Thermal explosions with variable thermal conductivity

1982 ◽  
Vol 60 (2) ◽  
pp. 165-167 ◽  
Author(s):  
Avygdor Moise ◽  
Huw O. Pritchard
Keyword(s):  
Thermal Conductivity ◽  
Critical Temperature ◽  
Thermal Explosion ◽  
Numerical Solutions ◽  
Variable Thermal Conductivity ◽  
The Other ◽  
Critical Parameters ◽  
Temperature Profiles ◽  
Thermal Explosions

Numerical solutions are presented for the case of a thermal explosion in a sphere, in which the thermal conductivity varies linearly with temperature. The behaviour of the critical temperature profiles and of the other critical parameters for variations in the thermal conductivity are demonstrated.

scholarly journals Heat loss analysis in a radiating slab of variable thermal conductivity

2018 ◽  
Vol 7 (2.23) ◽  
pp. 228 ◽  
Author(s):  
Ramoshweu S. Lebelo ◽  
Kholeka C. Moloi
Keyword(s):  
Differential Equation ◽  
Thermal Conductivity ◽  
Chemical Reaction ◽  
Combustion Process ◽  
Variable Thermal Conductivity ◽  
Temperature Profiles ◽  
Reactive Material ◽  
Loss Analysis ◽  
Exothermic Chemical Reaction ◽  
Rectangular Slab

This article investigates the transfer of heat in a stockpile of reactive materials, that is assumed to lose heat to the environment by radiation. The study is modeled in a rectangular slab whose materials are of variable thermal conductivity. The stockpile’s reactive material in this context is one that readily reacts with the oxygen trapped within the stockpile due to exothermic chemical reaction. The study of the combustion process in this case is conducted theoretically by using the Mathematical approach. The differential equation governing the problem is tackled numerically by applying the Runge-Kutta Fehlberg (RKF45) method coupled with the Shooting technique. To investigate the heat transfer phenomena, some kinetic parameters embedded in the governing differential equation, are varied to observe the behavior of the temperature profiles during the combustion process. The results obtained from the temperature profiles, are depicted graphically and discussed accordingly. It was discovered that kinetic phenomena such as the reaction rate parameter, accelerates the exothermic chemical reaction. However, the radiation parameter decelerates the exothermic chemical reaction by lowering the temperature profiles.  

scholarly journals Unsteady/Steady Hydromagnetic Convective Flow between Two Vertical Walls in the Presence of Variable Thermal Conductivity

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
M. M. Hamza ◽  
I. G. Usman ◽  
A. Sule
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Steady State ◽  
Skin Friction ◽  
Numerical Solutions ◽  
Nonlinear Partial Differential Equations ◽  
Vertical Channel ◽  
Approximate Solutions ◽  
Variable Thermal Conductivity ◽  
Convection Flow

Unsteady as well as steady natural convection flow in a vertical channel in the presence of uniform magnetic field applied normal to the flow region and temperature dependent variable thermal conductivity is studied. The nonlinear partial differential equations governing the flow have been solved numerically using unconditionally stable and convergent semi-implicit finite difference scheme. For steady case, approximate solutions have been derived for velocity, temperature, skin friction, and the rate of heat transfer using perturbation series method. Results of the computations for velocity, temperature, skin friction, and the rate of heat transfer are presented graphically and discussed quantitatively for various parameters embedded in the problem. An excellent agreement was found during the numerical computations between the steady-state approximate solutions and unsteady numerical solutions at steady-state time. In addition, comparison with previously published work is performed and the results agree well.

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.

Analysis of Nonlinear Heat Transfer in Solids of Various Geometries with Variable Thermal Conductivity and Heat Source

2017 ◽  
Vol 377 ◽  
pp. 1-16
Author(s):  
Raseelo Joel Moitsheki ◽  
Oluwole Daniel Makinde
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Exact Solutions ◽  
Heat Generation ◽  
Numerical Solutions ◽  
Internal Heat ◽  
Variable Thermal Conductivity ◽  
Internal Heat Generation ◽  
Temperature Dependent ◽  
Power Law Function

In this paper we consider heat transfer in a hot body with different geometries. Here, the thermal conductivity and internal heat generation are both temperature-dependent. This assumption rendered the model considered to be nonlinear. We assume that thermal conductivity is given by a power law function. We employ the preliminary group classification to determine the cases of internal heat generation for which the principal Lie algebra extends by one. Exact solutions are constructed for the case when thermal conductivity is a differential consequence of internal heat generation term. We derive the approximate numerical solutions for the cases where exact solutions are difficult to construct or are nonexistent. The effects of parameters appearing in the model on temperature profile are studied.

APPLICATION OF THE NEW SPECTRAL HOMOTOPY ANALYSIS METHOD (SHAM) IN THE NON-LINEAR HEAT CONDUCTION AND CONVECTIVE FIN PROBLEM WITH VARIABLE THERMAL CONDUCTIVITY

2012 ◽  
Vol 09 (03) ◽  
pp. 1250039 ◽  
Author(s):  
S. S. MOTSA
Keyword(s):  
Thermal Conductivity ◽  
Homotopy Analysis Method ◽  
Numerical Solutions ◽  
Variable Thermal Conductivity ◽  
Analysis Method ◽  
Linear Heat ◽  
Non Linear ◽  
Homotopy Analysis ◽  
Convective Fin ◽  
Spectral Homotopy Analysis Method

In this work, we demonstrate the efficiency of the newly developed spectral homotopy analysis method (SHAM) in solving non-linear heat transfer equations. We demonstrate the applicability of the method by solving the problem of steady conduction in a slab and the convective fin equation with variable thermal conductivity. New closed form explicit analytic solutions of the governing non-linear equations are obtained and compared with the SHAM results and numerical solutions. The results reveal that the new SHAM approach is very accurate and efficient and converges much faster than the standard homotopy analysis method.

Radiative Flow with Variable Thermal Conductivity in Porous Medium

2012 ◽  
Vol 67 (3-4) ◽  
pp. 153-159 ◽  
Author(s):  
Tasawar Hayat ◽  
Sabir Ali Shehzad ◽  
Muhammad Qasim ◽  
A. Alsaedi
Keyword(s):  
Thermal Conductivity ◽  
Porous Medium ◽  
Differential Equations ◽  
Radiation Effect ◽  
Numerical Solutions ◽  
Variable Thermal Conductivity ◽  
Analysis Method ◽  
Nusselt Numbers ◽  
Similarity Transformations ◽  
Homotopy Analysis

This article considers the radiation effect on the flow of a Jeffery fluid with variable thermal conductivity. Similarity transformations are employed to convert the partial differential equations into ordinary differential equations. The resulting equations have been computed by the homotopy analysis method (HAM). The numerical values of the local Nusselt numbers are also computed. The comparison with the numerical solutions of qƟ'(0) is presented. The obtained results are displayed and physical aspects have been examined in detail

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