Search results for: free convection flow

Authors: Ashkan Vatani, Peter Woodfield, Nam-Trung Nguyen, Dzung Dao

Abstract:

Thermomagnetic convection of a ferrofluid flow induced by the non-uniform magnetic field around a current-carrying wire was theoretically analyzed and experimentally tested. To show this phenomenon, the temperature rise of a hot wire, immersed in DIW and Ferrofluid, as a result of joule heating has been measured using a transient hot-wire technique. When current is applied to the wire, a temperature gradient is imposed on the magnetic fluid resulting in non-uniform magnetic susceptibility of the ferrofluid that results in a non-uniform magnetic body force which makes the ferrofluid flow as a bulk suspension. For the case of the wire immersed in DIW, free convection is the only means of cooling, while for the case of ferrofluid a combination of both free convection and thermomagnetic convection is expected to enhance the heat transfer from the wire beyond that of DIW. Experimental results at different temperatures and for a range of constant currents applied to the wire show that thermomagnetic convection becomes effective for the currents higher than 1.5A at all temperatures. It is observed that the onset of thermomagnetic convection is directly proportional to the current applied to the wire and that the thermomagnetic convection happens much faster than the free convection. Calculations show that a 35% enhancement in heat transfer can be expected for the ferrofluid compared to DIW, for a 3A current applied to the wire.

Keywords: cooling, ferrofluid, thermomagnetic convection, magnetic field

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Authors: N. M. Arifin, S. P. M. Isa, R. Nazar, N. Bachok, F. M. Ali, I. Pop

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In this paper, the steady forced convection boundary layer flow of a Casson fluid past a moving permeable semi-infinite flat plate beneath a uniform free stream is investigated. The mathematical problem reduces to a pair of noncoupled ordinary differential equations by similarity transformation, which is then solved numerically using the shooting method. Both the cases when the plate moves into or out of the origin are considered. Effects of the non-Newtonian (Casson) parameter, moving parameter, suction or injection parameter and Eckert number on the flow and heat transfer characteristics are thoroughly examined. Dual solutions are found to exist for each value of the governing parameters.

Keywords: forced convection, Casson fluids, moving flat plate, boundary layer

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Authors: F. Hekmatipour, M. A. Akhavan-Behabadi, B. Sajadi

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In this paper, the combined free and forced convection heat transfer of the Copper Oxide-Heat Transfer Oil (CuO-HTO) nanofluid flow in horizontal and inclined microfin tubes is studied experimentally. The flow regime is laminar, and pipe surface temperature is constant. The effect of nanoparticle and microfin tube on the heat transfer rate is investigated with the Richardson number which is between 0.1 and 0.7. The results show an increasing nanoparticle concentration between 0% and 1.5% leads to enhance the combined free and forced convection heat transfer rate. According to the results, five correlations are proposed to provide estimating the free and forced heat transfer rate as the increasing Richardson number from 0.1 to 0.7. The maximum deviation of both correlations is less than 16%. Moreover, four correlations are suggested to assess the Nusselt number based on the Rayleigh number in inclined tubes from 1800000 to 7000000. The maximum deviation of the correlation is almost 16%. The Darcy friction factor of the nanofluid flow has been investigated. Furthermore, CuO-HTO nanofluid flows in inclined microfin tubes.

Keywords: nanofluid, heat transfer oil, mixed convection, inclined tube, laminar flow

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Authors: Si Abdallah Mayouf

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In this work, the effects of the wavy surface on free convection heat transfer boundary layer flow between two parallel wavy plates have been studied numerically. The two plates are considered at a constant temperature. The equations and the boundary conditions are discretized by the finite difference scheme and solved numerically using the Gauss-Seidel algorithm. The important parameters in this problem are the amplitude of the wavy surfaces and the distance between the two wavy plates. Results are presented as velocity profiles, temperature profiles and local Nusselt number according to the important parameters.

Keywords: free convection, wavy surface, parallel plates, fluid dynamics

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Authors: Ishak Hashim, Ammar Alsabery

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The problem of conjugate free convection in a square cavity filled with nanofluid and heated from below by spatial wall temperature is studied numerically using the finite difference method. Water-based nanofluid with copper nanoparticles are chosen for the investigation. Governing equations are solved over a wide range of nanoparticle volume fraction (0 ≤ φ ≤ 0.2), wave number ((0 ≤ λ ≤ 4) and thermal conductivity ratio (0.44 ≤ Kr ≤ 6). The results presented for values of the governing parameters in terms of streamlines, isotherms and average Nusselt number. It is found that the flow behavior and the heat distribution are clearly enhanced with the increment of the non-uniform heating.

Keywords: conjugate free convection, square cavity, nanofluid, spatial temperature

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Authors: Y. Lasbet, A. L. Boukhalkhal, K. Loubar

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The study of mixed convection is, usually, focused on the straight channels in which the onset of the mixed convection is well defined as function of the ratio between Grashof number and Reynolds number, Gr/Re. This is not the case for a complex channel wherein the mixed convection is not sufficiently examined in the literature. Our paper focuses on the study of the mixed convection in a complex geometry in which our main contribution reveals that the critical value of the ratio Gr/Re for the onset of the mixed convection increases highly in the type of geometry contrary to the straight channel. Furthermore, the accentuated secondary flow in this geometry prevents the thermal stratification in the flow and consequently the buoyancy driven becomes negligible. To perform these objectives, a numerical study in complex geometry for several values of the ratio Gr/Re with prescribed wall heat flux (H2), was realized by using the CFD code.

Keywords: complex geometry, heat transfer, laminar flow, mixed convection, Nusselt number

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Authors: Muhammad Khairul Anuar Mohamed, Mohd Zuki Salleh, Anuar Ishak, Nor Aida Zuraimi Md Noar

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In this study, the numerical investigation of viscous dissipation on convective boundary layer flow towards a horizontal circular cylinder with constant wall temperature is considered. The transformed partial differential equations are solved numerically by using an implicit finite-difference scheme known as the Keller-box method. Numerical solutions are obtained for the reduced Nusselt number and the skin friction coefficient as well as the velocity and temperature profiles. The features of the flow and heat transfer characteristics for various values of the Prandtl number and Eckert number are analyzed and discussed. The results in this paper is original and important for the researchers working in the area of boundary layer flow and this can be used as reference and also as complement comparison purpose in future.

Keywords: free convection, horizontal circular cylinder, viscous dissipation, convective boundary layer flow

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Authors: Anuar Ishak

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The mixed convection stagnation point flow toward a vertical plate is investigated. The external flow impinges normal to the heated plate and the surface temperature is assumed to vary linearly with the distance from the stagnation point. The governing partial differential equations are transformed into a set of ordinary differential equations, which are then solved numerically using MATLAB routine boundary value problem solver bvp4c. Numerical results show that dual solutions are possible for a certain range of the mixed convection parameter. A stability analysis is performed to determine which solution is linearly stable and physically realizable.

Keywords: dual solutions, heat transfer, mixed convection, stability analysis

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Authors: Ali Reza Tahavvor‚ Saeed Hosseini, Behnam Amiri

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Concentric and eccentric annulus is used frequently in technical and industrial applications such as nuclear reactors, thermal storage system and etc. In this paper, computational fluid dynamics (CFD) is used to investigate two dimensional free convection of laminar flow in annulus with isotherm cylinders surface and cooler inner surface. Problem studied in thirty different cases. Due to natural convection continuity and momentum equations are coupled and must be solved simultaneously. Finite volume method is used for solving governing equations. The purpose was to obtain the eccentricity effect on Nusselt number in different Rayleight numbers, so streamlines and temperature fields must be determined. Results shown that the highest Nusselt number values occurs in degree of eccentricity equal to 0.5 upward for inner cylinder and degree of eccentricity equal to 0.3 upward for outer cylinder. Side eccentricity reduces the outer cylinder Nusselt number but increases inner cylinder Nusselt number. The trend in variation of Nusselt number with respect to eccentricity remain similar in different Rayleight numbers. Correlations are included to calculate the Nusselt number of the cylinders.

Keywords: natural convection, concentric, eccentric, Nusselt number, annulus

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Authors: Emmanuel Omokhuale

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A mathematical model is presented to study free convective boundary layer flow in a semi-infinite vertical cylinder with heat sink effect in a porous medium. The governing dimensional governing partial differential equations (PDEs) with corresponding initial and boundary conditions are approximated and solved numerically employing finite difference method (FDM) the implicit type. Stability and convergence of the scheme are also established. Furthermore, the influence of significant physical parameters on the flow characteristics was analysed and shown graphically. The obtained results are benchmarked with previously published works in order to access the accuracy of the numerical method and found to be in good agreement.

Keywords: free convection flow, vertical cylinder, implicit finite difference method, heat sink and porous medium

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Authors: Nouri Sabrina, Benzeghiba Mohamed, Ghezal Abderrahmane

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Numerical parametric study is conducted to study the effects of ampoule rotation on the flows and the dopant segregation in vertical Bridgman (VB) crystal growth. Calculations were performed in unsteady state. The extended Darcy model, which includes the time derivative and Coriolis terms, has been employed in the momentum equation. It was found that the convection, and dopant segregation can be affected significantly by ampoule rotation, and the effect is similar to that by an axial magnetic field. Ampoule rotation decreases the intensity of convection and stretches the flow cell axially. When the convection is weak, the flow can be suppressed almost completely by moderate ampoule rotation and the dopant segregation becomes diffusion-controlled. For stronger convection, the elongated flow cell by ampoule rotation may bring dopant mixing into the bulk melt reducing axial segregation at the early stage of the growth. However, if the cellular flow cannot be suppressed completely, ampoule rotation may induce larger radial segregation due to poor mixing.

Keywords: numerical simulation, heat and mass transfer, vertical solidification, chemical segregation

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Authors: Roghayyeh Motallebzadeh, Shahin Hajizadeh, Mohammad Reza Ghasemi

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Laminar mixed convection heat transfer of a nanofluid with prescribed constant heat flux on the inner wall of horizontal annular tube has been studied numerically based on two-phase mixture model in different Rayleigh numbers and Azimuth angles. Effects of applying of different volume fractions of Al2O3 nanoparticles in water as a base fluid on hydrodynamic and thermal behaviours of the fluid flow such as axial velocity, secondary flow, temperature, heat transfer coefficient and friction coefficient at the inner and outer wall region, has been investigated. Conservation equations in elliptical form has been utilized and solved in three dimensions for a steady flow. It is observed that, there is a good agreement between results in this work and previously published experimental and numerical works on mixed convection in horizontal annulus. These particles cause to increase convection heat transfer coefficient of the fluid, meanwhile there is no considerable effect on friction coefficient.

Keywords: buoyancy force, laminar mixed convection, mixture model, nano-fluid, two-phase

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Authors: Habibis Saleh, Ishak Hashim

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Combined surface tension and natural convection heat transfer in an open cavity is studied numerically in this article. The cavity is filled with water-{Cu} nanofluids. The left wall is kept at low temperature, the right wall at high temperature and the bottom and top walls are adiabatic. The top free surface is assumed to be flat and non--deformable. Finite difference method is applied to solve the dimensionless governing equations. It is found that the insignificant effect of adding the nanoparticles were obtained about $Ma_{bf}=250$.

Keywords: natural convection, marangoni convection, nanofluids, square open cavity

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Authors: K. A. Sudjatmi, Endiah Puji Hastuti, Surip Widodo, Reinaldy Nazar

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Any pretensions to stop the production of TRIGA fuel elements by TRIGA reactor fuel elements manufacturer should be anticipated by the operating agency of TRIGA reactor to replace the cylinder type fuel element with plate type fuel element, that available on the market. This away was performed the calculation on U3Si2Al fuel with uranium enrichment of 19.75% and a load level of 2.96 gU/cm3. Maximum power that can be operated on free convection cooling mode at the BANDUNG TRIGA reactor fuel plate was 600 kW. This study has been conducted thermalhydraulic characteristic calculation model of the reactor core power 2MW. BANDUNG TRIGA reactor core fueled plate type is composed of 16 fuel elements, 4 control elements and one irradiation facility which is located right in the middle of the core. The reactor core is cooled using a pump which is already available with flow rate 900 gpm. Analysis on forced convection cooling mode with flow from the top down from 10%, 20%, 30% and so on up to a 100% rate of coolant flow. performed using the COOLOD-N2 code. The calculations result showed that the 2 MW power with inlet coolant temperature at 37 °C and cooling rate percentage of 50%, then the coolant temperature, maximum cladding and meat respectively 64.96 oC, 124.81 oC, and 125.08 oC, DNBR (departure from nucleate boiling ratio)=1.23 and OFIR (onset of flow instability ratio)=1:00. The results are expected to be used as a reference for determining the power and cooling rate level of the BANDUNG TRIGA reactor core plate types fueled.

Keywords: TRIGA, COOLOD-N2, plate type fuel element, force convection, thermal hydraulic characteristic

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Authors: Tania Sharmin Khaleque, Mohammad Ferdows

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The flow and heat transfer characteristics of a convection with temperature-dependent viscosity and thermal diffusivity along a vertical plate with internal heat generation effect have been studied. The plate temperature is assumed to follow a power law of the distance from the leading edge. The resulting governing two-dimensional equations are transformed using suitable transformations and then solved numerically by using fifth order Runge-Kutta-Fehlberg scheme with a modified version of the Newton-Raphson shooting method. The effects of the various parameters such as variable viscosity parameter β_1, the thermal diffusivity parameter β_2, heat generation parameter c and the Prandtl number Pr on the velocity and temperature profiles, as well as the local skin- friction coefficient and the local Nusselt number are presented in tabular form. Our results suggested that the presence of internal heat generation leads to increase flow than that of without exponentially decaying heat generation term.

Keywords: free convection, heat generation, thermal diffusivity, variable viscosity

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Authors: Hadi Kafil, Ali Ecder

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Heat transfer by natural convection in two-dimensional and three-dimensional axisymmetric enclosure fitted with partially heated vertical walls is investigated numerically. The range of Rayleigh number is varied from 10³ until convective flow becomes unstable. This research focuses on multiplicity and transition phenomena in natural convection and is based on a parametric analysis to study the onset of bifurcations. It is found that, even at low Rayleigh numbers, the flow undergoes a series of turning-point bifurcations which increase the rate of natural convention. On the other hand, by partially heating or cooling the walls, more effective results can be achieved for both heating and cooling applications, such as cooling of electronic devices and heating processes in solidification and crystal growth.

Keywords: natural convection, partial heated, onset of bifurcation, Rayleigh number

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Authors: Ashkan Vatani, Petere Woodfiel, Nam-Trung Nguyen, Dzung Dao

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Thermomagnetic convection of a ferrofluid flow induced by the non-uniform magnetic field around a current-carrying wire was theoretically analyzed, numerically studied and experimentally validated. The dependency of the thermomagnetic convection on the current and fluid temperature has been studied. The Nusselt number for a heated 50um diameter wire in the ferrofluid exponentially scales with applied current to the micro-wire. This result is in good agreement with the correlated Nusselt number by curve-fitting the experimental data at different fluid temperatures. It was shown that at low currents, no significance is observed for thermomagnetic convection rather than the buoyancy-driven convection, while the thermomagnetic convection becomes dominant at high currents. Also, numerical simulations showed a promising cooling ability for large scale applications.

Keywords: ferrofluid, non-uniform magnetic field, Nusselt number, thermomagnetic convection

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Authors: Y. El Khchine, M. Sriti

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In the present work, the forced convection heat transfer and fluid flow past an unconfined semi-circular cylinder is investigated. The two-dimensional simulation is employed for Reynolds numbers ranging from 10 ≤ Re ≤ 200, employing air (Pr = 0.71) as an operating fluid with Newtonian constant physics property. Continuity, momentum, and energy equations with appropriate boundary conditions are solved using the Computational Fluid Dynamics (CFD) solver Ansys Fluent. Various parameters flow such as lift, drag, pressure, skin friction coefficients, Nusselt number, Strouhal number, and vortex strength are calculated. The transition from steady to time-periodic flow occurs between Re=60 and 80. The effect of the Reynolds number on heat transfer is discussed. Finally, a developed correlation of Nusselt and Strouhal numbers is presented.

Keywords: forced convection, semi-circular cylinder, Nusselt number, Prandtl number

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Authors: A. B. Disu, M. S. Dada

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This study was conducted to investigate two dimensional heat transfer of a free convective-radiative MHD (Magneto-hydrodynamics) flow with temperature dependent viscosity and heat source of a viscous incompressible fluid in a porous medium between two vertical wavy walls. The fluid viscosity is assumed to vary as an exponential function of temperature. The flow is assumed to consist of a mean part and a perturbed part. The perturbed quantities were expressed in terms of complex exponential series of plane wave equation. The resultant differential equations were solved by Differential Transform Method (DTM). The numerical computations were presented graphically to show the salient features of the fluid flow and heat transfer characteristics. The skin friction and Nusselt number were also analyzed for various governing parameters.

Keywords: differential transform method, MHD free convection, porous medium, two dimensional radiation, two wavy walls

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Authors: Safia Akram

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In this article, the effects of peristaltic transport with double-diffusive convection in nanofluids through an asymmetric channel with different waveforms is presented. Mathematical modelling for two-dimensional and two directional flows of a Jeffrey fluid model along with double-diffusive convection in nanofluids are given. Exact solutions are obtained for nanoparticle fraction field, concentration field, temperature field, stream functions, pressure gradient and pressure rise in terms of axial and transverse coordinates under the restrictions of long wavelength and low Reynolds number. With the help of computational and graphical results the effects of Brownian motion, thermophoresis, Dufour, Soret, and Grashof numbers (thermal, concentration, nanoparticles) on peristaltic flow patterns with double-diffusive convection are discussed.

Keywords: nanofluid particles, peristaltic flow, Jeffrey fluid, magnetic field, asymmetric channel, different waveforms

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Authors: Mohammadreza Sedighi, Mohammad Said Saidi, Hesamoddin Salarian

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A numerical study has been performed to investigate the effect of using different turbulent models on natural convection flow field and temperature distributions in partially heated square cavity compare to benchmark. The temperature of the right vertical wall is lower than that of heater while other walls are insulated. The commercial CFD codes are used to model. Standard k-w model provided good agreement with the experimental data.

Keywords: Buoyancy, Cavity, CFD, Heat Transfer, Natural Convection, Turbulence

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Authors: Syukri Himran, Erwin Eka Putra, Nanang Roni

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This study explains the natural convection of viscous fluid flowing on semi-infinite vertical plate. A set of the governing equations describing the continuity, momentum and energy, have been reduced to dimensionless forms by introducing the references variables. To solve the problems, the equations are formulated by explicit finite-difference in time dependent form and computations are performed by Fortran program. The results describe velocity, temperature profiles both in transient and steady state conditions. An approximate value of heat transfer coefficient and the effects of Pr on convection flow are also presented.

Keywords: natural convection, vertical plate, velocity and temperature profiles, steady and unsteady

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Authors: Rashmi Dubey

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The study aims at investigating the onset of thermal convection in an inclined porous layer saturated with a non-Newtonian fluid. The layer is infinitely extended and has a finite width confined between two boundaries with constant pressure conditions, where the lower one is maintained at a higher temperature. Over the years, this area of research has attracted many scientists and researchers, for it has a plethora of applications in the fields of sciences and engineering, such as in civil engineering, geothermal sites, petroleum industries, etc.Considering the possibilities in a practical scenario, an inclined porous layer is considered, which can be used to develop a generalized model applicable to any inclination. Using the isobaric boundaries, the hydrodynamic boundary conditions are derived for the power-law model and are used to obtain the basic state flow. The convection in the basic state flow is driven by the thermal buoyancy in the flow system and is carried away further due to hydrodynamic boundaries. A linear stability analysis followed by a normal-mode analysis is done to investigate the onset of convection in the buoyancy-driven flow. The analysis shows that the convective instability is always initiated by the non-traveling modes for the Newtonian fluid, but prevails in the form of oscillatory modes, for up to a certain inclination of the porous layer. However, different behavior is observed for the dilatant and pseudoplastic fluids.

Keywords: thermal convection, linear stability, porous media flow, Inclined porous layer

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Authors: Anna Bykalyuk, Frédéric Kuznik, Kévyn Johannes

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In this paper, the influence of a vertical plate’s thermal capacity is numerically investigated in order to evaluate the evolution of the thermal boundary layer structure, as well as the convective heat transfer coefficient and the velocity and temperature profiles. Whereas the heat flux of the heated vertical plate is evaluated under time depending boundary conditions. The main important feature of this problem is the unsteadiness of the physical phenomena. A 2D CFD model is developed with the Ansys Fluent 14.0 environment and is validated using unsteady data obtained for plasterboard studied under a dynamic temperature evolution. All the phenomena produced in the vicinity of the thermal conductive vertical plate (plasterboard) are analyzed and discussed. This work is the first stage of a holistic research on transient free convection that aims, in the future, to study the natural convection in the vicinity of a vertical plate containing Phase Change Materials (PCM).

Keywords: CFD modeling, natural convection, thermal conductive plate, time-depending boundary conditions

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Authors: Gangacharyulu Dasaroju, Sumeet Sharma, Sanjay Singh

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Heat pipe is characterised as superconductor of heat because of its excellent heat removal ability. The operation of several engineering system results in generation of heat. This may cause several overheating problems and lead to failure of the systems. To overcome this problem and to achieve desired rate of heat dissipation, there is need to study the performance of heat pipe with annular fins under free convection at different inclinations. This study demonstrates the effect of different mass flow rate of hot fluid into evaporator section on the condenser side heat transfer coefficient with annular fins under natural convection at different inclinations. In this study annular fins are used for the experimental work having dimensions of length of fin, thickness of fin and spacing of fin as 10 mm, 1 mm and 6 mm, respectively. The main aim of present study is to discover at what inclination angles the maximum heat transfer coefficient shall be achieved. The heat transfer coefficient on the external surface of heat pipe condenser section is determined by experimental method and then predicted by empirical correlations. The results obtained from experimental and Churchill and Chu relation for laminar are in fair agreement with not more than 22% deviation. It is elucidated the maximum heat transfer coefficient of 31.2 W/(m²-K) at 25˚ tilt angle and minimal condenser heat transfer coefficient of 26.4 W/(m²-K) is seen at 45˚ tilt angle and 200 ml/min mass flow rate. Inclination angle also affects the thermal performance of heat pipe. Beyond 25^o inclination, heat transport rate starts to decrease.

Keywords: heat pipe, annular fins, natural convection, condenser heat transfer coefficient, tilt angle

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Authors: Faisal Salah, Z. A. Aziz, K. K. Viswanathan

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In this article, the effects of g-jitter induced and combined with heat and mass transfer by mixed convection of MHD Maxwell fluid in microgravity situation is investigated for a simple system. This system consists of two heated vertical parallel infinite flat plates held at constant but different temperatures and concentrations. By using modified Darcy’s law, the equations governing the flow are modelled. These equations are solved analytically for the induced velocity, temperature and concentration distributions. Many interesting available results in the relevant literature (i.e. Newtonian fluid) is obtained as the special case of the present general analysis. Finally, the graphical results for the velocity profile of the oscillating flow in the channel are presented and discussed for different values of the material constants.

Keywords: g-jitter, heat and mass transfer, mixed convection, Maxwell fluid, porous medium

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Authors: Saeed Hosseini, Ali Reza Tahavvor

Abstract:

Sound processing is one the subjects that newly attracts a lot of researchers. It is efficient and usually less expensive than other methods. In this paper the flow generated sound is used to estimate the flow speed of free flows. Many sound samples are gathered. After analyzing the data, a parameter named wave power is chosen. For all samples, the wave power is calculated and averaged for each flow speed. A curve is fitted to the averaged data and a correlation between the wave power and flow speed is founded. Test data are used to validate the method and errors for all test data were under 10 percent. The speed of the flow can be estimated by calculating the wave power of the flow generated sound and using the proposed correlation.

Keywords: the flow generated sound, free stream, sound processing, speed, wave power

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Authors: Cha’o-Kuang Chen, Ching-Chang Cho

Abstract:

This paper investigates the natural convection heat transfer performance in a complex-wavy-wall cavity filled with power-law fluid. In performing the simulations, the continuity, Cauchy momentum and energy equations are solved subject to the Boussinesq approximation using a finite volume method. The simulations focus specifically on the effects of the flow behavior index in the power-law model and the Rayleigh number on the flow streamlines, isothermal contours and mean Nusselt number within the cavity. The results show that pseudoplastic fluids have a better heat transfer performance than Newtonian or dilatant fluids. Moreover, it is shown that for Rayleigh numbers greater than Ra=103, the mean Nusselt number has a significantly increase as the flow behavior index is decreased.

Keywords: non-Newtonian fluid, power-law fluid, natural convection, heat transfer enhancement, cavity, wavy wall

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Authors: Nouri Sabrina

Abstract:

Numerical parametric study is conducted to study the effects of ampoule rotation on the flows and the dopant segregation in Vertical Bridgman (VB) crystal growth. Calculations were performed in unsteady state. The extended darcy model, whıch includes the time derivative and coriolis terms, has been employed in the momentum equation. It is found that the convection, and dopant segregation can be affected significantly by ampoule rotation, and the effect is similar to that by an axial magnetıc field. Ampoule rotation decreases the intensity of convection and stretches the flow cell axıally. When the convectıon is weak, the flow can be suppressed almost completely by moderate ampoule rotation and the dopant segregation becomes diffusion-controlled. For stronger convection, the elongated flow cell by ampoule rotation may bring dopant mixing into the bulk melt reducing axial segregation at the early stage of the growth. However, if the cellular flow cannot be suppressed completely, ampoule rotation may induce larger radial segregation due to poor mixing.

Keywords: rotating vertical solidification, Finite Volume Method, heat and mass transfer, porous medium, phase change

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Authors: P. G. Siddheshwar, B. N. Veena

Abstract:

Rayleigh-B´enard convection of a nanoliquid in shallow, square and tall enclosures is studied using the Khanafer-Vafai-Lightstone single-phase model. The thermophysical properties of water, copper, copper-oxide, alumina, silver and titania at 3000 K under stagnant conditions that are collected from literature are used in calculating thermophysical properties of water-based nanoliquids. Phenomenological laws and mixture theory are used for calculating thermophysical properties. Free-free, rigid-rigid and rigid-free boundary conditions are considered in the study. Intractable Lorenz model for each boundary combination is derived and then reduced to the tractable Ginzburg-Landau model. The amplitude thus obtained is used to quantify the heat transport in terms of Nusselt number. Addition of nanoparticles is shown not to alter the influence of the nature of boundaries on the onset of convection as well as on heat transport. Amongst the three enclosures considered, it is found that tall and shallow enclosures transport maximum and minimum energy respectively. Enhancement of heat transport due to nanoparticles in the three enclosures is found to be in the range 3% - 11%. Comparison of results in the case of rigid-rigid boundaries is made with those of an earlier work and good agreement is found. The study has limitations in the sense that thermophysical properties are calculated by using various quantities modelled for static condition.

Keywords: enclosures, free-free, rigid-rigid, rigid-free boundaries, Ginzburg-Landau model, Lorenz model

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