Mixed convection boundary layer flow from a vertical flat plate embedded in a porous medium filled with nanofluids

The steady mixed convection boundary layer flow past a vertical flat plate embedded in a porous medium filled with nanofluids is studied using different types of nanoparticles as Cu (cuprom), Al₂O₃ (aluminium) and TiO₂ (titanium). The model used for the nanofluid is the one which incorporates only the nanoparticle volume fraction parameter. The basic partial equations are reduced to an ordinary differential equation which is solved numerically for some values of the volume fraction and mixed convection parameters. It is shown that the solution has two branches in a certain range of the parameters. The effects of these parameters on the velocity distribution are presented graphically.     

幂律流体连续运动平板边界层的数值研究

利用数值模拟方法研究了幂律流体在连续运动平板上的层流边界层问题。利用相似变换理论推导出无量纲剪切力的计算公式,数值求解了不同幂律指数n的流体在不同运动参数ξ的连续运动平板上的层流边界层流场,分析了各个参数对边界层速度分布和剪切力大小的影响。结果表明,边界层偏微分方程组的数值解与经过相似变换求得的非线性常微分方程的数值解吻合得很好,这既说明对幂律流体连续运动平板上的层流边界层问题的研究是有效且可靠的,同时也证明了连续运动平板问题存在相似解。     

Magnetohydrodynamic boundary layer flow of nanofluid with variable chemical reaction in a radiative vertical plate

The nanotechnology-based nanofluid has extraordinary prospects in heat transfer engineering. Analysis of these applied nanofluids can yield the appropriate combinations of various useful physical parameters. In the present study, the incompressible boundary layer flow of a nanofluid in the presence of the variable chemical reaction, temperature-dependent viscosity, hydromagnetic force, and the radiation past an infinite vertical plate has been investigated. The governing nanofluid equations are simplified to ordinary differential equations, which are solved using the function bvp4c from MATLAB. The effects of the physical parameters including the similarity parameter, magnetic field, two dimensionless constant temperatures, Schmidt number, local Grashof number, radiation parameter, local chemical reaction parameter, kinematic diffusion parameter, and temperature-independent kinematic diffusion parameter on the velocity, temperature, concentration and the local Nusselt number are demonstrated. The results show that as the magnetic field parameter increases, the heat transfer decreases, and the increase of the radiation parameter yields the opposite effect. The kinematic diffusion and the chemical reaction parameters greatly stimulate the concentration of nanofluid and reduce the heat transfer.     

Improved velocity and temperature profiles for integral solution in the laminar boundary layer flow on a semi‐infinite flat plate

One of the most important problems in Mechanical Engineering is the determination of laminar boundary layer thickness over a flat plate. Integral solution and similarity solutions are two well‐known methods for calculation of boundary layer thickness. However, integral solution method is a computational cost‐effective method rather than the similarity solution method. Velocity and temperature profiles must be determined for the integral solution method. Velocity boundary layer thickness can be determined by the velocity profile whereas for determination of thermal boundary layer thickness both velocity and temperature profiles must be used. Available velocity profiles do not give an exact value for velocity boundary layer thickness, while the Nusselt number is affected by these profiles. In this study, a new velocity profile is proposed which gives an exact value for laminar boundary layer thickness on a flat plate. In addition, two temperature profiles are proposed that give the exact values of the Nusselt number over a flat plate for uniform temperature and uniform heat flux boundary conditions. The calculated constants in the velocity boundary layer thickness equation and the Nusselt relations are validated with the results of the similarity solution method. Excellent agreement between the results of the two methods is observed.     

Analytical and numerical solutions of heat and mass transfer of boundary layer flow in the presence of a transverse magnetic field

The present investigation aims to study the effect of a transverse magnetic field with the presence of an adverse pressure gradient on the two‐dimensional laminar incompressible boundary layer flow over a flat plate. Using appropriated similarity transformations, the partial differential equations governing the studied problems are transformed into the ordinary nonlinear differential equations. Thereafter, these equations are solved numerically and analytically using the fourth‐order Runge‐Kutta method featuring shooting technique and the Adomian decomposition method, respectively. Obtained results reveal an excellent agreement between analytical and numerical data for temperature and concentration profiles.     

Effect of thermal radiation on an unsteady MHD flow over an impulse vertical infinite plate with variant temperature in existence of Hall current

In this paper, the effects of thermal radiation on unsteady MHD flow viscous incompressible electrically conducting fluid past an impulsively started oscillating vertical plate with variable temperature and constant mass diffusion in the presence of Hall current have been presented. The dimensionless governing partial differential equations of the flow have been solved numerically by using the Galerkin finite element method. The numerical solutions for fluid velocity, angular velocity, temperature, and concentration are represented graphically whereas the numerical results of primary skin friction, rate of heat and mass transfer are presented in tabular form for various parameters involved. The current results were compared to the existing analytical solution based on the Crank–Nicolson implicit finite difference technique. The current study's findings have been shown to be extremely consistent with earlier findings.     

The effect of Joule heating and viscous dissipation on the boundary layer flow of a magnetohydrodynamics micropolar-nanofluid over a stretching vertical Riga plate

Joule heating and viscous dissipation effects on the behavior of the boundary layer flow of a micropolar nanofluid over a stretching vertical Riga plate (electro magnetize plate) are considered. The flow is disturbed by an external electric magnetic field. The problem is formulated mathematically by nonlinear system of partial differential equations (PDEs). By using suitable variables transformations, this system is transformed onto a system of nonlinear ordinary differential equations (ODEs). The Parametric NDsolve package of the commercial software Mathematica is used to solve the obtained ODEs as well as the considered numerical results for different physical parameters with appropriate boundary conditions. Novel results are obtained by studying the stream lines flow around the plate in two and three dimensions. Moreover, the effects of the pertinent parameters on the skin friction coefficient, couple stress, local Nusselt, and Sherwood number are discussed. Special cases of the obtained results show excellent agreements with previous works. The results showed that as the magnetic field parameter increases the velocity of the boundary layer adjacent to the stretching sheet decreases. Also, for a productive chemical reaction near the sheet surface, the angular velocity decreases but opposite trend is observed far from the sheet surface. The importance of this study comes from its significant applications in many scientific fields, such as nuclear reactors, industry, medicine, and geophysics.     

Analytical study of heat and mass transfer effects on unsteady Casson fluid flow over an oscillating plate with thermal and solutal boundary conditions

In this study, the impacts of heat and mass transfer characteristics on an isotropic incompressible Casson fluid flow over an oscillatory plate with the incidences of solutal and thermal boundary conditions have been investigated. Exact solutions of the fundamental equations governing the fluid flow are determined by using the Laplace transform technique. Numerical results based on analytical solutions are presented in graphical and tabular illustrations to clarify the behaviors of the fluid. Most interestingly, both fluid velocity and species concentration increase with an increment of mass transfer coefficient, whereas the fluid velocity diminishes as oscillating frequency increases near the surface of the plate. This happens due to the presence of high fluctuation of the plate in the flow system. Finally, this investigation is helpful to the scientific community, and the obtained results can be used as benchmark solutions for solving nonlinear flow governing problems fully via various numerical methods.     

Study of transition from laminar to turbulent boundary layer on a tilted flat plate using heat transfer measurements

The boundary layer transition over a flat tilted plate has been studied by means of heat transfer measurements.Aheat flux sensor has been developed,in order to measure the efficiency of convective heat transfer for varioustypes of surfaces or flows.Its operation at constant temperature allows direct and fast measurements of heat flux.The present paper reports the development of the sensor and presents its application to the study of transition in aboundary layer depending on the angle of incidence of the external flow.An exponential relationship betweencritical Reynolds number and pressure gradient parameter has been found.     

Effects of free stream turbulence on a turbulent boundary layer on a flat plate with zero pressure gradient part IV: Calculation of the flow field

The effects of free stream turbulence on a turbulent boundary layer were calculated by using a k-ϵ two-equation model. The calculations were performed with respect to velocity profiles on a flat plate, wall shear stress, turbulence energy, integral length scales of turbulence, and decay of free stream turbulence, and the results were compared with the experimental results. The energy of the free stream turbulence and the dissipation values at the leading edge of the flat plate were used as the initial calculation conditions. These initial values of dissipation were determined from the integral length scales of the free stream turbulence at the leading edge. The calculated wall shear stress increased with the free stream turbulence and integral length scales of turbulence. The velocity profiles and turbulence energy agreed well with the experimental results, and the effects of free stream turbulence on the wall shear stress agreed fairly well with those observed in experiments. © 1997 Scripta Technica. Inc. Heat Trans Jpn Res. 25 (2): 65–75, 1996     

Effect of Prandtl number on the average exit temperature of coolant in a heat‐generating vertical parallel plate channel: A conjugate analysis

A coupled conduction–convection heat transfer analysis is carried out for a two‐dimensional rectangular, vertical parallel plate channel producing volumetric energy (uniform and nonuniform), subjected to laminar forced‐convection incompressible fluid flow under steady‐state conditions. The equations governing the thermal and flow field are solved by using finite difference method, and the resulting algebraic equations are solved by using the tridiagonal matrix algorithm method. Four coolants with their Prandtl numbers (Pr), namely, liquid sodium (Pr = 0.005), sodium‐potassium (Pr = 0.00753), lead (Pr = 0.02252), and helium (Pr = 0.666) are used for the present conjugate analysis. Effects of different thermal and fluid flow parameters such as Reynolds number (Re_H) ranging from 500 to 1500, conduction–convection parameter (N_cc), and total heat generation (Q_t) on average exit temperature (θ_ae) of coolants are studied. From the obtained results, it is found that the θ_ae of coolant strongly depends on Pr, Re_H, N_cc, and Q_t when the aspect ratio (A_r) is kept constant. It is also found that with a nonuniform rate of heat generation, the coolant θ_ae is high compared to uniform heat generation rate, whereas with increasing N_cc, the θ_ae decreases, and with increasing Q_t, the θ_ae increases irrespective of coolants.     

Analysis of a boundary layer flow over moving an exponentially stretching surface with variable viscosity and Prandtl number

Boundary layer flow phenomenons on a stretching sheet find numerous applications in industrial processes such as manufacture and extraction of rubber and polymer sheets. The current study focuses on two‐dimensional water boundary layer flow on exponential stretching surface with a vertical plate for variable physical properties of fluid such as viscosity and Prandtl number. The Quasilinearization technique has been used on governing equations to transform nonlinear to linear equations and these equations are discretized by finite difference techniques to get numerical solutions. The effect of buoyancy parameters (λ), velocity ratio parameter () and streamwise coordinator (ξ) on velocity profiles (F), temperature profiles (θ), local skin‐friction coefficient (C_fx(Re_Lξexp(ξ)^)1/2) and the local Nusselt number (Nu_x(Re_Lξexp(ξ)^)?1/2) has been analyzed graphically based on numerical outcome. The magnitude of velocity profiles increases and temperature profile decreases approximately by 4% and 16% with increases the buoyancy parameter from λ = 1 to λ = 3 at = 0.5 and ξ = 1.0. The skinfriction and heat transfer coefficient increases approximately by 22% and 27% with an increase in ξ from 0.5 to 1.0 at fixed = 0.5 and λ = 1.0. The variations of velocity profiles and temperature profiles have more impact with as compared to ξ and λ. The benchmark studies were carried out to validate the current results with previously published work and found to be in excellent agreement.     

A computational study of unsteady radiative magnetohydrodynamic Blasius and Sakiadis flow with leading‐edge accretion (ablation)

The present study investigates the influence of the magnetic field, thermal radiation, Prandtl number, and leading‐edge accretion/ablation on Blasius and Sakiadis flow. The convective boundary condition is employed to investigate the heat transfer. The nondimensional governing boundary layer equations have been solved by the homotopy analysis method for different values of the pertinent parameters. The effects of these parameters on the dimensionless velocity, temperature, skin friction, and Nusselt number are also investigated for various values of relevant parameters affecting the flow and heat transfer phenomena. The most relevant outcomes of the present study are that enhancement in magnetic field strength undermines the flow velocity establishing thinner velocity boundary layer for both Blasius and Sakiadis flows while an increase in accretion/ablation effect at leading‐edge manifests in a deceleration in velocity for Blasius case and the opposite trend is observed for Sakiadis flow. Another important outcome is that an increase in radiation and accretion/ablation at leading‐edge upsurges the fluid temperature leading to enhancement in the thermal boundary layer. For both Blasius and Sakiadis flow, the skin friction coefficient and the heat transfer rate decline with the enhancement of the leading‐edge accretion parameter. The results are compared with the existing data and are found in good agreement.     

Turbulence modeling of atmospheric boundary layer flow over complex terrain: a comparison of models at wind tunnel and full scale

The aim of this work is to evaluate the performance of two popular k ? ? turbulence closure schemes for atmospheric boundary layer (ABL) flow over hills and valleys and to investigate the effect of using ABL‐modified model constants. The standard k ? ? and the RNG k ? ? models are used to simulate flow over the two‐dimensional analytical shapes from the RUSHIL and RUSHVAL wind tunnel experiments. Furthermore, the mean turbulent flow over the real complex terrain of Blashaval hill is simulated and the results verified with a data set of full‐scale measurements. In general, all models yield similar results. However, use of ABL‐modified constants in both models tends to decrease the predicted velocity and increase the predicted turbulent kinetic energy. Copyright © 2010 John Wiley & Sons, Ltd.     

Modeling electrification of suspended particulate matter (SPM) in a two phase laminar boundary layer flow and heat transfer over a semi-infinite flat plate

The present paper envisages the effects of electrification of particles, volume fraction and diffusion of SPM on the boundary layer flow and heat transfer over a semi-infinite flat plate. Irrespective of the particle material density, it has been observed that the range of validity of the solution remains fixed and at x = 2.12 the nature of the profiles of the flow variables changes. Electrification of particles causes the particles to move faster for x < 1.0 and slows down for x > 1.0 but particle temperature increases with increase of M. It has been observed that heat transfer always occurs from the fluid to plate.     

Incidences of aligned magnetic field on unsteady MHD flow past a parabolic accelerated inclined plate in a porous medium

An exact analysis of a radiative hydromagnetic flow behavior over a tilted parabolic plate through a permeable medium along with variable species concentration and fluid temperature in the presence of a slanted magnetic field parameter, chemical reaction, and heat generation has been carried out in this study. Closed-form analytical benchmark solutions for flow-governing equations are obtained by using the Laplace transform method. Thereafter, the incidences of different important physical entities on the nondimensional velocity field, temperature distribution, and species concentration are presented using graphs, whereas impacts of various physical entities on wall shear stress, heat and mass transfer rates are presented in tables. It is worth noting that an increase in the magnetic field and its inclination angle causes the reduction in the fluid velocity. However, wall shear stress increases with the increase of magnetic field and its inclination angle. The novel results in this article can be used to improve quicker cooling and producing miniaturized heat flow systems with upgraded efficiency and cost-effectiveness.     

Mixed convection heat and mass transfer over a vertical plate in a power‐law fluid‐saturated porous medium with radiation and chemical reaction effects

Mixed convection heat and mass transfer from a vertical plate embedded in a power‐law fluid‐saturated Darcy porous medium with chemical reaction and radiation effects is studied. The governing partial differential equations are transformed into ordinary differential equations using similarity transformations and then solved numerically using the shooting method. A parametric study of the physical parameters involved in the problem is conducted and a representative set of numerical results is illustrated graphically. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21058     

Study of a nonuniform heat source over a Riga plate using nth-order chemical reaction on Oldroyd-B nanofluid flow for two-dimensional motion

A variety of fluid models are proposed, due to the uncertain flow diversity and rheological features of non-Newtonian fluids, out of which, viscoelastic Oldroyd-B nanofluid is considered here with a nonuniform heat source over a Riga plate using an nth-order chemical reaction. The ever increasing demand for chemical reactions in hydrometallurgical, chemical, and biomedical industries necessitates studying the behavior of heat and mass transfer in the presence of chemical reaction; a few of its applications are manufacturing of glassware or ceramics, food processing, polymer production, particulate water inflows, dehydration and drying operations in the chemical industry, and numerous applications in agricultural fields and many branches of engineering and sciences. To solve the set of nonlinear DEs, which are found after applying a suitable transformation on the governing nonlinear PDEs, a robust numerical technique, such as the fourth-order Runge–Kutta method, is employed in the current motion problem. Also, the influences of all substantial thermophysical parameters are discussed graphically and analytically. Furthermore, the major outcomes of the results are: attenuation in the relaxation time leads to a rise in the fluid momentum significantly near the wall and the solutal profile retards with an enhanced Brownian motion that results in the retardation in the bounding surface thickness of the profile.     

Influence of carbon nanotubes on heat transfer in MHD nanofluid flow over a stretchable rotating disk: A numerical study

The transfer of heat is an important phenomenon in the several areas due to its numerous applications in industries. Several fluids like water, ethylene glycol and oil, and so on have very‐low thermal conductivities due to which the transfer of heat in these fluids become very low. To enhance heat transfer rate, carbon nanotubes (CNTs) including single‐walled CNTs and multi‐walled CNTs are suspended into base fluids, this mixture is known as nanofluid. The aim of this study is to examine the heat transfer rate of nanofluid in the presence of CNTs over a stretchable rotating disk. The mathematical model, developed by Tiwari and Das, is used and solved numerically by using the shooting method. The impacts of governing constraints on the dimensionless velocities, temperature, skin friction, and Nusselt number are investigated. It is noted that heat transfer rate increases by enhancing the concentration of CNTs into base fluids. The numerical results show that the solid volume fraction of the CNTs augment heat transfer rate more in ethylene glycol as compared with water.     

Effect of Dufour and chemical reaction on an unsteady magneto hydrodynamics flow past an exponentially moving plate

The aim of the study is to measure the Dufour number effects on the flow patterns and heat transfer in an exponentially accelerated infinite vertical plate embedded in a porous medium in the presence of heat source and chemical reaction. Time-dependent variations in temperature, velocity, and other factors should be taken into consideration due to the flow's unsteadiness. The fluid considered is a gray, absorbing/emitting radiation but nonscattering medium. Using the finite element method, a set of nondimensionless equations is solved analytically. Results are discussed graphically for concentration, temperature, and velocity profiles. Skin friction, Sherwood number, and Nusselt number are also explained for flow parameters through graphs.