Cooling of a Hot Torus

2015 ◽  
Vol 138 (4) ◽  
Author(s):  
Rajai S. Alassar ◽  
Mohammed A. Abushoshah
Keyword(s):  
Heat Transfer ◽  
Aspect Ratio ◽  
Boundary Conditions ◽  
Heat Transfer Rate ◽  
Governing Equation ◽  
Transfer Rate ◽  
Radial Direction ◽  
Convective Boundary Conditions ◽  
Convective Boundary ◽  
Toroidal Coordinates

The problem of a hot torus left to cool in a medium of known temperature is studied. We write the governing equation in toroidal coordinates and expand the temperature in terms of a series in the angular direction. The resulting modes in the radial direction are numerically obtained. We consider both isothermal and convective boundary conditions and study the effect of Biot number and aspect ratio on the heat transfer rate.

MHD hybrid nanofluid flow with convective heat transfer over a permeable stretching/shrinking surface with radiation

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Nur Syahirah Wahid ◽  
Norihan Md Arifin ◽  
Najiyah Safwa Khashi'ie ◽  
Ioan Pop ◽  
Norfifah Bachok ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Volume Fraction ◽  
Hybrid Nanofluid ◽  
Convective Boundary Conditions ◽  
Nanofluid Flow ◽  
Convective Boundary ◽  
Content Type ◽  
Shrinking Surface

Purpose The purpose of this paper is to numerically investigate the hybrid nanofluid flow with the imposition of magnetohydrodynamic (MHD) and radiation effects alongside the convective boundary conditions over a permeable stretching/shrinking surface. Design/methodology/approach The mathematical model is formulated in the form of partial differential equations (PDEs) and are then transformed into the form of ordinary differential equations (ODEs) by using the similarity variables. The deriving ODEs are solved numerically by using the bvp4c solver in MATLAB software. Stability analysis also has been performed to determine the stable solution among the dual solutions obtain. For method validation purposes, a comparison of numerical results has been made with the previous studies. Findings The flow and the heat transfer of the fluid at the boundary layer are described through the plot of the velocity profile, temperature profile, skin friction coefficient and local Nusselt number that are presented graphically. Dual solutions are obtained, but only the first solution is stable. For the realizable solution at the shrinking surface, the proliferation of nanoparticle volume fraction (copper) and magnetic (magnetohydrodynamics) parameters can impede the boundary layer separation. Also, Biot number could enhance the temperature profile and the heat transfer rate at the shrinking surface region. The incrementation of 0.1% of Biot number has enhanced the heat transfer rate by approximately 0.1% and the incrementation of 0.5% volume fraction for copper has reduced the heat transfer rate by approximately 0.17%. Originality/value The presented model and numerical results are original and new. It can be used as a future reference for further investigation and related practical application. The main contribution of this investigation includes giving the initial prediction and providing the numerical data for the other researchers for their future reference regarding the impacts of nanoparticles volumetric concentration towards the main physical quantities of interest in the presence of magnetic and radiation parameters with the convective boundary conditions.

Unsteady and porous media flow of reactive non-Newtonian fluids subjected to buoyancy and suction/injection

2015 ◽  
Vol 25 (7) ◽  
pp. 1682-1704 ◽  
Author(s):  
Tirivanhu Chinyoka ◽  
Daniel Oluwole Makinde
Keyword(s):  
Heat Transfer ◽  
Porous Media ◽  
Boundary Conditions ◽  
Flow Velocity ◽  
Flow System ◽  
Finite Difference Methods ◽  
Porous Media Flow ◽  
Convective Boundary Conditions ◽  
Convective Boundary ◽  
Content Type

Purpose – The purpose of this paper is to examine the unsteady pressure-driven flow of a reactive third-grade non-Newtonian fluid in a channel filled with a porous medium. The flow is subjected to buoyancy, suction/injection asymmetrical and convective boundary conditions. Design/methodology/approach – The authors assume that exothermic chemical reactions take place within the flow system and that the asymmetric convective heat exchange with the ambient at the surfaces follow Newton’s law of cooling. The authors also assume unidirectional suction injection flow of uniform strength across the channel. The flow system is modeled via coupled non-linear partial differential equations derived from conservation laws of physics. The flow velocity and temperature are obtained by solving the governing equations numerically using semi-implicit finite difference methods. Findings – The authors present the results graphically and draw qualitative and quantitative observations and conclusions with respect to various parameters embedded in the problem. In particular the authors make observations regarding the effects of bouyancy, convective boundary conditions, suction/injection, non-Newtonian character and reaction strength on the flow velocity, temperature, wall shear stress and wall heat transfer. Originality/value – The combined fluid dynamical, porous media and heat transfer effects investigated in this paper have to the authors’ knowledge not been studied. Such fluid dynamical problems find important application in petroleum recovery.

scholarly journals A RANS K-? SIMULATION OF 2D TURBULENT NATURAL CONVECTION IN AN ENCLOSURE WITH HEATING SOURCES

2019 ◽  
Vol 20 (1) ◽  
pp. 229-244
Author(s):  
Mehdi Ahmadi ◽  
Seyed Ali Agha Mirjalily ◽  
Seyed Amir Abbas Oloomi
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Kinetic Energy ◽  
Aspect Ratio ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Turbulent Natural Convection ◽  
Cold Source ◽  
Thermal Sources

ABSTRACT: This study is conducted to investigate turbulent natural convection flow in an enclosure with thermal sources using the low-Reynolds number (LRN) k-? model. This enclosure has a cold source with temperature Tc and a hot source with temperature Th as thermal sources, other walls of the enclosure are adiabatic. The aim of this study is to predict the effect of change in Rayleigh number, repositioning of cold and hot sources, and thermal sources aspect ratio on the flow field, temperature, and rate of heat transfer. To achieve this aim, the equations of continuity, momentum, energy, turbulent kinetic energy, and kinetic energy dissipation are employed in the case of 2D turbulence with constant thermo-physical properties except the density in the buoyancy term (Boussinesq approximation). To numerically solve these equations, the finite volume method and SIMPLE algorithm are used. According to the modeling results, the most optimal temperature distribution in the enclosure is seen when the hot source is below the cold source. With decreasing distance between hot and cold sources, heat transfer rate increases. The maximal heat transfer rate is derived via study of the heating sources aspect ratio. In constant positions of cold and hot sources on a wall, the heat transfer rate increases with increasing Rayleigh number (Ra=109-1011). ABSTAK: Kajian ini dijalankan bagi mengkaji perubahan semula jadi aliran perolakan dalam tempat tertutup dengan sumber haba menggunakan model k-? nombor Reynolds-rendah (LRN). Bekas tertutup ini mempunyai dua sumber haba iaitu sumber sejuk dengan suhu Tc dan sumber panas dengan suhu Th, manakala dinding lain bekas ini adalah adiabatik. Tujuan kajian ini adalah bagi mengesan perubahan nombor Rayleigh, mengubah sumber sejuk dan panas dan nisbah sumber haba kepada kawasan aliran, suhu dan halaju perubahan haba. Bagi mencapai tujuan tersebut, persamaan sambungan, momentum, tenaga, tenaga kinetik perolakan, dan pengurangan tenaga kinetik telah dilaksanakan dalam kes perolakan 2D dengan sifat fizikal-haba berterusan (malar) kecuali isipadu terma keapungan (anggaran Boussinesq). Bagi menyelesaikan persamaan ini secara berangka, kaedah isipadu terhad dan algorithma MUDAH telah digunakan. Berdasarkan keputusan model, suhu distribusi optimal dalam bekas tertutup dilihat apabila sumber panas adalah kurang daripada sumber sejuk. Dengan pengurangan jarak antara sumber panas dan sejuk, kadar pertukaran haba meningkat. Kadar pertukaran haba maksima telah diperoleh melalui kajian nisbah  aspek sumber pemanasan. Kadar pertukaran haba bertambah dengan bertambahnya nombor Rayleigh  (Ra=109-1011), pada posisi tetap sumber sejuk dan panas pada dinding bekas.

An Analytical Study of Heat Transfer in Finite Tissue With Two Blood Vessels and Uniform Dirichlet Boundary Conditions

2005 ◽  
Vol 127 (2) ◽  
pp. 179-188 ◽  
Author(s):  
Devashish Shrivastava ◽  
Benjamin McKay ◽  
Robert B. Roemer
Keyword(s):  
Heat Transfer ◽  
Boundary Conditions ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Source Term ◽  
Dirichlet Boundary ◽  
Total Heat ◽  
Dirichlet Boundary Conditions ◽  
Total Heat Transfer ◽  
Transfer Rates

Counter-current (vessel–vessel) heat transfer has been postulated as one of the most important heat transfer mechanisms in living systems. Surprisingly, however, the accurate quantification of the vessel–vessel, and vessel–tissue, heat transfer rates has never been performed in the most general and important case of a finite, unheated/heated tissue domain with noninsulated boundary conditions. To quantify these heat transfer rates, an exact analytical expression for the temperature field is derived by solving the 2-D Poisson equation with uniform Dirichlet boundary conditions. The new results obtained using this solution are as follows: first, the vessel–vessel heat transfer rate can be a large fraction of the total heat transfer rate of each vessel, thus quantitatively demonstrating the need to accurately model the vessel–vessel heat transfer for vessels imbedded in tissues. Second, the vessel–vessel heat transfer rate is shown to be independent of the source term; while the heat transfer rates from the vessels to the tissue show a significant dependence on the source term. Third, while many previous studies have assumed that (1) the total heat transfer rate from vessels to tissue is zero, and/or (2) the heat transfer rates from paired vessels (of different sizes and at different temperatures) to tissue are equal to each other the current analysis shows that neither of these conditions is met. The analytical solution approach used to solve this two vessels problem is general and can be extended for the case of “N” arbitrarily located vessels.

Modeling and Optimization of Gaseous Slip Flow Forced Convection in Rectangular Microducts Using Particle Swarm Optimization Algorithm

2018 ◽  
Author(s):  
Waqar A. Khan ◽  
Nawaf N. Hamadneh
Keyword(s):  
Heat Transfer ◽  
Shear Stress ◽  
Particle Swarm Optimization ◽  
Aspect Ratio ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Particle Swarm Optimization Algorithm ◽  
Slip Flow ◽  
Swarm Optimization ◽  
Gaseous Slip Flow

In this study, pressure driven gaseous slip flow is investigated in microducts of rectangular cross-section. The range of Knudsen numbers Kn in the flow regime is taken as 0.001 ≤ Kn ≤ 0.1 and aspect ratio is taken as 0 ≤ ε ≤ 1. To incorporate rarefaction effects, the effects of slip velocity and temperature jump boundary conditions are taken in to account. The dimensionless momentum and energy equations are solved using MATLAB to obtain the dimensionless velocity and temperature gradients for different values of Knudsen numbers and aspect ratio. Using these gradients, the dimensionless shear stress and heat transfer rate are obtained numerically. The numerical solution can be validated for the special cases when there is no slip (continuum flow), ε = 0 (parallel plates) and ε = 1 (square microducts). An artificial neural network is used to develop separate models for dimensionless shear stress and heat transfer rate and particle swarm optimization algorithm is used to obtain optimum values for both parameters. Using these results, minimum dimensionless shear stress and maximum heat transfer rate can be determined in the microducts under consideration in the slip flow regime. The optimal values of P0 and Nu are found when ε = 1 and Kn = 0.001.

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