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.

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.

scholarly journals STEADY-STATE HEAT TRANSFER IN A PLATE WITH TEMPERATURE-DEPENDENT THERMAL CONDUCTIVITY (AN EXACT SOLUTION)

2019 ◽  
Vol 18 (2) ◽  
pp. 85
Author(s):  
A. Miguelis ◽  
R. Pazetto ◽  
R. M. S. Gama
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Steady State ◽  
Transfer Problem ◽  
Internal Heat ◽  
Temperature Dependent ◽  
State Heat ◽  
Kirchhoff Transformation ◽  
Steady State Heat ◽  
Steady State Heat Transfer

This work presents the solution of the steady-state heat transfer problem in a rectangular plate with an internal heat source in a context in which the thermal conductivity depends on the local temperature. This generalization of one of the most classical heat transfer problems is carried out with the aid of the Kirchhoff transformation and employs only well known tools, as the superposition of solutions and the Fourier series. The obtained results illustrate how the usual procedures may be extended for solving more realistic physical problems (since the thermal conductivity of any material is temperature-dependent). A general formula for evaluating the Kirchhoff transformation as well as its inverse is presented too. This work has a strong didactical contribution since such analytical solutions are not found in any classical heat transfer book. In addition, the main idea can be used in a lot of similar problems.

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.

Steady-State Conduction With Variable Thermal Conductivity

1962 ◽  
Vol 84 (1) ◽  
pp. 92-93 ◽  
Author(s):  
Robert K. McMordie
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Steady State ◽  
Variable Thermal Conductivity ◽  
Two Dimensional ◽  
The Real ◽  
State Heat ◽  
Steady State Heat ◽  
Steady State Heat Transfer ◽  
Transfer Problems

A method is developed for solving two-dimensional, steady-state heat-transfer problems with thermal conductivity dependent on temperature. The quantity ∫ KdT is employed in the analysis and although this quantity has been known for some time,2, 3 it seems that the real usefulness of this quantity in analysis has not been, in general, recognized.

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.

Steady State Heat Transfer Within a Nanoscale Spatial Domain

2012 ◽  
Vol 134 (7) ◽  
Author(s):  
Kirill V. Poletkin ◽  
Vladimir Kulish
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Heat Transfer Coefficient ◽  
Steady State ◽  
Transfer Coefficient ◽  
Spatial Domain ◽  
Thermal Waves ◽  
Steady State Heat ◽  
Steady State Heat Transfer ◽  
The Heat Transfer Coefficient

In this paper, we study the steady state heat transfer process within a spatial domain of the transporting medium whose length is of the same order as the distance traveled by thermal waves. In this study, the thermal conductivity is defined as a function of a spatial variable. This is achieved by analyzing an effective thermal diffusivity that is used to match the transient temperature behavior in the case of heat wave propagation by the result obtained from the Fourier theory. Then, combining the defined size-dependent thermal conductivity with Fourier’s law allows us to study the behavior of the heat flux at nanoscale and predict that a decrease of the size of the transporting medium leads to an increase of the heat transfer coefficient which reaches its finite maximal value, contrary to the infinite value predicted by the classical theory. The upper limit value of the heat transfer coefficient is proportional to the ratio of the bulk value of the thermal conductivity to the characteristic length of thermal waves in the transporting medium.

scholarly journals A Linear Approach Suitable for a Class of Steady-State Heat Transfer Problems with Temperature-Dependent Thermal Conductivity

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
R. M. S. Gama ◽  
R. Pazetto
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Steady State ◽  
Robin Boundary Conditions ◽  
Temperature Dependent ◽  
Steady State Heat ◽  
Steady State Heat Transfer ◽  
Transfer Problems ◽  
Robin Boundary ◽  
Temperature Dependent Thermal Conductivity

This work presents an useful tool for constructing the solution of steady-state heat transfer problems, with temperature-dependent thermal conductivity, by means of the solution of Poisson equations. Specifically, it will be presented a procedure for constructing the solution of a nonlinear second-order partial differential equation, subjected to Robin boundary conditions, by means of a sequence whose elements are obtained from the solution of very simple linear partial differential equations, also subjected to Robin boundary conditions. In addition, an a priori upper bound estimate for the solution is presented too. Some examples, involving temperature-dependent thermal conductivity, are presented, illustrating the use of numerical approximations.

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