Similarity Solutions of Natural Convection With Internal Heat Generation

Crepeau, John; Clarksean, Randy

doi:10.1115/1.2824086

Cited by 106 publications

(72 citation statements)

References 9 publications

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“…Natural convection induced by internal heat generation is a common phenomenon in nature. Crepeau and Clarksean (1997) have reported a similarity solution of a fluid problem along a vertical plate with constant temperature in the presence of an exponential decaying heat generation term under the assumption that the fluid has an internal volumetric heat generation.…”

Section: Introductionmentioning

confidence: 99%

Upper-Convected Maxwell Fluid Flow with Variable Thermo-Physical Properties over a Melting Surface Situated in Hot Environment Subject to Thermal Stratification

Omowaye

Animasaun

2016

JAFM

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An upper-convected Maxwell (UCM) fluid flow over a melting surface situated in hot environment is studied. The influence of melting heat transfer and thermal stratification are properly accounted for by modifying the classical boundary condition of temperature to account for both. It is assumed that the ratio of inertia forces to viscous forces is high enough for boundary layer approximation to be valid. The corresponding influence of exponentially space dependent internal heat generation on viscosity and thermal conductivity of UCM is properly considered. The dynamic viscosity and thermal conductivity of UCM are temperature dependent. Classical temperature dependent viscosity and thermal conductivity models are modified to suit the case of both melting heat transfer and thermal stratification. The governing non-linear partial differential equations describing the problem are reduced to a system of nonlinear ordinary differential equations using similarity transformations and completed the solution numerically using the Runge-Kutta method along with shooting technique (RK4SM). The numerical procedure is validated by comparing the solutions of RK4SM with that of MATLAB based bvp4c. The results reveal that increase in stratification parameter corresponds to decrease in the heat energy entering into the fluid domain from freestream and this significantly reduces the overall temperature and temperature gradient of UCM fluid as it flows over a melting surface. The transverse velocity, longitudinal velocity and temperature of UCM are increasing function of temperature dependent viscous and thermal conductivity parameters. At a constant value of melting parameter, the local skin-friction coefficient and heat transfer rate increases with an increase in Deborah number.

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Section: Introductionmentioning

confidence: 99%

Upper-Convected Maxwell Fluid Flow with Variable Thermo-Physical Properties over a Melting Surface Situated in Hot Environment Subject to Thermal Stratification

Omowaye

Animasaun

2016

JAFM

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“…Natural convection flow of heat generating/absorbing fluid was studied by [4][5][6], and [7]. Vajravelu [8] concluded that the heat source/ sink play an important role in delaying the velocity and the temperature to reach the steady state condition.…”

Section: Introductionmentioning

confidence: 99%

Natural Convection Flow of Heat Generating/Absorbing Fluid near a Vertical Plate with Ramped Temperature

Jha¹,

Samaila²,

Ajibade³

2012

JEAS

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This study considers a theoretical analysis of natural convection flow of heat generating/absorbing fluid near an infinite vertical plate with ramped temperature. It is assumed that the bounding plate has a ramped temperature profile. Exact solutions of energy and momentum equations are obtained using the Laplace transform techniques. Solutions are obtained for different values of the Prandtl number (Pr) and the heat sink parameter (S). Results of the ramped and isothermal temperature and velocity as well as Nusselt number and skin friction have been compared and presented with the help of graphs.

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“…Also, [5] considered natural convective flow with suction and mass transfer in a porous medium. [6]examined the natural convection with internal heat generation which decays exponentially. Also the effect of mass transfer and free convection past a vertical porous plate was investigated by [7].…”

Section: Introductionmentioning

confidence: 99%

Radiation Effects on Magnetohydrodynamic Free Convective Flow over an Infinite Vertical Plate In a Porous Medium

Olisa¹

2017

IOSR JM

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Similarity Solutions of Natural Convection With Internal Heat Generation

Cited by 106 publications

References 9 publications

Upper-Convected Maxwell Fluid Flow with Variable Thermo-Physical Properties over a Melting Surface Situated in Hot Environment Subject to Thermal Stratification

Upper-Convected Maxwell Fluid Flow with Variable Thermo-Physical Properties over a Melting Surface Situated in Hot Environment Subject to Thermal Stratification

Natural Convection Flow of Heat Generating/Absorbing Fluid near a Vertical Plate with Ramped Temperature

Radiation Effects on Magnetohydrodynamic Free Convective Flow over an Infinite Vertical Plate In a Porous Medium

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