scholarly journals Effect of variable thermal conductivity on entropy generation in a plate with internal energy generation

2018 ◽  
Vol 144 ◽  
pp. 04001
Author(s):  
T. K. Favas ◽  
G. Jilani
Keyword(s):  
Thermal Conductivity ◽  
Mathematical Model ◽  
Entropy Generation ◽  
Energy Generation ◽  
Variable Thermal Conductivity ◽  
Entropy Generation Rate ◽  
Fluid Temperature ◽  
Numerical Predictions ◽  
Wide Range ◽  
Generation Parameter

The current numerical investigation aims at analyzing the effect of variable thermal conductivity on local and global entropy generation rates in an energy generating plate dissipating heat by conjugate conduction-forced convection heat transfer. In order to fulfill this objective, the physical model of the plate dissipating heat into surrounding coolant is transformed into a mathematical model governing the temperature field in the plate as well as flow and thermal fields in the fluid. The resulting mathematical model, being a set of coupled and non linear partial differential equations, is solved by adopting stream function-vorticity formulation and by employing Alternating direction implicit scheme. Keeping Prandtl number of the fluid, temperature of the free stream coolant and maximum permissible plate temperature as fixed, numerical predictions are obtained for wide range of values of aspect ratio, conduction-convection parameter, energy generation parameter and flow Reynolds number. It is concluded that unrealistic constant thermal conductivity assumption leads to underestimation of entropy generation rates. It is also found that an increase in energy generation parameter results in significant increase in underestimation of global entropy generation rate.

scholarly journals Mathematical model for thermal and entropy analysis of thermal solar collectors by using Maxwell nanofluids with slip conditions, thermal radiation and variable thermal conductivity

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 123-136 ◽  
Author(s):  
Asim Aziz ◽  
Wasim Jamshed ◽  
Taha Aziz
Keyword(s):  
Thermal Conductivity ◽  
Mathematical Model ◽  
Thermal Radiation ◽  
Entropy Generation ◽  
Mathematical Formulation ◽  
Variable Thermal Conductivity ◽  
Skin Friction Coefficient ◽  
Working Fluid ◽  
Convective Boundary ◽  
Unsteady Stretching Surface

Abstract In the present research a simplified mathematical model for the solar thermal collectors is considered in the form of non-uniform unsteady stretching surface. The non-Newtonian Maxwell nanofluid model is utilized for the working fluid along with slip and convective boundary conditions and comprehensive analysis of entropy generation in the system is also observed. The effect of thermal radiation and variable thermal conductivity are also included in the present model. The mathematical formulation is carried out through a boundary layer approach and the numerical computations are carried out for Cu-water and TiO2-water nanofluids. Results are presented for the velocity, temperature and entropy generation profiles, skin friction coefficient and Nusselt number. The discussion is concluded on the effect of various governing parameters on the motion, temperature variation, entropy generation, velocity gradient and the rate of heat transfer at the boundary.

Thermal and Entropy generation analysis of magnetohydrodynamic tangent hyperbolic slip flow towards a stretching sheet

2021 ◽  
pp. 095440892110411
Author(s):  
Shafiq Ahmad ◽  
Zafar H Khan ◽  
Salman Zeb ◽  
Muhammad Hamid
Keyword(s):  
Thermal Conductivity ◽  
Entropy Generation ◽  
Slip Flow ◽  
Variable Thermal Conductivity ◽  
Weissenberg Number ◽  
Temperature Fields ◽  
Generation Rate ◽  
Entropy Generation Rate ◽  
Bejan Number ◽  
Generation Model

This article examined the effects of boundary layer flow and heat transport of a two-dimensional incompressible magnetohydrodynamic tangent hyperbolic fluid under slip boundary conditions and variable thermal conductivity. The entropy generation model is also analysed for the said fluid. Non-similarity transformations transformed the governing equations of the fluid and entropy generation model into dimensionless form. Maple software is used to solve the transformed equations numerically. Effects of different dimensionless parameters on entropy generation rate, Bejan number, velocity and temperature fields are studied thoroughly through graphs. It is observed that for higher values of velocity slip parameter and power-law index, the entropy generation rate decreases while the Bejan number increases. Also, for the Hartmann number, Weissenberg number and Brinkman number, we found an increase in the entropy generation rate, and reverse behaviour is observed for the Bejan number. Nusselt number, temperature profile and Bejan’s number increase with an increase in variable thermal conductivity.

Effects of Energy Dissipation and Variable Thermal Conductivity on Entropy Generation Rate in Mixed Convection Flow

2018 ◽  
Vol 10 (4) ◽  
Author(s):  
Muhammad Qasim ◽  
Muhammad Idrees Afridi
Keyword(s):  
Thermal Conductivity ◽  
Energy Dissipation ◽  
Mixed Convection ◽  
Entropy Generation ◽  
Variable Thermal Conductivity ◽  
Convection Flow ◽  
Mixed Convection Flow ◽  
Entropy Generation Number ◽  
Similarity Transformations ◽  
Generation Number

Analysis of entropy generation in mixed convection flow over a vertically stretching sheet has been carried out in the presence of variable thermal conductivity and energy dissipation. Governing equations are reduced to self-similar ordinary differential equations via similarity transformations and are solved numerically by applying shooting and fourth-order Runge–Kutta techniques. The expressions for entropy generation number and Bejan number are also obtained by using similarity transformations. The influence of embedding physical parameters on quantities of interest is discussed through graphical illustrations. The results reveal that entropy generation number increases significantly in the vicinity of stretching surface and gradually dies out as one move away from the sheet. Also, the entropy generation number decreases with an increase in temperature difference parameter. Moreover, entropy generation number enhances with an enhancement in the Eckert number, Prandtl number, and variable thermal conductivity parameter.

Thermal transport of hybrid nanofluids with entropy generation: A numerical simulation

2021 ◽  
pp. 2150218
Author(s):  
Hassan Waqas ◽  
Faisal Fareed Bukhari ◽  
Taseer Muhammad ◽  
Umar Farooq
Keyword(s):  
Thermal Conductivity ◽  
Thermal Radiation ◽  
Entropy Generation ◽  
Industrial Process ◽  
Velocity Slip ◽  
Variable Thermal Conductivity ◽  
Process Improvements ◽  
Radiation Entropy ◽  
Hybrid Nanofluids ◽  
Nonlinear Pattern

In this research, thermal radiation, entropy generation and variable thermal conductivity effects on hybrid nanofluids by moving sheet are analyzed. The liquid is placed by stretchable flat wall that is flowing in a nonlinear pattern. Thermal conductivity changes with temperature governed by thermal radiation and MHD is incorporated. Approximations of boundary layer correspond to a set of PDEs which are then changed into ODEs by considering suitable variables. The resulting ODEs are solved using the bvp4c method. The implication with considerable physical characteristics on temperature, entropy generation and velocity profile is graphically represented and numerically discussed. Entropy generation increases for increasing Reynolds number, velocity slip parameter, Brinkman number and magnetic parameter. Scientists have recently established a rising interest in the importance of nanoparticles due to their numerous technical, industrial and commercial uses. The provided insights can be used in extrusion application areas, macromolecules, biomimetic systems, energy production and industrial process improvements.

Entropy Analysis of the Nonlinear Convective Flow of a Jeffrey Fluid over an Inclined Sheet with Variable Electrical Conductivity and Thermal Conductivity

2021 ◽  
Vol 52 ◽  
pp. 73-91
Author(s):  
Jacob A. Gbadeyan ◽  
Joseph O. Akinremi
Keyword(s):  
Thermal Conductivity ◽  
Electrical Conductivity ◽  
Boundary Conditions ◽  
Entropy Generation ◽  
Convective Flow ◽  
Transverse Magnetic ◽  
Entropy Generation Rate ◽  
Jeffrey Fluid ◽  
Convective Boundary ◽  
Fourth Order Method

A steady two-dimensional nonlinear convective flow of a viscous, incompressible, electrically conducting, and non-Newtonian Jeffrey fluid over an inclined stretching sheet with convective boundary conditions and entropy generation is studied under the influence of transverse magnetic field, electrical conductivity and thermal conductivity. The thermal conductivity and electrical conductivity are temperature dependent functions. The governing continuity, momentum and energy equations are transformed to ordinary differential equations (ODEs) using appropriate similarity variables. The resulting coupled ODEs and the corresponding boundary conditions, are solved numerically using Runge-Kutta fourth order method and shooting technique. The velocity, entropy generation rate, temperature and Bejan distributions are presented graphically and discussed. The numerical values of the skin-friction and Nusselt number are obtained and also discussed for various thermophysical parameters through a Table. Furthermore, a comparison with earlier work done with limiting case was carried out and found to be in excellent agreement.

Adaptive Thermal Conductivity Metamaterials: Enabling Active and Passive Thermal Control

2018 ◽  
Vol 10 (5) ◽  
Author(s):  
Austin A. Phoenix ◽  
Evan Wilson
Keyword(s):  
Thermal Conductivity ◽  
Thermal Management ◽  
Passive Control ◽  
Coefficient Of Thermal Expansion ◽  
Thermal Strain ◽  
Thermal Control ◽  
Variable Thermal Conductivity ◽  
Highly Nonlinear ◽  
Wide Range ◽  
Nonlinear Thermal Conductivity

The novel adaptive thermal metamaterial developed in this paper provides a unique thermal management capability that can address the needs of future spacecraft. While advances in metamaterials have provided the ability to generate materials with a broad range of material properties, relatively little advancement has been made in the development of adaptive metamaterials. This metamaterial concept enables the development of materials with a highly nonlinear thermal conductivity as a function of temperature. Through enabling active or passive control of the metamaterials bulk effective thermal conductivity, this metamaterial that can improve the spacecraft's thermal management systems performance. This variable thermal conductivity is achieved through induced contact that results in changes in the F path length and the conductive path area. The contact can be generated internally using thermal strain from shape memory alloys, bimetal springs, and mismatches in coefficient of thermal expansion (CTE) or it can be generated externally using applied mechanical loading. The metamaterial can actively control the temperature of an interface by dynamically changing the bulk thermal conductivity controlling the instantaneous heat flux through the metamaterial. The design of thermal stability regions (regions of constant thermal conductivity versus temperature) into the nonlinear thermal conductivity as a function of temperature can provide passive thermal control. While this concept can be used in a wide range of applications, this paper focuses on the development of a metamaterial that achieves highly nonlinear thermal conductivity as a function of temperature to enable passive thermal control of spacecraft systems on orbit.

scholarly journals Time Evolution Features of Entropy Generation Rate in Turbulent Rayleigh-Bénard Convection with Mixed Insulating and Conducting Boundary Conditions

Entropy ◽  
2020 ◽  
Vol 22 (6) ◽  
pp. 672
Author(s):  
Yikun Wei ◽  
Pingping Shen ◽  
Zhengdao Wang ◽  
Hong Liang ◽  
Yuehong Qian
Keyword(s):  
Energy Transfer ◽  
Kinetic Energy ◽  
Boundary Conditions ◽  
Time Evolution ◽  
Entropy Generation ◽  
Thermal Convection ◽  
Entropy Generation Rate ◽  
Total Entropy ◽  
Wide Range ◽  
Rayleigh Benard

Time evolution features of kinetic and thermal entropy generation rates in turbulent Rayleigh-Bénard (RB) convection with mixed insulating and conducting boundary conditions at Ra = 109 are numerically investigated using the lattice Boltzmann method. The state of flow gradually develops from laminar flow to full turbulent thermal convection motion, and further evolves from full turbulent thermal convection to dissipation flow in the process of turbulent energy transfer. It was seen that the viscous, thermal, and total entropy generation rates gradually increase in wide range of t/τ < 32 with temporal evolution. However, the viscous, thermal, and total entropy generation rates evidently decrease at time t/τ = 64 compared to that of early time. The probability density function distributions, spatial-temporal features of the viscous, thermal, and total entropy generation rates in the closed system provide significant physical insight into the process of the energy injection, the kinetic energy, the kinetic energy transfer, the thermal energy transfer, the viscous dissipated flow and thermal dissipation.

scholarly journals Second Law Analysis of Dissipative Flow over a Riga Plate with Non-Linear Rosseland Thermal Radiation and Variable Transport Properties

Entropy ◽  
2018 ◽  
Vol 20 (8) ◽  
pp. 615 ◽  
Author(s):  
Muhammad Afridi ◽  
Muhammad Qasim ◽  
Abid Hussanan
Keyword(s):  
Thermal Conductivity ◽  
Entropy Generation ◽  
Numerical Solutions ◽  
Variable Viscosity ◽  
Frictional Heating ◽  
Variable Thermal Conductivity ◽  
Heat Transfer Analysis ◽  
Entropy Generation Number ◽  
Non Linear ◽  
Riga Plate

In this article, we investigated entropy generation and heat transfer analysis in a viscous flow induced by a horizontally moving Riga plate in the presence of strong suction. The viscosity and thermal conductivity of the fluid are taken to be temperature dependent. The frictional heating function and non-linear radiation terms are also incorporated in the entropy generation and energy equation. The partial differential equations which model the flow are converted into dimensionless form by using proper transformations. Further, the dimensionless equations are reduced by imposing the conditions of strong suction. Numerical solutions are obtained using MATLAB boundary value solver bvp4c and used to evaluate the entropy generation number. The influences of physical flow parameters arise in the mathematical modeling are demonstrated through various graphs. The analysis reveals that velocity decays whereas entropy generation increases with rising values of variable viscosity parameter. Furthermore, entropy generation decays with increasing variable thermal conductivity parameter.

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