K. Vajravelu

Convective heat transfer in an electrically conducting fluid at a stretching surface with uniform free stream

Abstract An analysis is carried out to study the flow and heat transfer characteristics in an electrically conducting fluid near an isothermal sheet. The sheet is linearly stretched in the presence of a uniform free stream of constant velocity and temperature. The effects of free convection and internal heat generation or absorption are also considered. The resulting coupled nonlinear differential equations are integrated numerically and the flow and heat transfer characteristics are discussed. Although the velocity profiles are similar in the absence of free stream, it is shown that the differential system gives rise to nonsimilar velocity profiles in the boundary layer.

Convective heat transfer at a stretching sheet

SummaryAnalysis of convection flow and heat transfer of a viscous heat-generating fluid near an infinite vertical stretching surface is carried out. The effects of free convection and the presence of heat generation/absorption on the flow and heat transfer characteristics are considered. The equations of conservation of momentum, mass, and energy, which govern the flow and heat transfer problem, are solved numerically by using a variable order, variable step size finite-difference method. The numerical results obtained for the flow and heat transfer characteristics reveal many interesting behaviors. These behaviors warrant further study of the effects of free convection on the flow and heat transfer characteristics.

Fourth order non-linear systems arising in combined free and forced convection flow of a second order fluid

Solutions to the fourth-order non-linear systems arising in combined free and forced convection flow of a second-order fluid, over a stretching sheet, are obtained. Existence (or non-existence) and uniqueness (or non-uniqueness) results of the problem are obtained and discussed. Moreover, ranges of parametric values are obtained for which the system has a unique pair of solutions, a double pair of solutions, and infinitely many monotonically decaying solutions at infinity.

Fluid flow and heat transfer in horizontal wavy channels

SummaryThe equations governing the fluid flow and heat transfer have been solved subject to the relevant boundary conditions by assuming that the solution consists of two parts: a mean part and a perturbed part. To obtain the perturbed part of the solution, use has been made of the long-wave approximation. The mean part of the solution has been found to be in good agreement with that of the plane Poiseuille flow. The perturbed part of the solution is the contribution from the waviness of the walls. The mean part, the perturbed part and the total solution of the problem have been evaluated numerically for several sets of values of the parameters. Certain qualitatively interesting properties of the fluid flow and heat transfer, along with the changes in the fluid pressure on the wavy walls, are recorded in § § 5 and 6.ZusammenfassungDie Grundgleichungen des Problems werden für das Stromfeld und den Wärmeübergang unter den gegebenen Randbedingungen gelöst. Dabei wird angenommen, daß die Lösung aus zwei Anteilen besteht: einem Mittelwert und den Störgrößen. Der Störanteil wird ermittelt durch eine Approximation im Sinne langer Wellen. Der Mittelwert des Stromfeldes stimmt gut mit der ebenen Poiseuille-Strömung überein. Der Störanteil rührt von der Welligkeit der Wände her. Die Gesamtströmung wurde numerisch für zahlreiche Werte der eingehenden Parameter bestimmt. Zahlreiche interessante Eigenschaften der Strömungsgrößen sowie des Wärmeüberganges sowie der Druckverteilung längs der welligen Wand werden in § § 5 und 6 besprochen.

Existence and nonuniqueness of solutions of a singular nonlinear boundary-layer problem

Abstract Sufficient conditions for existence and nonuniqueness of positive solutions of the singular boundary value problem g ( x ) g ″( x ) + h ( x ) = 0, − k ⩽ x k > 0, g ′(− k ) = C , g (1) = 0 are obtained. Also, it is proved that the solutions with g(−k) > −Ck ( for C and g(−k) > ( k 2 ) √ −2h(−k) ( for C > 0) are unique. Furthermore, it is shown numerically that for h ( x ) = x there are exactly two Solutions for the problem.

On solutions of some singular, non-Linear differential equations arising in boundary layer theory

Abstract Solutions for a class of singular, non-linear, second-order differential equations arising in boundary layer theory with suction/injection, when Crocco variables are employed, are obtained. Existence, uniqueness, and analyticity results are established for boundary conditions corresponding to flow of a uniform stream past a semi-infinite flat plate (classical problem of Blasius) and for the flow behind weak expansion. Since the standardization technique (in Refs. [8, 9, 11]) does not work, a new technique is developed and used in proving existence and uniqueness theorems. Furthermore, the analytical solutions are compared with the numerical ones.

Combined free and forced convection in hydromagnetic flows, in vertical wavy channels, with travelling thermal waves

Abstract Numerical results are presented (through graphs) for the stream function, temperature, and flow and heat transfer characteristics. These results are obtained by solving the coupled nonlinear partial differential equations describing the conservation of mass, momentum and energy by a perturbation technique. Two cases are studied; namely, the hydrodynamic (HD) case and the hydromagnetic (HM) case. Values of the stream function Ψ in the HD case are larger than those in the HM case. This qualitatively agrees with the expectations, since the magnetic field exerts a retarding force on the free convection flow. Furthermore, the stream function and the temperature field are more prominent in the presence of heat sources than in their absence.

The effect of variable fluid properties on the free convective flow of air/water confined between two parallel vertical walls

SummaryThe title problem has been considered for detailed analysis in view of its varied physical applications taking into account the temperature-dependent fluid properties. The governing equations of the problem have been reduced to two coupled nonlinear ordinary differential equations, which have been solved numerically by the Runge-Kutta method as modified by Gill. Several qualitatively interesting behaviours of the flow and heat transfer characteristics have been pointed out after making a comparative study of the VFP-results with the CFP-counterparts and some of them are presented in the Conclusion-section, which results warrant further study of the effect of variable fluid properties on the flow and heat transfer characteristics.ZusammenfassungDas angegebene Problem wurde studiert im Hinblick auf zahlreiche physikalische Anwendungen, in denen temperaturabhängige Stoffwerte auftreten. Die Grundgleichungen des Problems wurden auf zwei gekoppelte nichtlineare gewöhnliche Differentialgleichungen reduziert, die mit dem von Gill modifizierten Runge-Kutta-Verfahren gelöst wurden. Es werden zahlreiche interssante Eigenschaften der Stromfelder sowie des Wärmeüberganges aufgezeigt, insbesondere durch Vergleich der Einflüsse konstanter und variabler Stoffgrößen. Diese Resultate regen an, weitere Untersuchungen dieser Medien mit variablen Stoffgrößen im Hinblick auf Stromfeld und Wärmeübergang durchzuführen.

Hydromagnetic convection at a heated semi-infinite vertical plate

Abstract Numerical results are presented for the transient and steady-state velocity field, temperature field, and heat transfer characteristics. These results are obtained by solving the highly nonlinear partial differential equations describing the conservation of mass, momentum and energy (with variable fluid properties) by an explicit finite-difference method in time-dependent form. Two cases are studied, namely the hydromagnetic (HM) case and the hydrodynamic (HD) case. Values of the velocity components u and v (absolute) in the HD case are larger than those in the HM case. Quite opposite is the phenomenon in the case of the temperature field θ. Further, the velocity and temperature fields are more prominent in the presence of heat sources than in their absence. Numerical results indicate that the presence of magnetic field delays attainment of the steady-state condition. Furthermore, in the hydromagnetic case, it is observed that the variable fluid-property has almost negligible effect on the flow and heat transfer characteristics, which is contrary to that in the hydrodynamic case.