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 ◽  
Internal Energy ◽  
Entropy Generation ◽  
Energy Generation ◽  
Variable Thermal Conductivity

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.

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.

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.

Instability of Variable Thermal Conductivity Magnetohydrodynamic Nanofluid Flow in a Vertical Porous Channel of Varying Width

2017 ◽  
Vol 378 ◽  
pp. 85-101
Author(s):  
Md. Sarwar Alam ◽  
Oluwole Daniel Makinde ◽  
Md. Abdul Hakim Khan
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Differential Equations ◽  
Entropy Generation ◽  
Fluid Velocity ◽  
Nonlinear Partial Differential Equations ◽  
Vertical Channel ◽  
Porous Wall ◽  
Variable Thermal Conductivity ◽  
Physical Parameters

A numerical investigation is performed into the heat transfer and entropy generation of a variable thermal conductivity magnetohydrodynamic flow of Al2O3-water nanofluid in a vertical channel of varying width with right porous wall, which enable the fluid to enter. The effects of the Lorentz force, buoyancy force, viscous dissipation and Joule heating are considered and modeled using the transverse momentum and energy balance equations respectively. The governing nonlinear partial differential equations are transformed into a system of coupled nonlinear ordinary differential equations using appropriate similarity transformations and then solved numerically using power series with Hermite-Padé approximation method. A stability analysis has been performed for the local rate of shear stress and Nusselt number that indicates the existence of dual solution branches. Numerical results are achieved for the fluid velocity, temperature as well as the rate of heat transfer at the wall and the entropy generation of the system. The present results are original and new for the flow and heat transfer past a channel of varying width in a nanofluid which shows that the physical parameters have significant effects on the flow field.

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.

Semi-analytical Evaluation of Entropy Generation in 1-D Heat Conduction with Variable Thermal Conductivity

2019 ◽  
Vol 11 (4) ◽  
Author(s):  
T. Anupkumar ◽  
A. Praveen Reddy ◽  
Noble Sharma ◽  
N. Narayan Rao ◽  
B. Srinivasa Rao
Keyword(s):  
Thermal Conductivity ◽  
Entropy Generation ◽  
Governing Equation ◽  
Internal Heat ◽  
Variable Thermal Conductivity ◽  
Heat Diffusion ◽  
Entropy Generation Number ◽  
Entropy Transport ◽  
Steady State Heat ◽  
Steady State Heat Transfer

In the present study, steady state heat transfer in a slab is analysed by applying the principle of variation calculus to the entropy generation minimization. The governing equation of the phenomena is obtained by minimizing the total entropy generation over the slab by considering the irreversibility and variation of thermal conductivity as a function of spatial co-ordinates. The governing equation is solved to obtain the temperature distribution, internal heat generation due to irreversibility, entropy generation number and entropy transport into system. The apparent heat sources that come into existence because of the irreversibility in heat diffusion have made the minimization of entropy generation feasible.

scholarly journals Irreversibility Analysis of Dissipative Fluid Flow Over A Curved Surface Stimulated by Variable Thermal Conductivity and Uniform Magnetic Field: Utilization of Generalized Differential Quadrature Method

Entropy ◽  
2018 ◽  
Vol 20 (12) ◽  
pp. 943 ◽  
Author(s):  
Muhammad Afridi ◽  
Abderrahim Wakif ◽  
Muhammad Qasim ◽  
Abid Hussanan
Keyword(s):  
Thermal Conductivity ◽  
Entropy Generation ◽  
Differential Quadrature Method ◽  
Variable Thermal Conductivity ◽  
Differential Quadrature ◽  
Curved Surface ◽  
Quadrature Method ◽  
Generalized Differential Quadrature Method ◽  
Self Similar ◽  
Generalized Differential

The effects of variable thermal conductivity on heat transfer and entropy generation in a flow over a curved surface are investigated in the present study. In addition, the effects of energy dissipation and Ohmic heating are also incorporated in the modelling of the energy equation. Appropriate transformations are used to develop the self-similar equations from the governing equations of momentum and energy. The resulting self-similar equations are then solved by the Generalized Differential Quadrature Method (GDQM). For the validation and precision of the developed numerical solution, the resulting equations are also solved numerically using the Runge-Kutta-Fehlberg method (RKFM). An excellent agreement is found between the numerical results of the two methods. To examine the impacts of emerging physical parameters on velocity, temperature distribution and entropy generation, the numerical results are plotted against the various values of physical flow parameters and discussed physically in detail.

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.

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