Numerical results for influence the flow of MHD nanofluids on heat and mass transfer past a stretched surface

Due to its significant applications in physics, chemistry, and engineering, some interest has been given in recent years to research the boundary layer flow of magnetohydrodynamic nanofluids. The numerical results were analyzed for temperature profile, concentration profile, reduced number of Nusselt and reduced number of Sherwood. It has also been shown that the magnetic field, the Eckert number, and the thermophoresis parameter boost the temperature field and raise the thermal boundary layer thickness while the Prandtl number reduces the temperature field at high values and lowers the thermal boundary layer thickness. However, if Lewis number is higher than the unit and the Eckert number increases, the concentration profiles decrease as well. Ultimately, the concentration profiles are reduced for the variance of the Brownian motion parameter and the Eckert number, where the thickness of the boundary layer for the mass friction feature is reduced.

A Unified Treatment for Local Thermal Nonequilibrium Free, Forced, and Mixed Convective Boundary Layer Flows Over an Arbitrarily Shaped Nonisothermal Body in a Fluid Saturated Porous Medium

A unified integral solution procedure has been proposed to analyze all possible Darcian local thermal nonequilibrium (LTNE) free, forced, and mixed convective boundary layer flows, commonly encountered in porous media engineering applications. The heated body may be arbitrarily shaped, and its temperature may vary over the surface. The integral energy equation for the solid phase yields an algebraic equation between the dimensionless fluid thermal boundary layer thickness and its ratio to the solid-phase counterpart, while the integral energy equation for the fluid phase reduces to a first order ordinary differential equation in terms of the dimensionless fluid thermal boundary layer thickness. This set of the equations for determining the local Nusselt number of our primary interest proved to be valid for all possible Darcian cases of LTNE free, forced, and mixed convective boundary layer flows over an arbitrarily shaped nonisothermal body in a fluid saturated porous medium. Asymptotic expressions for the cases of arbitrary shapes were also obtained analytically for both leading edge and far downstream regions. The results are found to agree well with available direct numerical integration results. Furthermore, the regime map has been constructed to show the boundary layer transition point from the LTNE to equilibrium. The proposed unified method is found quite useful when designing thermal engineering systems associated with fluid saturated porous media.

Magnetohydrodynamic free convection of non-Newtonian power-law fluids over a uniformly heated horizontal plate

The MHD free convection flow of non-Newtonian power-law fluids over a horizontal plate subjected to a constant heat flux is studied. The results are presented for various values of the three influential parameters, i. e. the generalized Hart?mann number, the generalized Prandtl number, and the non-Newtonian power-law viscosity index. Increasing the Hartmann number increases the thermal boundary-layer thickness and the surface temperature and consequently decreases the wall skin friction and Nusselt number. A lower generalized Prandtl number results in a larger skin friction coefficient and higher wall temperature as well as thicker thermal boundary-layer. The viscosity index is predicted to influence the flow conditions depending on the value of generalized Hartmann number. At high generalized Prandtl number numbers, by decreasing non-Newtonian power-law index, the wall skin friction, temperature scale, and thermal boundary-layer thickness are increased and the Nusselt number is decreased, while the opposite trend is observed for low generalized Prandtl number. A general correlation for the Nusselt number is derived using the numerical results

Significance of Prandtl Number on the Heat Transport and Flow Structure in Rotating Rayleigh–Bénard Convection

A direct numerical simulation of rotating Rayleigh–Bénard convection (RBC) for different fluids (Pr=0.015,0.7,1,7,20, and 100) in a cylindrical cell of aspect ratio Γ=0.5 is carried out in this work. The effect of rotation on the heat transfer rate, flow structures, their associated dynamics, and influence on the boundary layers are investigated. The Rayleigh number is fixed to Ra=106 and the rotation rates are varied for a wide range, starting from no rotation (Ro→∞) to high rotation rates (Ro≈0.01). For all the Prandtl numbers (Pr=0.015–100), a reduction in heat transfer with increase in rotation is observed. However, for Pr=7 and 20, a marginal increase of the Nusselt number for low rotation rates is obtained, which is attributed to the change in the flow structure from quadrupolar to dipolar state. The change in flow structure is associated with the statistical behavior of the boundary layers. As the flow makes a transition from quadrupolar to dipolar state, a reduction in the thermal boundary layer thickness is observed. At higher rotation rates, the thermal boundary layer thickness shows a power law variation with the rotation rate. The power law exponent is close to unity for moderate Pr, while it reduces for both lower and higher Pr. At extremely high rotation rates, the flow makes a transition to the conduction state. The critical rotation rate (1/Roc) for which transition to the conduction state is observed depends on the Prandtl number according to 1/Roc∝Pr0.5.

Effect of Chemical Reaction on Maxwell Nanofluid Slip Flow over a Stretching Sheet

The main focus of the present study is to analyze the effect of chemical reaction and nonlinear thermal radiation on Maxwell fluid suspended with nanoparticles through a porous medium along horizontal stretching sheet. The governing partial differential equations of the defined problem are reduced into a set of nonlinear ordinary differential equations using adequate similarity transformations. Obtained set of similarity equations are then solved with the help of efficient numerical method fourth fifth order Runge-Kutta-Fehlberg method. The effects of different flow pertinent parameters on the flow fields like velocity, temperature, and concentration are shown in the form of graphs and tables. The detailed analysis of the problem is carried out based on the plotted graphs and tables. It is observed that an increase in the radiation parameter, temperature ratio parameter, Brownian motion parameter and thermophoretic parameter lead to increase in the thermal boundary layer thickness but quite opposite phenomenon can be seen for the effect of Prandtl number.

Linear stability and energetics of rotating radial horizontal convection

The effect of rotation on horizontal convection in a cylindrical enclosure is investigated numerically. The thermal forcing is applied radially on the bottom boundary from the coincident axes of rotation and geometric symmetry of the enclosure. First, a spectral element method is used to obtain axisymmetric basic flow solutions to the time-dependent incompressible Navier–Stokes equations coupled via a Boussinesq approximation to a thermal transport equation for temperature. Solutions are obtained primarily at Rayleigh number $\mathit{Ra}=10^{9}$ and rotation parameters up to $Q=60$ (where $Q$ is a non-dimensional ratio between thermal boundary layer thickness and Ekman layer depth) at a fixed Prandtl number $\mathit{Pr}=6.14$ representative of water and enclosure height-to-radius ratio $H/R=0.4$. The axisymmetric solutions are consistently steady state at these parameters, and transition from a regime unaffected by rotation to an intermediate regime occurs at $Q\approx 1$ in which variation in thermal boundary layer thickness and Nusselt number are shown to be governed by a scaling proposed by Stern (1975, Ocean Circulation Physics. Academic). In this regime an increase in $Q$ sees the flow accumulate available potential energy and more strongly satisfy an inviscid change in potential energy criterion for baroclinic instability. At the strongest $Q$ the flow is dominated by rotation, accumulation of available potential energy ceases and horizontal convection is suppressed. A linear stability analysis reveals several instability mode branches, with dominant wavenumbers typically scaling with $Q$. Analysis of contributing terms of an azimuthally averaged perturbation kinetic energy equation applied to instability eigenmodes reveals that energy production by shear in the axisymmetric mean flow is negligible relative to that produced by conversion of available potential energy from the mean flow. An evolution equation for the quantity that facilitates this exchange, the vertical advective buoyancy flux, reveals that a baroclinic instability mechanism dominates over $5\lesssim Q\lesssim 30$, whereas stronger and weaker rotations are destabilised by vertical thermal gradients in the mean flow.

Passive Heat Transfer in Solid-State Lighting: Relaxing the Boussinesq Approximation Analytically in the Vertical Channel

Analytical relations between the heat flux, temperature rise, thermal boundary layer thickness, and characteristic velocity have been derived for the two-dimensional vertical channel, without use of the Boussinesq approximation. Results have been put into the context of well-established scaling behavior in the literature. In addition, useful implications of the analytical results have been described, including a criterion to determine the suitability of a heat-sink configuration to a particular application.

KARAKTERISASI TEBAL LAPISAN BATAS FLUIDA NANO ZrO2 DI PERMUKAAN PEMANAS PADA PROSES KONVEKSI ALAMIAH

ABSTRAK KARAKTERISASI Tebal Lapisan Batas Fluida Nano ZrO2 di permukaan pemanas pada Proses Konveksi Alamiah. Pendinginan sistem sangat dipengaruhi oleh proses perpindahan panas konveksi dari sumber panas ke fluida pendingin. Biasanya sebagai fluida pendingin digunakan fluida konvensional seperti air. Pendinginan suatu sistem dengan air tersebut dapat ditingkatkan dengan menggunakan fluida lain seperti fluida nano, yaitu fluida yang dibuat dari campuran air ditambah partikel dengan ukuran nano. Peneliti Batan Bandung telah membuat fluida nano ZrO2 dari bahan local. Telah dibuat pula peralatan eksperimen untuk mempelajari sifat-sifat termohidrolik fluida nano tersebut. Hal ini dilakukan untuk mendapatkan fluida nano yang tepat jika digunakan sebagai fluida pendingin sistem. Dalam penelitian ini dilakukan eksperimen untuk mempelajari sifat-sifat termohidrolik fluida nano ZrO2 yang terbuat dari campuran air dengan partikel nano ZrO2 yang berukuran 10-7-10-９nm dengan konsentrasi 1 gr/lt yang digunakan sebagai pendingin pada proses pendinginan konveksi alamiah. Proses tersebut sangat bergantung pada perubahan temperatur dari sumber panas ke fluida pendingin. Dalam pendinginan konveksi alamiah perubahan temperatur itu akan terjadi di dalam tebal lapisan batas termalnya. Oleh karena itu perlu diteliti tebal lapisan batas termal dari fluida nano ZrO2 yang selanjutnya juga dapat untuk menentukan kecepatan aliran lokalnya. Eksperimen dilakukan melalui proses perpindahan panas konveksi alamiah dengan memasukkan beberapa variasi daya pemanas, kemudian dilakukan pengukuran temperatur di beberapa titik secara horizontal untuk melihat distribusi temperaturnya. Hasil pengukuran distribusi temperatur tersebut dapat digunakan untuk menentukan tebal lapisan batas dan kecepatan alirannya. Diperoleh bahwa tebal lapisan batas termal dan kecepatan konveksi alamiah fluida nano ZrO2 tidak jauh berbeda dari fluida konvensional air. Kata kunci: Lapisan batas, fluida nano ZrO2, konveksi alamiah. ABSTRACT CHARACTERIZATION of boundary layer thickness OF nano FLUID ZrO2 on natural convection process. Cooling system is highly influenced by the process of convection heat transfer from the heat source to the cooling fluid. The cooling fluid usually used conventional fluid such as water. Cooling system performance can be improved by using fluids other than water such as nano fluid that is made from a mixture of water and nano-sized particles. Researchers at Batan Bandung have made nano fluid ZrO2 from local materials, as well as experimental equipment for studying the thermohidraulic characteristics of nano fluid as the cooling fluid. In this study, thermohidraulic characteristics of nano fluid ZrO2 are observed through experimentation. Nano fluid ZrO2 is made from a mixture of water with ZrO2 nano-sized particles of 10-7-10-9 nm whose concentration is 1 g/ltr. This nano fluid is used as coolant in the cooling process of natural convection. The natural convection process depends on the temperature difference between heat source and the cooling fluid, which occur in the thermal boundary layer. Therefore it is necessary to study the thermal boundary layer thickness of nano fluid ZrO2, which is also able to determine the local velocity. Experimentations are done with several variation of the heater power and then the temperature are measured at several horizontal points to see the distribution of the temperatures. The temperature distribution measurement results can be used to determine the boundary layer thickness and flow rate. It is obtained that thermal boundary layer thickness and velocity of nano fluid ZrO2 is not much different from the conventional fluid water. Keywords: Boundary layer, nanofluid ZrO2, natural convection.

Effect of Nonlinear Thermal Radiation on MHD Flow between Rotating Plates with Homogeneous-Heterogeneous Reactions

In this study we investigated the effect of nonlinear thermal radiation on magnetohydrodynamic flow between horizontal rotating plates in the presence of homogeneous-heterogeneous reactions. By making use of the appropriate similarity transformations, the equations which govern the flow are reduced to a set of nonlinear ordinary differential equations. Further, these equations are solved numerically using the Runge-Kutta based shooting technique. Also, the effects of various pertinent parameters on velocity, temperature and concentration profiles along with the friction factor, local Nusselt and Sherwood numbers are discussed and presented with the help of graphs and tables. We found an excellent agreement of the present results with the existed literature under some special limited cases. Results indicate that concentration profiles are highly influenced by the homogeneous-heterogeneous parameters. Nonlinear thermal radiation have tendency to enhance the thermal boundary layer thickness.

Plume emission statistics in turbulent Rayleigh–Bénard convection

Direct numerical simulations (DNS) of turbulent thermal convection in a $\mathit{Pr}=0.7$ fluid up to $\mathit{Ra}=10^{12}$ are used to study the statistics of thermal plumes. At various vertical locations in a cylindrical set-up with aspect ratio ${\it\Gamma}=\text{width}/\text{height}=1/3$, plumes are identified and their properties extracted. It is found that plumes are much less likely to be emitted from plate regions with large wind shear. Close to the plates, the plumes have a unimodal log–normal distribution, whereas at more central locations the distribution becomes weakly bimodal, which can be traced back to clustering of the plumes and influence of the large-scale circulation. The number of hot plumes decreases with height. The width of the plumes scales with $\mathit{Ra}$ approximately as $\mathit{Nu}^{-1}$, indicating that it is determined by the thermal boundary layer thickness.