Numerical Treatment of the MHD Convective Heat and Mass Transfer in an Electrically Conducting Fluid over an Infinite Solid Surface in Presence of the Internal Heat Generation

2003 ◽  
Vol 58 (11) ◽  
pp. 601-611 ◽  
Author(s):  
N. T. Eldabe ◽  
A. G. El-Sakka ◽  
Ashraf Fouad
Keyword(s):  
Mass Transfer ◽  
Heat Generation ◽  
Solid Surface ◽  
Numerical Solutions ◽  
Internal Heat ◽  
Internal Heat Generation ◽  
Conducting Fluid ◽  
Electrically Conducting ◽  
Linear Partial Differential Equations ◽  
Electrically Conducting Fluid

Numerical solutions of a set of non-linear partial differential equations are investigated. We obtained the velocity distribution of a conducting fluid flowing over an infinite solid surface in the presence of an uniform magnetic field and internal heat generation. The temperature and concentration distributions of the fluid are studied as well as the skin-friction, rate of mass transfer and local wall heat flux. The effect of the parameters of the problem on these distributions is illustrated graphically.

scholarly journals The Effect of Internal Heat Generation of a Reactive Hydromagnetic (MHD) Fluid Flow through a Vertical Plate

2019 ◽  
Vol 1 ◽  
pp. 200-213
Author(s):  
L N Ikpakyegh ◽  
M M Shio ◽  
G T Okedayo
Keyword(s):  
Fluid Flow ◽  
Heat Generation ◽  
Vertical Plate ◽  
Computer Software ◽  
Internal Heat ◽  
Internal Heat Generation ◽  
Temperature Fields ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid ◽  
Flow Through

In this study, we discussed the flow of an electrically conducting fluid with internal heat generation over a vertical plate on a reactive MHD fluid. We obtained the semi analytical solutions of the dimensionless equations governing the fluid flow using the method of weighted residual by the collocation method. The parameters with their effect on velocity and temperature fields are discussed graphically using Mapple 17 computer software. We showed that the internal heat generation, magnetic field intensityand the reactive rate have significant effects on the velocity profiles and temperature distributions.

Heat Transfer on Nanofluid Flow With Homogeneous–Heterogeneous Reactions and Internal Heat Generation

2014 ◽  
Vol 136 (12) ◽  
Author(s):  
Raj Nandkeolyar ◽  
Peri K. Kameswaran ◽  
Sachin Shaw ◽  
Precious Sibanda
Keyword(s):  
Heat Transfer ◽  
Mass Transfer ◽  
Heat And Mass Transfer ◽  
Heat Generation ◽  
Internal Heat ◽  
Internal Heat Generation ◽  
Heterogeneous Reactions ◽  
Transfer Coefficients ◽  
Transfer Characteristics ◽  
Fluid Properties

We investigated heat and mass transfer on water based nanofluid due to the combined effects of homogeneous–heterogeneous reactions, an external magnetic field and internal heat generation. The flow is generated by the movement of a linearly stretched surface, and the nanofluid contains nanoparticles of copper and gold. Exact solutions of the transformed model equations were obtained in terms of hypergeometric functions. To gain more insights regarding subtle impact of fluid and material parameters on the heat and mass transfer characteristics, and the fluid properties, the equations were further solved numerically using the matlab bvp4c solver. The similarities and differences in the behavior, including the heat and mass transfer characteristics, of the copper–water and gold–water nanofluids with respect to changes in the flow parameters were investigated. Finally, we obtained the numerical values of the skin friction and heat transfer coefficients.

Integral Solutions of Phase Change With Internal Heat Generation

2004 ◽  
Author(s):  
Ali Siahpush ◽  
John Crepeau
Keyword(s):  
Differential Equation ◽  
Phase Change ◽  
Heat Generation ◽  
Numerical Solutions ◽  
Internal Heat ◽  
Melting Rate ◽  
Internal Heat Generation ◽  
Stefan Number ◽  
Temperature Boundary ◽  
Solid Liquid

This paper presents solutions to a one-dimensional solid-liquid phase change problem using the integral method for a semi-infinite material that generates internal heat. The analysis assumed a quadratic temperature profile and a constant temperature boundary condition on the exposed surface. We derived a differential equation for the solidification thickness as a function of the internal heat generation (IHG) and the Stefan number, which includes the temperature of the boundary. Plots of the numerical solutions for various values of the IHG and Stefan number show the time-dependant behavior of both the melting and solidification distances and rates. The IHG of the material opposes solidification and enhances melting. The differential equation shows that in steady-state, the thickness of the solidification band is inversely related to the square root of the IHG. The model also shows that the melting rate initially decreases and reaches a local minimum, then increases to an asymptotic value.

Fourier-Bessel Series Model for the Stefan Problem With Internal Heat Generation in Cylindrical Coordinates

2018 ◽  
Author(s):  
Lyudmyla Barannyk ◽  
John Crepeau ◽  
Patrick Paulus ◽  
Ali Siahpush
Keyword(s):  
Differential Equation ◽  
Steady State ◽  
Heat Generation ◽  
Numerical Solutions ◽  
Internal Heat ◽  
Internal Heat Generation ◽  
Time Dependent ◽  
Cylindrical Coordinates ◽  
System Approaches ◽  
Melting And Solidification

A nonlinear, first-order ordinary differential equation that involves Fourier-Bessel series terms has been derived to model the time-dependent motion of the solid-liquid interface during melting and solidification of a material with constant internal heat generation in cylindrical coordinates. The model is valid for all Stefan numbers. One of the primary applications of this problem is for a nuclear fuel rod during meltdown. The numerical solutions to this differential equation are compared to the solutions of a previously derived model that was based on the quasi-steady approximation, which is valid only for Stefan numbers less than one. The model presented in this paper contains exponentially decaying terms in the form of Fourier-Bessel series for the temperature gradients in both the solid and liquid phases. The agreement between the two models is excellent in the low Stefan number regime. For higher Stefan numbers, where the quasi-steady model is not accurate, the new model differs from the approximate model since it incorporates the time-dependent terms for small times, and as the system approaches steady-state, the curves converge. At higher Stefan numbers, the system approaches steady-state faster than for lower Stefan numbers. During the transient process for both melting and solidification, the temperature profiles become parabolic.

Finite element thermal analysis of a moving porous fin with temperature-variant thermal conductivity and internal heat generation

2020 ◽  
Vol 1 (1) ◽  
pp. 110
Author(s):  
Gbeminiyi Sobamowo ◽  
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Finite Element ◽  
Heat Generation ◽  
Peclet Number ◽  
Numerical Solutions ◽  
Internal Heat ◽  
Internal Heat Generation ◽  
Péclet Number ◽  
Porous Fin

This paper focuses on finite element analysis of the thermal behaviour of a moving porous fin with temperature-variant thermal conductivity and internal heat generation. The numerical solutions are used to investigate the effects of Peclet number, Hartmann number, porous and convective parameters on the temperature distribution, heat transfer and efficiency of the moving fin. The results show that when the convective and porous parameters increase, the adimensional fin temperature decreases. However, the value of the fin temperature is amplified as the value Peclet number is enlarged. Also, an increase in the thermal conductivity and the internal heat generation cause the fin temperature to fall and the rate of heat transfer from the fin to decrease. Therefore, the operational parameters of the fin must be carefully selected to avoid thermal instability in the fin.

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