Mohamed E. Ali

On thermal boundary layer on a power-law stretched surface with suction or injection

Similarity solutions of the laminar boundary-layer equations describing heat and flow in a quiescent fluid driven by a stretched surface subject to suction or injection are obtained herein. The surface is moving with a power-law velocity distribution, and its temperature has a power-law variation. The effect of various governing parameters, such as Prandtl number Pr, temperature exponent n, velocity exponent m, and the injection parameter d, which determine the temperature profiles and heat transfer coefficient are studied. Three boundary conditions of uniform temperature, variable temperature, and uniform heat flux at the surface have been investigated. The effect of decreasing d is found to be significant, particularly for high Prandtl numbers.

Heat transfer characteristics of a continuous stretching surface

The similarity solutions for the governing ordinary differential equations of the boundary layer corresponding to a stretching surface have been reported. Power law velocity and temperature distribution were assumed for velocity exponent 3≥m≥−0.41176, −1.1≥m≥−3, and for temperature exponent 3≥n≥−3. Solutions have been found forn=0 and allm where heat transferred from the stretching surface to the ambient. The direction and amount of heat flow were found to be dependent on the magnitude ofn andm for the same Prandtl number. Nusselt number increases with increasingm andPr for uniform and variable surface temperature however, for uniform surface heat flux it decreases with increasingm for constantPr.ZusammenfassungEs werden die Ähnlichkeitslösungen für die bestimmenden gewöhnlichen Grenzschichtdifferentialgleichungen bezüglich einer verstreckten Oberfläche mitgeteilt. Für Geschwindigkeits-und Temperaturverteilungen gelten Potenzansätze mit den Exponenten 3≥m≥−0,41176 und −1,1≥m≥−3 für das Geschwindigkeitsprofil und 3≥n≥−3 für das Temperaturprofil. Fürn=0 und allem ließen sich Lösungen finden; dabei floß Wärme von der verstreckten Fläche an die Umgebung. Es zeigte sich, daß Höhe und Richtung des Wärmestroms bei gleicher Prandtl-Zahl von den Werten fürn undm abhängen. Die Nußelt-Zahl wächst mit steigendemm undPr bei gleichförmiger und veränderlicher Oberflächentemperatur; sie fällt bei gleichförmigem Wärmefluß, wennm bei konstantemPr zunimmt.

Numerical simulation of natural convection of the nanofluid in heat exchangers using a Buongiorno model

Natural convection of nanofluids in a cavity is studied using a Buongiorno model.By reducing the diameter of the nanoparticles the heat transfer rate increases.At high Ra, the distribution of the solid particles remains almost uniform.There is an optimum volume fraction of nanoparticles for maximum Nusselt number. A numerical study is carried out concerning natural convection heat transfer of nanofluid in a two-dimensional square cavity containing several pairs of heater and coolers (HACs). Walls of the cavity are insulated and several pairs of heater and coolers (HACs) with isothermal walls of Th and Tc (ThTc) are placed inside the cavity. Two-dimensional Navier-Stokes, energy and volume fraction equations are solved using finite volume discretization method. The effects of various design parameters on the heat transfer rate and distribution of nanoparticles such as Rayleigh number ( 10 4 ≤ Ra ≤ 10 7 ), volume fraction ( 0 ≤ ? ≤ 0.05 ) and size of nanoparticles ( 25 nm ≤ d p ≤ 145 nm ), type of the nanoparticles (Cu, Al2O3 and TiO2), nanofluid average temperature ( 294 K ≤ T ave ≤ 324 K ), number of the cooler, location of the heater and arrangement of the HAC are investigated. The simulation results are indicated that, HACs location has the most significant influence on the heat transfer rate. It is also found that at low Rayleigh numbers, the particle distribution is fairly non-uniform while at high Ra, particle distribution remains almost uniform. Moreover, it is found that there is an optimal volume fraction of the nano-particles at each Rayleigh number in which the maximum heat transfer rate can be obtained.

Mixed Convective Heat Transfer for MHD Viscoelastic Fluid Flow over a Porous Wedge with Thermal Radiation

The main concern of the present paper is to study the MHD mixed convective heat transfer for an incompressible, laminar, and electrically conducting viscoelastic fluid flow past a permeable wedge with thermal radiation via a semianalytical/numerical method, called Homotopy Analysis Method (HAM). The boundary-layer governing partial differential equations (PDEs) are transformed into highly nonlinear coupled ordinary differential equations (ODEs) consisting of the momentum and energy equations using similarity solution. The current HAM solution demonstrates very good agreement with previously published studies for some special cases. The effects of different physical flow parameters such as wedge angle (β), magnetic field (M), viscoelastic (k1), suction/injection (fw), thermal radiation (Nr), and Prandtl number (Pr) on the fluid velocity component (f′(η)) and temperature distribution (θ(η)) are illustrated graphically and discussed in detail.

Laminar mixed convection boundary layers induced by a linearly stretching permeable surface

Abstract The boundary layer flow on a linearly moving permeable vertical surface is studied when the buoyancy force assists or opposes the flow. Similarity and local similarity solutions are obtained for the boundary layer equations subject to power law temperature and velocity variation. The effect of various governing parameters, such as Prandtl number Pr, injection parameter d, and the mixed convection parameter λ=Grx/Rex2, which determine the velocity and temperature distributions, the heat transfer coefficient, and the shear stress at the surface are studied. The heat transfer coefficient increases as λ assisting the flow for all d for uniformly or linearly heated surface and as Pr increases it becomes almost independent of λ. However, as the temperature inversely proportional to the distance up the surface, the buoyancy has no effects on the heat transfer coefficient. Critical buoyancy parameter values are obtained for vanished shear stress and for predominate natural convection. Critical values are also presented for predominate buoyancy shear stress at the surface for assisting or opposing flow. A closed form analytical solution is also presented as a special case of the energy equation.

On the stability of circular Couette flow with radial heating

The stability of circular Couette flow with radial heating across a vertically oriented annulus with inner cylinder rotating and outer cylinder stationary is investigated using linear stability theory. Infinite aspect ratio and constant fluid properties are assumed and critical stability boundaries are calculated for a conduction-regime base flow. Buoyancy is included through the Boussinesq approximation and stability is tested with respect to both toroidal and helical disturbances of uniform wavenumber. Symmetries of the linearized disturbance equations based on the sense of radial heating and the sense of cylinder rotation and their effect on the kinematics and morphology of instability waveforms are presented. The numerical investigation is primarily restricted to radius ratios 0.6 and 0.959 at Prandtl numbers 4.35, 15 and 100. The results follow the development of critical stability from Taylor cells at zero heating through a number of asymmetric modes to axisymmetric cellular convection at zero rotation. Increasing the Prandtl number profoundly destabilizes the flow in both wide and narrow gaps and the number of contending critical modes increases with increasing radius ratio. Specific calculations made to compare with the stability measurements of Snyder & Karlsson (1964) and Sorour & Coney (1979) exhibit good agreement considering the idealizations built into the linear stability analysis.

Entropy Generation on MHD Casson Nanofluid Flow over a Porous Stretching/Shrinking Surface

In this article, entropy generation on MHD Casson nanofluid over a porous Stretching/Shrinking surface has been investigated. The influences of nonlinear thermal radiation and chemical reaction have also taken into account. The governing Casson nanofluid flow problem consists of momentum equation, energy equation and nanoparticle concentration. Similarity transformation variables have been used to transform the governing coupled partial differential equations into ordinary differential equations. The resulting highly nonlinear coupled ordinary differential equations have been solved numerically with the help of Successive linearization method (SLM) and Chebyshev spectral collocation method. The impacts of various pertinent parameters of interest are discussed for velocity profile, temperature profile, concentration profile and entropy profile. The expression for local Nusselt number and local Sherwood number are also analyzed and discussed with the help of tables. Furthermore, comparison with the existing is also made as a special case of our study.

Experimental investigation of natural convection from vertical helical coiled tubes

Abstract An experimental study has been made on steady state natural convection heat transfer from vertical helical coiled tubes. Average heat transfer coefficients were obtained for turbulent natural convection to water. The experiments have been carried out for four coil diameter to tube diameter ratios, for five and ten coil turns, and for five pitch to outer diameter ratios. The data are correlated with the Rayleigh number for two different coil sets. The heat transfer coefficient decreases with coil length for tube diameter d o = 0.012 m, but increases with coil length for d o = 0.008 m. A critical D/d 0 is obtained for a maximum heat transfer coefficient for tube diameter of 0.012 m with either five or ten coil turns.

Numerical Simulation of Entropy Generation with Thermal Radiation on MHD Carreau Nanofluid towards a Shrinking Sheet

In this article, entropy generation with radiation on non-Newtonian Carreau nanofluid towards a shrinking sheet is investigated numerically. The effects of magnetohydrodynamics (MHD) are also taken into account. Firstly, the governing flow problem is simplified into ordinary differential equations from partial differential equations with the help of similarity variables. The solution of the resulting nonlinear differential equations is solved numerically with the help of the successive linearization method and Chebyshev spectral collocation method. The influence of all the emerging parameters is discussed with the help of graphs and tables. It is observed that the influence of magnetic field and fluid parameters oppose the flow. It is also analyzed that thermal radiation effects and the Prandtl number show opposite behavior on temperature profile. Furthermore, it is also observed that entropy profile increases for all the physical parameters.

Peristaltic Flow of Carreau Fluid in a Rectangular Duct through a Porous Medium

We have examined the peristaltic flow of Carreau fluid in a rectangular channel through a porous medium. The governing equations of motion are simplified by applying the long wavelength and low Reynolds number approximations. The reduced highly nonlinear partial differential equations are solved jointly by homotopy perturbation and Eigen function expansion methods. The expression for pressure rise is computed numerically by evaluating the numerical integration. The physical features of pertinent parameters have been discussed by plotting graphs of velocity, pressure rise, pressure gradient, and stream functions.