• Title/Summary/Keyword: Local Nusselt Number

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Runge-Kutta method for flow of dusty fluid along exponentially stretching cylinder

  • Iqbal, Waheed;Jalil, Mudassar;Khadimallah, Mohamed A.;Ayed, Hamdi;Naeem, Muhammad N.;Hussain, Muzamal;Bouzgarrou, Souhail Mohamed;Mahmoud, S.R.;Ghandourah, E.;Taj, Muhammad;Tounsi, Abdelouahed
    • Steel and Composite Structures
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    • v.36 no.5
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    • pp.603-615
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    • 2020
  • The present manuscript focuses on the flow and heat transfer of the dusty fluid along exponentially stretching cylinder. Enormous attempts are made for fluid flow along cylinder but the study of fluid behavior along exponentially stretching cylinder is discussed lately. Using appropriate transformations, the governing partial differential equations are converted to non-dimensional ordinary differential equations. The transformed equations are solved numerically using Shooting technique with Runge-Kutta method. The influence of the physical parameters on the velocity and temperature profiles as well as the skin fraction coefficient and the local Nusselt number are examined in detail. The essential observations are as the fluid velocity decreases but temperature grows with rise in particle interaction parameter, and both the fluid velocity and temperature fall with increase in mass concentration parameter, Reynold number, Particle interaction parameter for temperature and the Prandtl number.

Three-Dimensional Natural Convection from a Single Module on the Wall of a Vertical Parallel-Plate Channel (수직평행채널의 벽면에 부착된 단일모듈로부터의 3차원 자연대류 열전달)

  • Riu, K.J.;Lee, J.H.;Kim, H.W.
    • Solar Energy
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    • v.19 no.3
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    • pp.29-41
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    • 1999
  • Three-dimensional natural convective heat transfer in a vertical channel with a protruding single module was investigated experimentally. The particular interest was in the removal of thermal energy from the module by convective heat transfer. Hence radiative and conductive heat losses were estimated by using thermocouples and heat flux sensor respectively. The flow fields in the channel were visualized by means of a smoke-method. Also, local temperatures were measured by thermocouples inside the channel, along the vertical wall and module surface. It is found that convective heat transfer was promoted at the lower comer of the module and was decreased at the upper comer due to a recirculation zone. A general correlation of the critical channel ratios was found as a function of Rayleigh number. For the range of $8.28{\times}10^3<Ra^*_c<3.48{\times}10^6$, a useful correlation for the mean Nusselt number was proposed as a function of modified channel Rayleigh number.

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On the Thermal Boundary Conditions at the Interface Between the Porous Medium and the Impermeable Wall (다공성 매질과 비투과성 벽면 사이의 경계면에 대한 열적 경계 조건)

  • Kim, Deok-Jong;Kim, Seong-Jin
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.24 no.12
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    • pp.1635-1643
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    • 2000
  • The present work investigates a heat transfer phenomenon at the interface between a porous medium and an impermeable wall. In an effort to appropriately describe the heat transfer phenomenon at the interface, the heat transfer at the interface between the microchannel heat sink, which is an ideally organized porous medium, and the finite-thickness substrate is examined. From the examination, it is clarified that the he heat flux distribution at the interface is not uniform for the impermeable wall with finite thickness. On the other hand, the first approach, based on the energy balance for the representative elementary volume in the porous medium, is physically reason able. When the first approach is applied to the thermal boundary condition, and additional boundary condition based on the local thermal equilibrium assumption at the interface is used. This additional boundary condition is applicable except for the very th in impermeable wall. Hence, for practical situations, the first approach in combination with the local thermal equilibrium assumption at the interface is suggested as an appropriate thermal boundary condition. In order to confirm our suggestion, convective flows both in a microchannel heat sink and in a sintered porous channel subject to a constant heat flux condition are analyzed. The analytically obtained thermal resistance of the microchannel heat sink and the numerically obtained overall Nusselt number for the sintered porous channel are shown to be in close agreement with available experimental results when our suggestion for the thermal boundary conditions is applied.

An Experimental Study of the Turbulent Swirling Flow and Heat Transfer Downstream of an Abrupt Expansion in a Circulat Pipe with Uniform Heat Flux (급확대관내에서 류유선회유동의 열전달에 관한 연구)

  • 권기린;허종철
    • Journal of Ocean Engineering and Technology
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    • v.10 no.3
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    • pp.138-152
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    • 1996
  • Many studies of heat transfer on the swirling flow or unswirled flow in a abrupt pipe expansion are widely carried out. The mechanism is not fully found evidently due to the instabilities of flow in a sudden change of the shape and appearance of turbulent shear layers in a recirculation region and secondary vortex near the corner. The purpose of this study is to obtain data through an experimental study of the swirling flow and heat transfer downstream of an abrupt expansion in a circular pipe with uniform heat flux. Experiments were carried out for the turbulent flow nd heat transfer downstream of an abrupt circular pipe expansion. The uniform heat flux condition was imposed to the downstream of the abrupt expansion by using an electrically heated pipe. Experimental data are presented for local heat transfer rates and local axial velocities in the tube downstream of an abrupt 3:1 & 2:1 expansion. Air was used as the working fluid in the upstream tube, the Reynolds number was varied from 60, 00 to 120, 000 and the swirl number range (based on the swirl chamber geometry, i.e. L/d ratio) in which the experiments were conducted were L/d=0, 8 and 16. Axial velocity increased rapidly at r/R=0.35 in the abrupt concentric expansion turbulent flow through the test tube in unswirled flow. It showed that with increasing axial distance the highest axial velocities move toward the tube wall in the case of the swirling flow abrupt expansion. A uniform wall heat flux boundary condition was employed, which resulted in wall-to-bulk temperatures ranging from 24.deg. C to 71.deg. C. In swirling flow, the wall temperature showed a greater increase at L/d=16 than any other L/d. The bulk temperature showed a minimum value at the pipe inlet, it also exhibited a linear increase with axial distance along the pipe. As swirl intensity increased, the location of peak Nu numbers was observed to shift from 4 to 1 step heights downstream of the expansion. This upstream movement of the maximum Nusselt number was accompanied by an increase in its magnitude from 2.2 to 8.8 times larger than fully developed tube flow values.

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The heat transfer characteristics of viscoelastic non-newtonian fluids in the entrance region of circular tube flows (원형관속을 유동하는 점탄성 유체의 입구 영역 열전달 특성에 관한 연구)

  • 엄정섭;황태성;유상신
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.13 no.5
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    • pp.1032-1043
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    • 1989
  • The heat transfer characteristics of the drag reducing polymer solutions are investigated experimentally in the thermal entrance region of circular tube flows. Fluids used in experiments are the aqueous solutions of high molecular polymer, polyacrylamide Separan AP-273 and the range of polymer concentrations is from 20 to 1000 wppm. Two stainless steel tubes with inside diameter 8.5mm(L/D=712) and 10.3mm(L/D=1160) are used for the heat transfer flow loops. The flow loop is set up to measure friction factors and heat transfer coefficients of test sections in two different modes; the recirculating flow system and once-through flow system. The test tubes are heated directly by electricity to apply the constant heat flux boundary conditions to the wall. Three different types of adaptors are used to observe the effects of the upstream flow conditions of the heat transfer test sections. The viscosity and characteristic relaxation time of the test fluids circulating in the flow system are measured by the capillary tube viscometer and falling ball viscometer at regular time intervals. The installed adaptors exhibit slight effect on the entrance heat transfer of Newtonian fluid. However, no noticeable effects are observed for the entrance heat transfer of the drag reducing fluids. The order of magnitude of the thermal entrance lengths of the drag reducing fluids which follow the minimum friction asymptote is much longer than that of Newtonian fluids in turbulent flows. A new dimensionless parameter, the viscoelastic Graetz number, is defined and all the experimental data are recasted in terms of the viscoelastic Graetz number. The local Nusselt number of the viscoelastic fluids is represented as a function of flow behavior index n and the viscoelastic Graetz number. As degradation continues the viscosity and the characteristic relaxation time of the testing fluids decrease. Weissenberg number defined by the relaxation time and D/V appears to be a proper dimensionless parameter in describing degradation effects on heat transfer of the viscoelastic fluids.

Energy effects on MHD flow of Eyring's nanofluid containing motile microorganism

  • Sharif, Humaira;Naeem, Muhammad N.;Khadimallah, Mohamed A.;Ayed, Hamdi;Bouzgarrou, Souhail Mohamed;Al Naim, Abdullah F.;Hussain, Sajjad;Hussain, Muzamal;Iqbal, Zafar;Tounsi, Abdelouahed
    • Advances in concrete construction
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    • v.10 no.4
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    • pp.357-367
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    • 2020
  • The impulse of this paper is to examine the influence of unsteady flow comprising of Eyring-Powell nanofluid over a stretched surface. This work aims to explore efficient transfer of heat in Eyring-Powell nanofluid with bio-convection. Nanofluids possess significant features that have aroused various investigators because of their utilization in industrial and nanotechnology. The influence of including motile microorganism is to stabilize the nanoparticle suspensions develop by the mixed influence of magnetic field and buoyancy force. This research paper reveals the detailed information about the linearly compressed Magnetohydrodynamics boundary layer flux of two dimensional Eyring-Powell nanofluid through disposed surface area due to the existence of microorganism with inclusion the influence of non- linear thermal radiation, energy activation and bio-convection. The liquid is likely to allow conduction and thickness of the liquid is supposed to show variation exponentially. By using appropriate similarity type transforms, the nonlinear PDE's are converted into dimensionless ODE's. The results of ODE's are finally concluded by employing (HAM) Homotopy Analysis approach. The influence of relevant parameters on concentration, temperature, velocity and motile microorganism density are studied by the use of graphs and tables. We acquire skin friction, local Nusselt and motil microorganism number for various parameters.

A Study on Heat Transfer Characteristics for Cross Flow Heat Exchanger of Staggered Arrangement (어긋나기배열 직교류 열교환기의 열전달특성에 관한 연구)

  • Yoo, Jae-Hwan;Yoon, Jun-Kyu
    • Journal of Advanced Marine Engineering and Technology
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    • v.36 no.8
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    • pp.1016-1023
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    • 2012
  • Because heat exchanger consists of many circular tubes, the analysis of local heat transfer and pressure drop at the surrounding of circular tubes, performance and calculation of size, economics play important roles in design. In this study, This study conducted experiment and analysis in order to observe convective heat transfer coefficient LMTD (logarithm mean temperature difference) and pressure losses according to water temperature and air flow rate using a cross flow heat exchanger of staggered arrangement. This heat exchanger was composed of staggered arrangement for five rows and seven columns of tube banks, and the condition of experiment and analysis are $40{\sim}65^{\circ}C$ of water temperature and $5.0{\sim}12.3m^3/s$ of air flow rate. As a result of it, since air density decreases as water temperature and flow rate increases, Reynolds number decreases with characteristics of low flow velocity but mean heat transfer coefficient increases with air flow rate increase, heat transfer performance has been improved and pressure losses decreased. And since heat transfer rate shows about 8~12% and pressure drop around 0.01~7.5% error as the analysis result, the feasibility of this study could be evaluated.

Numerical study on conjugate heat transfer in a liquid-metal-cooled pipe based on a four-equation turbulent heat transfer model

  • Xian-Wen Li;Xing-Kang Su;Long Gu;Xiang-Yang Wang;Da-Jun Fan
    • Nuclear Engineering and Technology
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    • v.55 no.5
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    • pp.1802-1813
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    • 2023
  • Conjugate heat transfer between liquid metal and solid is a common phenomenon in a liquid-metal-cooled fast reactor's fuel assembly and heat exchanger, dramatically affecting the reactor's safety and economy. Therefore, comprehensively studying the sophisticated conjugate heat transfer in a liquid-metal-cooled fast reactor is profound. However, it has been evidenced that the traditional Simple Gradient Diffusion Hypothesis (SGDH), assuming a constant turbulent Prandtl number (Prt,, usually 0.85 - 1.0), is inappropriate in the Computational Fluid Dynamics (CFD) simulations of liquid metal. In recent decades, numerous studies have been performed on the four-equation model, which is expected to improve the precision of liquid metal's CFD simulations but has not been introduced into the conjugate heat transfer calculation between liquid metal and solid. Consequently, a four-equation model, consisting of the Abe k - ε turbulence model and the Manservisi k𝜃 - ε𝜃 heat transfer model, is applied to study the conjugate heat transfer concerning liquid metal in the present work. To verify the numerical validity of the four-equation model used in the conjugate heat transfer simulations, we reproduce Johnson's experiments of the liquid lead-bismuth-cooled turbulent pipe flow using the four-equation model and the traditional SGDH model. The simulation results obtained with different models are compared with the available experimental data, revealing that the relative errors of the local Nusselt number and mean heat transfer coefficient obtained with the four-equation model are considerably reduced compared with the SGDH model. Then, the thermal-hydraulic characteristics of liquid metal turbulent pipe flow obtained with the four-equation model are analyzed. Moreover, the impact of the turbulence model used in the four-equation model on overall simulation performance is investigated. At last, the effectiveness of the four-equation model in the CFD simulations of liquid sodium conjugate heat transfer is assessed. This paper mainly proves that it is feasible to use the four-equation model in the study of liquid metal conjugate heat transfer and provides a reference for the research of conjugate heat transfer in a liquid-metal-cooled fast reactor.