Boundary Layer Flow and Heat Transfer over an Exponentially Shrinking Sheet
TL;DR: In this article, an analysis is made to study boundary layer flow and heat transfer over an exponentially shrinking sheet using similarity transformations in exponential form, the governing boundary layer equations are transformed into self-similar nonlinear ordinary differential equations, which are then solved numerically using a very efficient shooting method.
Abstract: An analysis is made to study boundary layer flow and heat transfer over an exponentially shrinking sheet. Using similarity transformations in exponential form, the governing boundary layer equations are transformed into self-similar nonlinear ordinary differential equations, which are then solved numerically using a very efficient shooting method. The analysis reveals the conditions for the existence of steady boundary layer flow due to exponential shrinking of the sheet and it is found that when the mass suction parameter exceeds a certain critical value, steady flow is possible. The dual solutions for velocity and temperature distributions are obtained. With increasing values of the mass suction parameter, the skin friction coefficient increases for the first solution and decreases for the second solution.
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TL;DR: In this article, the boundary layer flow of a non-Newtonian fluid accompanied by heat transfer toward an exponentially stretching surface in presence of suction or blowing at the surface is investigated.
328 citations
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...as y!1; u! 0; T! T1 ð7Þ Here, U 1⁄4 U0e x L is the stretching velocity (Magyari and Keller [2]), Tw 1⁄4 T1 þ T0e x 2L is the temperature at the sheet, U0 and T0 are the reference velocity and temperature, respectively, V(x) = V0e x 2L, a special type of velocity at the wall is considered (Bhattacharyya [34]) where V0 is a constant, V(x) > 0 is the velocity of suction and V(x) < 0 is the velocity of blowing....
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TL;DR: In this article, the effects of variable surface heat flux and first-order chemical reaction on MHD flow and radiation heat transfer of nanofluids against a flat plate in porous medium were investigated.
317 citations
TL;DR: In this paper, the unsteady flow and heat transfer past a stretching/shrinking sheet in a hybrid nanofluid is studied, and the governing equations of the problem are transformed to the similarity equations by using similarity transformation technique.
219 citations
TL;DR: In this article, the effects of thermal radiation on the flow of micropolar fluid and heat transfer past a porous shrinking sheet is investigated and self-similar ODEs are obtained using similarity transformations from the governing PDEs and are then solved numerically by very efficient shooting method.
189 citations
Cites background from "Boundary Layer Flow and Heat Transf..."
...Bhattacharyya [34] investigated the steady boundary layer flow and heat transfer over an exponentially shrinking sheet....
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TL;DR: In this paper, the motion of temperature dependent plastic dynamic viscosity and thermal conductivity of steady incompressible laminar free convective magnetohydrodynamic (MHD) Casson fluid flow over an exponentially stretching surface with suction and exponentially decaying internal heat generation was studied.
141 citations
Cites background from "Boundary Layer Flow and Heat Transf..."
...19 Ishak [10] studied the magnetohydrodynamic (MHD) boundary layer flow over an exponentially shrinking sheet in 20 the presence of thermal radiation, Bhattacharyya [11] discussed the boundary layer flow and heat transfer caused due 21 to an exponentially shrinking sheet and Bhattacharyya and Pop [12] showed the effect of external magnetic field on 22 the flow over an exponentially shrinking sheet....
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References
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TL;DR: In this paper, a plastischem material fliesst aus einem Spalt with einer Geschwindigkeit, die proportional zum Abstand vom Spalt ist.
Abstract: Eine Platte aus plastischem Material fliesst aus einem Spalt mit einer Geschwindigkeit, die proportional zum Abstand vom Spalt ist. Eine exakte Losung der Grenzschichtgleichungen fur die von der Platte erzeugte Luftbewegung wird gegeben. Oberflachenreibung und Warmeleitungskoeffizient werden berechnet.
3,317 citations
1,408 citations
TL;DR: In this article, the similarity solutions describing the steady plane (flow and thermal) boundary layers on an exponentially stretching continuous surface with an exponential temperature distribution are examined both analytically and numerically.
Abstract: The similarity solutions describing the steady plane (flow and thermal) boundary layers on an exponentially stretching continuous surface with an exponential temperature distribution are examined both analytically and numerically. The mass- and heat-transfer characteristics of these boundary layers are described and compared with the results of earlier authors, obtained under the more familiar power-law boundary conditions.
617 citations
TL;DR: In this paper, a similarity transform was used to reduce the Navier-Stokes equations to a set of non-linear ordinary differential equations, which are then integrated numerically.
Abstract: The stagnation flow towards a shrinking sheet is studied. A similarity transform reduces the Navier–Stokes equations to a set of non-linear ordinary differential equations which are then integrated numerically. Both two-dimensional and axisymmetric stagnation flows are considered. It is found that solutions do not exist for larger shrinking rates and may be non-unique in the two-dimensional case. The non-alignment of the stagnation flow and the shrinking sheet complicates the flow structure. Convective heat transfer decreases with the shrinking rate due to an increase in boundary layer thickness.
610 citations
TL;DR: In this paper, the viscous flow induced by a shrinking sheet is studied and its existence and uniqueness are proved. Exact solutions, both numerical and in closed form, are found.
Abstract: The viscous flow induced by a shrinking sheet is studied. Existence and (non)uniqueness are proved. Exact solutions, both numerical and in closed form, are found.
589 citations