Numerical Investigation of Transient Natural Convection of Viscoelastic Fluid Due to a Nonlinearly Stretching Surfaces with a Power-Law Surface Temperature

The transient natural-convection process is analyzed using an integral method of analysis. Differential equations are derived which relate average surface temperature and time for either heating or cooling for vertical elements having arbitrary thermal capacity. The equations are applicable to laminar flow for all fluids. The coefficients are Prandtl number dependent and are estimated for Prandtl numbers in the range 0.01 to 1000. A solution of the equations is presented for the extreme case of a vertical plate of negligible thermal capacity subjected to a step in flux at its surface. Fluids having Prandtl numbers of 0.01, 0.1, 0.72, 1.0, 5, 10, 100, and 1000 are considered. The results, in terms of generalized variables, are practically independent of Prandtl number. Simple one-dimensional transient behavior is followed for approximately 20 per cent of the transient with a subsequent quick approach to the asymptotic value. The results show no substantial overshoot of the average surface temperature. It is doubted that significant temperature overshoot actually occurs for vertical surfaces even for a step in flux.

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Natural Convection of Viscoelastic Fluid from a Cone Embedded in a Porous Medium with Viscous Dissipation

Mathematical Problems in Engineering ◽

10.1155/2013/934712 ◽

2013 ◽

Vol 2013 ◽

pp. 1-11 ◽

Cited By ~ 16

Author(s):

Gilbert Makanda ◽

O. D. Makinde ◽

Precious Sibanda

Keyword(s):

Porous Medium ◽

Natural Convection ◽

Differential Equations ◽

Surface Temperature ◽

Viscoelastic Fluid ◽

Fourth Order ◽

Linearization Method ◽

Similarity Transformations ◽

Fluid Properties ◽

Successive Linearization Method

We study natural convection from a downward pointing cone in a viscoelastic fluid embedded in a porous medium. The fluid properties are numerically computed for different viscoelastic, porosity, Prandtl and Eckert numbers. The governing partial differential equations are converted to a system of fourth order ordinary differential equations using the similarity transformations and then solved together by using the successive linearization method (SLM). Many studies have been carried out on natural convection from a cone but they did not consider a cone embedded in a porous medium with linear surface temperature. The results in this work are validated by the comparison with other authors.

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Natural Convection Flow of Power-Law Fluids over a Heated Horizontal Plate Surface

Zeitschrift für Naturforschung A ◽

10.1515/zna-2019-0045 ◽

2019 ◽

Vol 74 (11) ◽

pp. 971-987 ◽

Cited By ~ 1

Author(s):

Shibdas Dholey

Keyword(s):

Heat Flux ◽

Natural Convection ◽

Surface Temperature ◽

Power Law ◽

Similarity Solution ◽

Infinite Plate ◽

Convection Flow ◽

Fundamental Parameter ◽

Plate Surface ◽

Power Law Fluids

AbstractThe current work attempts to investigate the existence of similarity solution for the natural convection boundary layer flow of a power-law fluid over a heated horizontal semi-infinite plate surface. Three types of surface temperature variation are considered, namely (i) constant surface temperature (CST), (ii) power-law variation of surface temperature (PST) and (iii) power-law variation of surface heat flux (PHF). A reduction of the governing partial differential equations is achieved by using a suitable similarity transformation. But, a careful mathematical verification confirms that the similarity solution does not exist in the CST case and for the PST case it exists only under a particular value of the wall temperature parameter r = 1/3. It also ensured the existence of similarity solution for the PHF case and this will happen only when the plate surface is held at a constant heat flux situation. A new fundamental parameter S arises from the dimensionless analysis which is reduced to the reciprocal of the usual Prandtl number Pr for Newtonian fluids. A novel result of this analysis is that the salient features of the Grashof number Gr which differentiates the thermal responses of the shear-thinning fluid (0 < n < 1) flows from the shear-thickening fluid (n > 1) flows while the Newtonian fluid (n = 1) flows remain unaffected by this parameter no matter what be the value of S.

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