Simulation of natural convection heat transfer in a 2-D trapezoidal enclosure

Natural convection within trapezoidal enclosures finds significant practical applications. The natural convection flows play a prominent role in the transport of energy in energy-related applications, in case of proper design enclosures to achieve higher heat transfer rates. In the present study, a two-dimensional cavity with adiabatic right side wall is studied. The left side vertical wall is maintained at the constant hot temperature and the top slat wall is maintained at cold temperature. The dimensionless governing partial differential equations for vorticity-stream function are solved using the finite difference method with incremental time steps. The parametric study involves a wide range of Rayleigh number, Ra, 10(3)<ra<10(5) and Prandtl number (Pr=0.025, 0.71 and 10). The fluid flow within the enclosure is formed with different shapes for different Pr values. The flow rate is increased by enhancing the Rayleigh number (Ra=10(4)). The numerical results are validated with previous results. The governing parameters in the present article, namely Rayleigh number and Prandtl number on flow patterns, isotherms as well as local Nusselt number are reported

Outsourcing selective maintenance problem in failure prone multi-component systems

In many industrial settings, there are systems designed to perform consecutive missions interspersed with finite breaks during which only a set of component repairs can be carried out due to limited time, budget, or resources. The decision maker then has to decide which components to repair in order to guarantee a given performance level. This is known as the selective maintenance problem (SMP). This paper introduces a new variant of the SMP by specifically taking into account the maintenance outsourcing alternative. A novel integrated non-linear programming formulation where both the in-house and outsourcing maintenance alternatives are accounted for is developed and optimally solved. The effect of the outsourcing alternative on maintenance decisions is investigated through numerical experiments. The overall results obtained demonstrate the validity of the proposed approach. (C) 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved

Melting heat transfer analysis on magnetohydrodynamics buoyancy convection in an enclosure : a numerical study

Therollof melting heat transfer on magnetohydrodynamic natural convection in a square enclosurewithheatingof the bottom wall is examinednumericallyin this article.The dimensionlessgoverning partial differential equations are transformed into vorticity and stream functionformulationand then solved using the finite difference method(FDM). The effects of thermal Rayleigh number(Ra), melting parameter(M) and Hartmann number(Ha) are illustrated graphically.With an increasing melting parameter and Rayleigh number, the rate of fluid flow and temperature gradients are seen to increase. And in the presence of magnetic field, the temperature gradient reduces and hence the conductionmechanism dominated for larger Ha. Greater heat transfer rate is observed in the case of uniform heating compared with non-uniform case. The average Nusselt number reduces with increasing magnetic parameterin the both cases of heating of bottom wall

Magneto-convective flow through a porous enclosure with Hall current and Thermal radiation effects : numerical study

This paper reports the numerical study of magnetohydrodynamic radiative-convective flow in a square cavity containing a porous medium with Hall currents. This study is relevant to hydromagnetic fuel cell design and thermofluidic dynamics of complex magnetic liquid fabrication in enclosures. The governing equations of this fluid system are solved by a finitedifference vorticity stream function approach executed in MATLAB software. A detailed parametric investigation of the impact of Rayleigh number (thermal buoyancy parameter), Hartman number (magnetic body force parameter), Darcy number (permeability parameter), Hall parameter and radiation parameter on the streamline, temperature contours, local Nusselt number along the hot wall and mid-section velocity profiles is computed. Validation with previous special cases in the literature is included. Hall current and radiative effects are found to significantly modify thermofluidic characteristics. From the numerical results, it is found that the magnetic field suppresses the natural convection only for small buoyancy ratios. But, for larger buoyancy ratio, the magnetic field is effective in suppressing the thermal convective flow

Numerical simulation of thermal radiation influence on natural convection in a trapezoidal enclosure : heat flow visualization through energy flux vectors

A theoretical and numerical study of natural convection intwo-dimensional laminar incompressible flow in a trapezoidal enclosurein the presence of thermal radiation is conducted, motivated by energy systems applications. Heat flow visualization via the method of energy flux vectors (EFVs) is also included. The trapezoidal cavity has an inclined top wall which in addition to the bottom wall is maintained at constant temperature, whereas the remaining (vertical side) walls are adiabatic. The governing partial differential conservation equations are transformed using a vorticity-stream function formulation and non-dimensional variables and the resulting nonlinear boundary value problem is solved using a finite difference method with incremental time steps. EFVs provide abundant details of the heat flow at the core of the enclosure. The larger energy flux vectors indicate high temperature gradient zones and the sparse EFVs correspond to low temperature gradient zone. Heat flow distribution in the trapezoidal enclosure can be clearly elaborated via energy flux vectors and provides a deeper insight into thermal characteristics. A comprehensive parametric study is performed to evaluate the impact of Rayleigh number (buoyancy parameter) and radiation parameter on transport phenomena. The computations indicate that local Nusselt number and velocity are increasing functions of the Rayleigh number and radiation parameter. Significant changes in streamlines, temperature contours and energy streamlines for high Rayleigh number are observed. The energy flux vectors show that a large eddy is formed within the enclosure which migrates towards the cold wall. Greater thermal buoyancy force accelerates the primary flow whereas it decelerates the secondary flow. The simulations are relevant to solar collector systems, enclosure fire dynamics, electronic cooling and fuel cell systems. Furthermore, the computations furnish a good benchmark for more general computational fluid dynamics (CFD) analysis with commercial software e.g. ANSYS FLUENT

Simulation of unsteady natural convection flow of a Casson viscoplastic fluid in a square enclosure utilizing a MAC algorithm

Non-Newtonian fluids are increasingly being deployed in energy systems and materials processing. Motivated by these developments, in the current study, a numerical simulation is performed on two-dimensional, unsteady buoyancy-driven flow in a square cavity filled with non-Newtonian fluid (Casson liquid). The enclosure geometry features vertical isothermal walls (with one at higher temperature than the other) and thermally insulated horizontal walls. The conservation equations for mass, momentum and energy are normalized via appropriate transformations and the resulting dimensionless partial differential boundary value problem is solved computationally with a Marker and Cell (MAC) algorithm which features a finite difference scheme along with a staggered grid system. The projection method is employed to evaluate the pressure term. Extensive visualizations of the impact of emerging physical parameters (Rayleigh number and Casson viscoplastic parameter) on streamline and isotherm distributions in the cavity are presented for fixed Prandtl number. Nusselt number i.e. heat transfer rate is increased with rising values of the Casson viscoplastic fluid parameter for any value of Rayleigh number. The density of streamlines increases with increasing values of Casson viscoplastic fluid parameter up to 1. Overall the Casson fluid parameter plays a vital role in controlling the convective heat transfer within the enclosure. The computations are relevant to hybrid solar collectors, materials fabrication (polymer melts) etc

Melting heat transfer analysis of electrically conducting nanofluid flow over an exponentially shrinking/stretching porous sheet with radiative heat flux under magnetic field

Modern magnetic nanomaterials processing operations are progressing rapidly and require increasingly sophisticated mathematical models for their optimization. Stimulated by such developments, in this article, a theoretical and computational study of steady magnetohydrodynamic (MHD) flow of nanofluid from an exponentially stretching/shrinking permeable sheet with melting (phase change) and radiative heat transfer is presented. Wall transpiration i.e. suction and blowing (injection) is included. Buongiorno’s nanofluid model is deployed which simulates the effects of Brownian motion and thermophoresis. The transport equations and boundary conditions are normalized via similarity transformations and appropriate variables and similarity solutions are shown to depend on the transpiration parameter. The emerging dimensionless nonlinear coupled ordinary differential boundary value problem is solved numerically with the Newton-Fehlberg iteration technique. Validation with special cases from the literature is included. Increasing magnetic field i.e. Hartmann number is observed to elevate nanoparticle concentration and temperature whereas it damps the velocity. Higher values of melting parameter consistently decelerate the boundary layer flow and suppress temperature and nanoparticle concentration. Higher radiative parameter strongly increases temperature (and thermal boundary layer thickness) and weakly accelerates the flow. Increasing Brownian motion reduces nanoparticle concentrations whereas greater thermophoretic body force strongly enhances them. Nusselt number and Sherwood number are decreased with increasing Hartmann number whereas they are elevated with stronger wall suction and melting parameter

Numerical simulation and energy flux vector visualization of radiative-convection heat transfer in a porous triangular enclosure

A detailed theoretical examination laminar natural convection heat flow in a triangular porous cavity with significant radiative heat transfer and porosity variation is presented. Twodimensional laminar incompressible flow is considered with the left slant and right walls are low and high temperature respectively, and the remaining (top) wall prescribed as adiabatic. The Darcy-Brinkman isotropic model is utilized, and the coupled governing equations are solved by a numerical method utilizing finite differences. Visualization of isotherms and streamlines is achieved with the method of Energy Flux Vectors (EFVs). The impacts of the different model parameters (Rayleigh number Ra, Darcy number-Da, porosity-E and radiation parameter-Rd) on the thermo fluid characteristics are studied in detail. The computations show that convective heat transfer is enhanced with greater Darcy parameter (permeability) which also leads to intensification in the density of energy flux vector patterns. The flow is accelerated with increasing buoyancy effect (Rayleigh number) and temperatures are also increased with greater radiative flux. Average Nusselt number is decreased with higher porosity. The simulations are relevant to hybrid porous media solar collectors

Numerical simulation and energy flux vector visualization of radiative-convection heat transfer in a porous triangular enclosure

A detailed theoretical examination laminar natural convection heat flow in a triangular porous cavity with significant radiative heat transfer and porosity variation is presented. Twodimensional laminar incompressible flow is considered with the left slant and right walls are low and high temperature respectively, and the remaining (top) wall prescribed as adiabatic. The Darcy-Brinkman isotropic model is utilized, and the coupled governing equations are solved by a numerical method utilizing finite differences. Visualization of isotherms and streamlines is achieved with the method of Energy Flux Vectors (EFVs). The impacts of the different model parameters (Rayleigh number Ra, Darcy number-Da, porosity-E and radiation parameter-Rd) on the thermo fluid characteristics are studied in detail. The computations show that convective heat transfer is enhanced with greater Darcy parameter (permeability) which also leads to intensification in the density of energy flux vector patterns. The flow is accelerated with increasing buoyancy effect (Rayleigh number) and temperatures are also increased with greater radiative flux. Average Nusselt number is decreased with higher porosity. The simulations are relevant to hybrid porous media solar collectors