over a wedge geometry. Analyzing the effects of heat generation and radiation effects is one of the key studies conducted by researchers in various nanofluid flows over some required geometries. However, a combined study of these effects has yet to be studied over a moving wedge, and that combination defines the novelty of the work. Similarity transformations are implemented to the governing equations to obtain the final set of nondimensional equations, which are solved using the bvp4c code in MATLAB. The results obtained were in close agreement with the published results. The Nusselt number decreased with an increase in the heat source parameter Q, and it increased with an increasing Hartree pressure gradient β and thermal radiation parameter Rd. The sensitivity is statistically analyzed for the variations in radiation effect, heat source, and pressure gradient parameters on the Nusselt number. The high values for R2=99.99% and Adj R2=99.96% validate the ANOVA results obtained using a Box–Behnken design (BBD) model in the response surface methodology (RSM) with 14 degrees of freedom. The input parameters Rd and β show positive sensitivity, while Q shows negative sensitivity toward the skin friction. The Nusselt number proves to be most sensitive toward the pressure gradient parameter. TiO2, graphene (Gr), and the derivative forms of graphene, are gaining much importance due to their wide applications in the oil and petroleum industries. Thus, this study contributes to lubrication purposes, emulsion stabilizers, oxalic acid removal, anti-corrosive properties, etc.

Generalised Couette flow of nanoliquid among two concentric channels with particles injection

In the presence of nanoparticle injection, buoyancy power, constant pressure gradient, variable viscosity coefficient, magnetic field, mass diffusivity of thermophoresis, and Brownian motion, the hydrodynamic nanoliquid conducted with electric current flows through the gap between two concentric cylindrical channels of infinite length. The focus of this article was on generalised Couette flow that is flow in which the outer channel plate moves at a uniform velocity while still being subjected to a pressure gradient. Here we use the RKF45 numerical method and the shooting technique to solve dimensionless momentum, energy, and concentration equations. How the obtained parameters controlled on flow rate, temperature and concentration of the fluid have been investigated and appearances through respective graphs. The high magnitude of nanoliquid flow rate with outer channel wall motion and pressure gradient parameters has been observed. The nanoliquid temperature declines with an annular gap parameter while amplified thermophoresis and magnetic parameter values enrich the fluid temperature. In addition, loftier values of variable viscosity and Brownian motion parameters boost the nanoliquid concentration.

Evidence of quasiequilibrium in pressure-gradient turbulent boundary layers

Two sets of measurements utilizing hot-wire anemometry and oil-film interferometry for flat-plate turbulent boundary layers, exposed to various controlled adverse and favourable pressure gradients, are used to evaluate history effects of the imposed and varying free-stream gradients. The results are from the NDF wind tunnel at Illinois Tech (IIT) and the MTL wind tunnel at KTH, over the range $800 < Re_\tau < 22\,000$ (where $Re_{\tau }$ is the friction Reynolds number). The streamwise pressure-gradient parameter $\beta \equiv (-\ell /\tau _{w}) \cdot (\partial P_{e}/\partial x)$ varied between $-2 < \beta < 7$ , where $\ell$ is an outer length scale for boundary layers equivalent to the half-height of channel flow and the radius of pipe flow, and is estimated for each boundary-layer profile; note that $\tau_w$ is the wall-shear stress and $P_e$ is the free-stream static pressure. Extracting from each profile the three parameters of the overlap region, following the recent work of Monkewitz & Nagib (J. Fluid Mech., vol. 967, 2023, p. A15) that led to an overlap region of combined logarithmic and linear parts, we find minimum history effects in the overlap region. Thus, the overlap region in this range of pressure-gradient boundary layers appears to be in ‘quasiequilibrium’.

Application of the Fibonacci wavelet approach to the MHD boundary layer analysis of a Casson fluid past a stretching sheet

The current work investigates the MHD boundary layer flow of Casson fluid over a stretching sheet with the help of Fibonacci wavelet approach. The stable laminar MHD flow, mass and heat transport properties of a nanofluid over a stretching sheet in the presence of a fluctuating magnetic field has been under scrutiny. By choosing relevant non-dimensional parameters, the governing boundary layer equation undergoes transformation into a dimensionless Falkner-Skan equation. The Fibonacci integral operational matrix is used to solve the achieved nonlinear equation and it has been used for the first time to solve stretching sheet problem in fluid dynamics. The nature of the boundary layer flow are analyzed graphically for a range of distinct values of physical parameters. Impact of parameters on axial and transverse velocity has been investigated. It can be observed that local skinfriction coefficient grows for larger values of Casson parameter for ϵ = 0.3 and decreases for higher values of Casson parameter and decreases for higher values of magnetic parameter, angle of inclination and pressure gradient parameter. To ensure the accuracy of the findings, local skin friction is recorded and contrasted with various approaches that are already documented in research.

Numerical analysis of novel wavy wall based control of turbulent boundary layer separation

In this work, a comprehensive insight into the new passive flow control method, i.e. a two-dimensional streamwise waviness (recently proposed by Dróżdż et al. [1]) is provided using Large Eddy Simulations. This approach was demonstrated to be effective in postponing turbulent boundary layer separation at high Re, which is out of reach for other commonly known passive flow control strategies. Although the effectiveness of the wavy wall in delaying flow separation has been confirmed, the physical mechanisms standing behind the skin friction enhancement are not fully understood which opens a space for future work. Of particular interest is an insight into the fluid flow in the near-wall region just above the waviness and this paper is aimed at doing so. To separate the effect of the global adverse pressure gradient, the results were confronted with the ones obtained under zero pressure gradient conditions for the identical wavy wall geometry and the same Reτ=2500. Also additional simulations of the turbulent boundary layer building up on the flat wall were conducted to have an additional reference for the flow fields obtained above the wavy wall under zero and adverse pressure gradients respectively. A detailed inspection of the streamwise velocity and its fluctuation profiles indicated that the contribution of the global adverse pressure gradient to the flow statistics begins when the Rotta-Clauser pressure gradient parameter β≥3. The paper confirms an enhancement of the wall shear stress τw downstream the corrugation, which is the necessary condition to postpone the separation. Interestingly, the effect of increased τw was not observed for the case with the same waviness and without pressure gradient.

A one-dimensional urban flow model with an eddy-diffusivity mass-flux (EDMF) scheme and refined turbulent transport (MLUCM v3.0)

Abstract. In recent years, urban canopy models (UCMs) have been used as fully coupled components of mesoscale atmospheric models as well as offline tools to estimate temperature and surface fluxes using atmospheric forcings. Examples include multi-layer urban canopy models (MLUCMs), where the vertical variability of turbulent fluxes is calculated by solving prognostic momentum and turbulent kinetic energy (TKE, k) using mixing length scale (l) and drag parameterizations. These parameterizations are based on the well-established 1.5-order k−l turbulence closure theory and are often informed by microscale fluid dynamics simulations. However, this approach can include simplifications such as assuming the same diffusion coefficient for momentum, TKE, and scalars. In addition, the dispersive stresses arising from spatially averaged flow properties have been parameterized together with the turbulent fluxes despite being controlled by different mechanisms. Both of these assumptions impact the quantification of the turbulent exchange of flow properties and subsequent air temperature predictions in urban canopies. To assess these assumptions and improve corresponding parameterization, we analyzed 49 large-eddy simulations (LES) for idealized urban arrays, encompassing variable building height distributions and a comprehensive range of urban densities (λp∈[0.0625,0.64]) seen in global cities. We find that the efficiency of turbulent transport (numerically described via diffusion coefficients) is similar for scalars and momentum but is 3.5 times higher for TKE. Additionally, parameterizing the dispersive momentum flux using the k−l closure was a source of error, while scaling with the pressure gradient and urban morphological parameters appears more appropriate. In response to these findings, we propose two changes to the previous version of MLUCM: (a) separate characterization for turbulent diffusion coefficient for momentum and TKE and (b) introduction of an explicit physics-based “mass-flux” term to represent the fraction of the dispersive momentum transport directly induced from buildings as an amendment to the existing “eddy-diffusivity” framework. The updated one-dimensional model, after being tuned for building height variability, is further compared against the original LES results and demonstrates improved performance in predicting vertical turbulent exchange in urban canopies.

Turbulent activity in the near-wall region of adverse pressure gradient turbulent boundary layers

Two direct numerical simulation (DNS) databases are investigated to understand the effect of the outer-layer turbulence on the inner layer’s structures and energy transfer mechanisms. The first DNS database is the non-equilibrium adverse-pressure-gradient (APG) turbulence boundary layer (TBL) of Gungor et al. [1]. Its Reynolds number and the inner-layer pressure gradient parameter reach above 8000 and 10, respectively. The shape factor spans between 1.4 and 3.3, which indicates the flow has various velocity defect situations. The second database is the same flow as the first one but the outer layer turbulence is artificially eliminated in this flow. Turbulence is removed above 0.15 local boundary layer thickness. For the analysis, we chose four streamwise positions with small, moderate, large, and very-large velocity defect. We compare the wall-normal distribution of Reynolds stresses, two-point correlations and spectral distributions of energy, production and pressure strain. The results show that the inner layer turbulence can sustain itself when the outer-layer turbulence does not exist regardless of the velocity defect or the pressure gradient. The two-point correlations of both cases show that outer large-scale structures affect the inner layer structures significantly. The streamwise extent of the correlation contours scales with pressure-viscous units. This shows the importance of the pressure gradient’s effect on the inner-layer structures. The spectral distributions demonstrate that the energy transfer mechanisms are probably the same in the inner layer regardless of the velocity defect, which suggests the near-wall cycle may exist even in very-large defect APG TBLs where the mean shear in the inner layer is considerably lower than small-defect APG TBLs.

Neural network architecture to optimize the nanoscale thermal transport of ternary magnetized Carreau nanofluid over 3D wedge

SignificanceIncorporation of nanoparticles in base fluid water is significant for analysis of thermal behavior of nanofluid mixtures, which has various applications in materials science and thermal engineering, and supervised neural scheme predicts the thermal behavior by solving Carreau nanofluid model. MotiveThis article brings the investigation related to prediction of thermal transport of a ternary magnetized hybrid nanofluid [(Al2O3, CuO, TiO2)/H2O] with a three-dimensional Carreau nanofluid model over a wedge. Three nanoparticles dispersed in water (H2O). Inclined magnetic field is considered for judgement of velocity profile and thermal radiation is utilized to scrutinize the temperature distribution of nanofluid. The Carreau mathematical model is chosen to depict the rheological characteristics of non-Newtonian fluids at very high and very low shear rate. MethodologyPhysical assumptions creates the system of Partial differential equations (PDEs) and these are converted into ordinary differential equations (ODEs) by similarity tool. Further ODEs are dealt with bvp4c scheme and further prediction of solution is made by Levenberg-Marquardt neural network (LM-NN) supervised neural scheme. FindingsIncreased volume friction coefficients of nanoparticles increases the transport of heat. High inclined magnetic effect, thermal radiation, pressure gradient and shear strain parameter predict higher thermal transport.

Consistent outer scaling and analysis of adverse pressure gradient turbulent boundary layers

Under adverse pressure gradient (APG) conditions, the outer regions of turbulent boundary layers (TBLs) are characterized by an increased velocity defect $U_{e}-U$ , an outwards shift of the peak value of the Reynolds shear stress $-\langle uv\rangle$ and an appearance of the outer peak value of the Reynolds normal stress $\langle uu\rangle$ . Here $U_{e}$ is the TBL edge velocity. Scaling APG TBLs is challenging due to the non-equilibrium effects caused by changes in the APG. To address this, the response distance of TBLs to non-equilibrium conditions is utilized to extend the Zagarola–Smits scaling $U_{zs} = U_{e}({\delta ^{*} }/{\delta })$ and ensure that the original properties of the Zagarola–Smits scaling are maintained as $Re \to \infty$ . Here $\delta ^{*}$ is the displacement thickness and $\delta$ is the boundary layer thickness. Based on the established correlation between $U_{e}-U$ and $-\langle uv\rangle$ , the scaling is extended to $-\langle uv\rangle$ . Furthermore, considering the coupling relationship between Reynolds stress components, the scaling is extended to encompass each Reynolds stress component. The proposed consistent scaling is verified using five non-equilibrium databases and five near-equilibrium databases, successfully collapsing the data of the TBL outer region. The pressure gradient parameter $\beta =({\delta ^{*} }/{\rho u_{\tau }^{2} }) ({\mathrm {d} P_{e} }/{\mathrm {d}\kern0.7pt x})$ of these databases spans two orders of magnitude. Here $P_{e}$ is the boundary layer edge pressure, $u_{\tau }$ is the friction velocity and $\rho$ is the density. Finally, the influence of the APG on the inner and outer regions of TBLs is analysed using the mean momentum balance equation. The analysis suggests that the shift of the $-\langle uv\rangle$ peak to the outer region under APG conditions is due to an insufficient inertia term near the inner region to balance the APG. It is observed that the APG promotes interaction between the inner and outer regions of TBLs, but the inner and outer regions still retain distinctive properties.

Analysis of MHD boundary layer flow of a viscous fluid past a stretching sheet employing the Legendre wavelet method

The current work introduces a novel approach to analyse the non-linear Falkner–Skan equation from fluid dynamics by utilising the Legendre wavelet method. In this paper, we relied on the Legendre wavelet to generate a new functional integration matrix and presented a novel approach known as the Legendre wavelet approach (LWA). The primary goal of this study is to provide a unified method via LWA to compute an approximate solution to a non-linear differential equation for a viscous fluid over a stretching sheet. The Legendre wavelet method has been used for the first time to solve the stretching sheet problem. A viscous fluid across a stretching sheet has been explored for its stable laminar magnetohydrodynamic (MHD) flow, transportation of mass and heat characteristics in the context of an intermittent magnetic field. By specifying appropriate non-dimensional parameters, the governing boundary layer equation evolves into a dimension devoid of the Falkner–Skan equation. Using the Legendre wavelet approach, the resulting nonlinear equation modified to an algebraic equation is addressed. With LWA, the undershoots and overshoots for a set of factors are noted. The boundary layer thickness appears to decrease with increasing pressure gradient and magnetic field parameters. The graphical interpretation of the boundary layer flow’s features is done for a range of physical parameter values. To ensure the accuracy of the findings, local skin friction has been tracked and contrasted with other techniques that are already documented in the previous research.

Activation energy with binary chemical reaction of convective radiative magnetized nanofluid flow with viscous dissipation and pressure gradient

ABSTRACT The present investigation deals with the study of activation energy with the binary chemical reaction on magnetohydrodynamic convective radiative heat and mass transfer of nanofluid flow with internal heat source/sink, viscous dissipation, pressure gradient force, and suction effects. The basic equations of conservation of momentum, energy, and mass diffusion are brought to a set of ordinary differential equations (nonlinear) using suitable similarity transformations, and these are then solved using the Homotopy Perturbation Method (HPM). The validity of the present results is established by comparing them with those obtained by the Runge-Kutta-Fehlberg method (RKFM). The results reveal that the temperature distribution increases with raising the value of the thermal radiation parameter. It is found that the concentration distribution increases by increasing the values of the activation energy parameter. In contrast, the reverse effect is observed by enhancing the chemical reaction parameter, Schmidt number, and pressure gradient parameter. Further, the skin-friction coefficient and Nusselt number decrement by enhancing the value of the Hartmann number, whereas the reverse trend is found by enhancing the pressure gradient and suction parameter values. Also, the Sherwood number retards with an enhancement in the Hartmann number, whereas it rises by increasing the pressure gradient and suction parameters.

Exact and analytical solutions for self‐similar thermal boundary layer flows over a moving wedge

AbstractThis article aims to achieve exact and analytical solutions for the classical Falkner–Skan equation with heat transfer (FSE‐HT). Specifically, when the pressure gradient parameter , there already exists a closed‐form solution in the literature for the Falkner–Skan flow equation. The main purpose here is to extend this case to obtain a closed‐form solution to the heat transport equation with the solubility condition . An algorithm is presented and is found to be new to the literature that enriches the physical properties of FSE‐HT. It is shown that for the moving wedge parameter , the momentum and temperature equations show multiple solutions analytically. The skin friction coefficient and the heat transfer rate are also obtained in analytical form. The thus‐obtained solution is then adapted to derive an analytical solution applicable to a wide range of pressure gradient parameters and Prandtl numbers . Furthermore, an asymptotic analysis is conducted, focusing on scenarios where the moving wedge parameter becomes significantly large (). Nevertheless, in all the above‐mentioned cases, the skin friction coefficient () and the heat transfer rate () are compared with the direct numerical solutions of the boundary layer equations, and it is found that the results are in good agreement. These solutions provide a benchmark and shed light on further studies on the families of FSE‐HT.

Local correlation, compressibility, and crossflow corrections of γ-Reθ transition model for high-speed flows

Based on the original γ-Reθ transition model framework, in this work, an improved local correlation-based transition closure model is developed for high-speed flows. The local correlation between the vorticity Reynolds number and the momentum thickness Reynolds number obtained by compressible boundary-layer self-similar solutions, local compressibility correction including the pressure gradient parameter and momentum thickness Reynolds number, and local crossflow correlation are applied to improve the original γ-Reθ model for hypersonic transition predictions. The function Fonset1 used to control the transition onset and several relevant model parameters are also modified to make the improved model suitable for high-speed flow. The improved transition model is validated through several basic test cases under a wide range of flow conditions, including high-speed flat plates, sharp cones, double ramp, Hypersonic International Flight Research Experimentation, and complex hypersonic configuration X-33 vehicles. The numerical results show that the transition onset locations and the changes of heat transfer rate predicted by the present improved transition model are reasonably consistent with experimental results. The proposed model predicts the high-speed boundary layer transition behaviors induced by streamwise and crossflow instabilities with reasonable precision.

Novel quartic spline method for boundary layer fluid flow problem of Falkner-Skan model with wall stretching and transfer of mass effects

The non-linear ordinary differential equations (NODEs) in this article are estimated and analyzed numerically using the capability of the Quartic Splines Method (QSM) for mathematical modeling of the Falkner-Skan fluidic system and its optimization through global search Genetic Algorithms (GAs) and local search Active-Set (AS) techniques. The concept of hybridization is used to optimize the obtained results and provide a boost to the suggested method, QSM, which allows for rapid iteration. Falkner-Skan fluid model (FSFM) is solved by the proposed technique QSM-GAs-AS. The FSFM is solved for three, seven, and twelve splines successfully. The problem is analyzed for three scenarios, in which each scenario is based on the variation of a parameter out of the three involved parameters, namely the wall mass transfer parameter (γ), the wall movement parameter (λ), and the stream-wise pressure gradient parameter (β), appearing in FSFM. The QSM-GAs-AS produces an interpolated function that is continuous up to its fourth derivative. The solution outcomes of FSFM, treated by the designed scheme QSM-GAs-AS, are presented graphically. The evaluation of the planned solution is done with a deterministic numerical solver, the Homotopy Analysis Method (HAM). Statistical analysis for multiple runs is used to examine the proposed scheme's convergence, exactness, and accuracy.

Numerical and analytical study of heat transfer in the wire coating process using Carreau–Yasuda fluid model

In this article, we present a non-isothermal study of the wire coating process using the Carreau–Yasuda fluid model. Our aim is to explore how the Carreau–Yasuda fluid model parameters are linked to key operational factors in the wire coating process. These factors encompass the radius of the coated wire, the volumetric flow rate, and the force needed to pull the wire. The equations that depict the flow and heat transfer within the die are solved: (a) analytically using the perturbation method to get the analytical expression for velocity, temperature distribution, and relevant engineering quantities; (b) numerically using shooting method with the “Runge–Kutta–Fehlberg algorithm.” The physical effects of the Weissenberg number (We), power law index (n), pressure gradient (A), and Brinkman number (Br) on the velocity profile, temperature distribution, and engineering quantities are discussed with the help of different graphs. Our findings reveal that, in the case of shear thinning (n < 1) with a constant pressure gradient, as compared to the Newtonian scenario, both the thickness of the coated wire and the force required to pull the wire decrease with an increase in the Weissenberg number (We). Moreover, the force required to pull the wire also decreases with an increase in the values of the pressure gradient parameter.

The mean wall-normal velocity in turbulent boundary layer flows under pressure gradient

Using a combination of proper variable transformation and integral methods, we rigorously derive an analytical formulation for the mean wall-normal velocity in turbulent boundary layers (TBLs) subjected to arbitrary pressure gradients. The accuracy and robustness of this novel formulation are validated extensively through comparisons with two independent sets of numerical simulation data, demonstrating excellent agreement in both near-equilibrium and non-equilibrium TBLs. In addition, the robustness of the analytical formulations to various choices of boundary-layer edge definition is further confirmed in non-equilibrium TBLs. Our formulation includes a streamwise derivative term, which has minimal significance in near-equilibrium TBLs but plays a crucial role in determining the mean wall-normal velocity in non-equilibrium TBLs. Moreover, we investigate the physical significance of the pre-factors associated with the mean wall-normal velocity components, and unveil a close connection between a previously defined pressure gradient parameter and the ratio of these pre-factors in the analytical equation governing the mean wall-normal velocity. The insights gained from the examination of the pre-factors and their connection to the pressure gradient parameter offer valuable knowledge for interpreting and predicting the behaviour of turbulent boundary layers in various practical applications.

Mixed Convection of Cu–H2O Nanofluid in a Darcy–Forchheimer Porous Medium Microchannel with Thermal Radiation and Convective Heating

Heat transfer and convective flow of Cu–H2O nanofluid in a microchannel with thermal radiation has many attributes in engineering, industries, and biomedical sciences including cooling of electronics, drug delivery, cancer therapy, optics, missiles, satellites, and lubricants. Therefore, this paper aims to investigate the hydrodynamical behaviors and heat transfer characteristics of Cu–H2O nanofluid through a porous medium microchannel with thermal radiation and convective heating. The highly non-linear partial differential equations that govern the momentum and energy equations are formulated, non-dimensionalized, transformed into ordinary differential equations and solved numerically via the fourth order Runge-Kutta integration scheme. Consequently, the numerical simulation reveals that the nanofluid velocity and temperature profiles show a rising pattern with increasing values of the pressure gradient parameter, variable viscosity parameter, Darcy number, thermal Grashof number and Eckert number. The temperature profile escalates with the Prandtl number however it diminishes with the Biot number, Forchheimer number, suction/injection Reynolds number and nanoparticles volume fraction. Furthermore, the thermal radiation parameter indicates a retarding effect on the temperature profile and hence, radiation quite effectively controls the microchannel temperature distribution which plays a significant role in cooling the flow transport system. The skin friction coefficient at both microchannel walls indicates a rising pattern with the suction/injection Reynolds number, thermal Grashof number, Eckert number and Darcy number. Moreover, at both microchannel walls the heat transfer rate enhances for large values of the suction/injection Reynolds number, thermal Grashof number, Eckert number, variable viscosity parameter and Darcy number whereas it decreases with the thermal radiation parameter, Forchheimer number and nanoparticles volume fraction. The Biot number reveals an opposite effect on the heat transfer rate at the left and right walls of the microvhannel.

VISCOSITY AND HALL EFFECTS ON UNSTEADY MHD CASSON FLUID FLOW THROUGH A PARALLEL POROUS PLATE

This study investigates the temperature viscosity and Hall effects of a Casson fluid flow through a porous medium of a viscous incompressible fluid bounded by two parallel porous plates under the influence of thermal radiation and chemical reaction. A uniform suction and injection are applied perpendicular to the plates while the fluid motion is subjected to variable pressure gradient. The transformed conservation equations are solved analytically subject to physically appropriate boundary conditions by using perturbation and Eigenfunction expansion techniques. The influence of a number of emerging non-dimensional parameters namely, variable pressure gradient parameter, suction parameter, radiation parameter and Hartman number are examined. It is observed that the primary velocity profile is increased with increasing temperature dependent viscosity while increase in Hall parameter leads to increase in secondary velocity profile of the flow.