Heat transfer in a peristaltic flow of MHD fluid with partial slip

In the present note, we have discussed the effects of partial slip on the peristaltic flow of a MHD Newtonian fluid in an asymmetric channel. The governing equations of motion and energy are simplified using a long wave length approximation. A closed form solution of the momentum equation is obtained by Adomian decomposition method and an exact solution of the energy equation is presented in the presence of viscous dissipation term. The expression for pressure rise is calculated using numerical integration. The trapping phenomena is also discussed. The graphical results are presented to interpret various physical parameter of interest. It is found that the temperature field decreases with the increase in slip parameter L, and magnetic field M, while with the increase in P_r and E_c, the temperature field increases.     

Slip flow on a microcylinder

This paper is concerned with uniform axial flow of a gas along a semi-infinite microcylinder in the slip regime. Following Glauert and Lighthill (Proc R Soc 230A:188–203, 1955), the effect of slip on the skin friction is investigated by employing an asymptotic series approach for large axial distances along the cylinder.     

Slip flow on a microcylinder

The purpose of this paper is to determine the heat transfer from a semi-infinite microcylinder under uniform axial flow in the slip regime. Following the treatments of Glauert and Lighthill (Proc Royal Soc 230A:188–203, 1955), and Crane (Ingenieur-Archiv 43:203–214, 1974), an asymptotic series solution is developed to account for the heat flux in terms of the Nusselt number for large axial distances along a cylinder maintained at constant temperature.     

Flow and heat transfer of a non-Newtonian fluid past a stretching sheet with partial slip

The entrained flow and heat transfer of a non-Newtonian third grade fluid due to a linearly stretching surface with partial slip is considered. The partial slip is controlled by a dimensionless slip factor, which varies between zero (total adhesion) and infinity (full slip). Suitable similarity transformations are used to reduce the resulting highly nonlinear partial differential equations into ordinary differential equations. The issue of paucity of boundary conditions is addressed and an effective second order numerical scheme has been adopted to solve the obtained differential equations even without augmenting any extra boundary conditions. The important finding in this communication is the combined effects of the partial slip and the third grade fluid parameter on the velocity, skin-friction coefficient and the temperature field. It is interesting to find that the slip and the third grade fluid parameter have opposite effects on the velocity and the thermal boundary layers.     

Stagnation slip flow and heat transfer over a nonlinear stretching sheet

Stagnation slip flow and heat transfer characteristics of a viscous fluid over a nonlinear stretching surface has been investigated. The governing partial differential equations are transformed to nonlinear ordinary differential equations using similarity transformations. The analytical solution of the nonlinear system is obtained in series form using the very efficient homotopy analysis method (HAM). Convergence of the series solution is shown explicitly. Important features of flow and heat transfer characteristics are plotted and discussed. Comparison is made with existing numerical results when the stagnation‐point and slip effects are excluded. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011     

Heat transfer in a growing vapor film

Zusammenfassung Es wird das Wachstum eines Dampffilms auf einer plötzlich erhitzten ebenen Fläche studiert. Der Effekt der Wärmestrahlung wird untersucht, und es zeigt sich, dass er von Bedeutung ist. In abwesenheit der Strahlung zeigt es sich, dass der Film mit der Quadratwurzel der Zeit zunimmt.     

Partial slip effects on the flow and heat transfer characteristics in a third grade fluid

This article looks at the slip effects on the flow and heat transfer of a third grade fluid past a porous plate. The resulting equations and boundary conditions are non-linear. The non-linear boundary condition is reduced into a linear one and a series solution of the problem is obtained using the homotopy analysis method (HAM). Variations of interesting parameters are seen on the velocity and temperature profiles.     

Simultaneous effects of slip and heat transfer on the peristaltic flow

Slip and heat transfer effects on the peristaltic flow in an asymmetric channel have been examined in this paper. The closed form solutions of momentum and energy equations are obtained for long wavelength and low Reynolds number approximations. Pumping and trapping phenomena are discussed by numerical integration. The variations of velocity and thermal slip parameters are particularly observed. Comparison of different wave forms for symmetric case is presented.     

Heat transfer and Reynolds' analogy in a turbulent flow with heat release

Zusammenfassung Es wird die Wärmeübertragung von und zu einer voll entwickelten, wärmeabgebenden, turbulenten Strömung in einem Rohr analysiert. Durch die Anwendung der Laplace-Transformation wird die partielle Randwertaufgabe der Temperaturverteilung in einem Rohr von kreisförmigem Querschnitt auf eine gewöhnliche Sturm-Liouvillesche Randwertaufgabe zurückgeführt. Die entsprechenden Eigenwerte und Eigenfunktionen können nun mittels des Ritzschen Verfahrens für verschiedene Werte der Prandtlschen und Reynoldsschen Zahlen berechnet werden.Die Verteilung der Temperatur und des Wärmeflusses entlang der Wand erhält man in Form einer Reihe, deren Glieder diese Eigenwerte und Eigenfunktionen enthalten. Durch Verallgemeinerung des Prandtlschen Wärmequellen-Satzes wird die Reynoldssche Analogie der Wärmeübertragung und der flüssigen Reibung für eine wärmeabgebende turbulente Strömung erweitert.Die genaue asymptotische Wärmefluss und Temperaturverteilung, die man erhält, gestattet eine Abschätzung des Fehlers, den man bei einer Anwendung der Ritzschen Methode und der daraus folgenden Reihenentwicklung erhalten würde. Diese Analyse kann für die wärmeabgebenden turbulenten Strömungen in Atomreaktoren angewendet werden.

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The results presented in this paper were obtained in the course of research sponsored by the Office of Scientific Research of the ARDC, US Air Force under Contract AF 18 (603)-104.     

Stagnation point flow and heat transfer over a non-linearly moving flat plate in a parallel free stream with slip

An analysis is presented for the steady boundary layer flow and heat transfer of a viscous and incompressible fluid in the stagnation point towards a non-linearly moving flat plate in a parallel free stream with a partial slip velocity. The governing partial differential equations are converted into nonlinear ordinary differential equations by a similarity transformation, which are then solved numerically using the function bvp4c from Matlab for different values of the governing parameters. Dual (upper and lower branch) solutions are found to exist for certain parameters. Particular attention is given to deriving numerical results for the critical/turning points which determine the range of existence of the dual solutions. A stability analysis has been also performed to show that the upper branch solutions are stable and physically realizable, while the lower branch solutions are not stable and, therefore, not physically possible.     

Heat transfer to magnetohydrodynamic flow in a flat duct

Zusammenfassung Die Untersuchung befasst sich mit der Wärmeübertragung von den Wänden eines flachwandigen Kanals auf eine elektrisch leitende Flüssigkeit bei erzwungener Laminarströmung und in Gegenwart eines quergerichteten Magnetfeldes. Betrachtet wird der Fall konstanter Wandtemperatur mit variierender innerer Wärmeentwicklung durch viskose und elektrische Energiedissipation. Die massgebende Differentialgleichung wird durch eine Differenzengleichung ersetzt und mit der elektronischen Rechenmaschine gelöst. Als Resultat wird die Nusseltzahl angegeben, für die Prandtlzahl 1, die Hartmannzahlen 0, 4, 10 und die Graetzzahlen von 10 bis 10 000, wobei die Kennzahlen für Zähigkeit und elektrische Feldstärke als Parameter auftreten.     

Heat transfer in a gas mixture between parallel plates

The one-dimensional steady-state heat flux and the temperature distribution in a rarefied gas mixture between two parallel plates with different temperatures are studied using the kinetic theory. The Boltzmann equation is solved by the projection method assuming that the gas consists of elastic hard spheres and the reflection from the surfaces is diffuse. The flow features are analyzed for a wide range of the Knudsen number. The molecular numerical densities of the components, the total temperature of the mixture, and the mixture heat flux are obtained. The behavior of the distribution functions for the components is discussed. A comparison with other authors’ results shows that the accuracy of the given method is good.     

Heat transfer in channel flow of a micropolar fluid

The study of heat transfer in channel flow has been done by previous authors for Newtonian and elastico-viscous fluids. It is the aim of the present paper to study the temperature profile for flow of a micropolar fluid in a channel induced by a constant axial pressure gradient, when the walls are maintained at constant temperatures. We have examined the effects of microrotation on the temperature profile and on the kinetic energy of the fluid. Three cases have been chosen by us for detailed study: (i) both the walls are maintained at different constant temperatures, (ii) both the walls are maintained at the same constant temperature, (iii) one wall is kept at a constant temperature and there is no heat flux at the other wall.     

Heat transfer in sliding of a plane-parallel layer over a base

An analytic solution of the thermal problem of friction for a plane-parallel layer–base tribosystem under conditions of incomplete thermal contact between contacting bodies is obtained. Asymptotics of the obtained solution for small and large values of time are determined. For the materials of a cermet layer–iron base friction pair, we investigate the influence of the thermal conductivity coefficient of the contact on the temperature distribution and intensity of a heat fluxes.     

Heat transfer of a generalized stretching/shrinking wall problem with convective boundary conditions

In this paper, we investigate the heat transfer of a viscous fluid flow over a stretching/shrinking sheet with a convective boundary condition. Based on the exact solutions of the momentum equations, which are valid for the whole Navier–Stokes equations, the energy equation ignoring viscous dissipation is solved exactly and the effects of the mass transfer parameter, the Prandtl number, and the wall stretching/shrinking parameter on the temperature profiles and wall heat flux are presented and discussed. The solution is given as an incomplete Gamma function. It is found the convective boundary conditions results in temperature slip at the wall and this temperature slip is greatly affected by the mass transfer parameter, the Prandtl number, and the wall stretching/shrinking parameters. The temperature profiles in the fluid are also quite different from the prescribed wall temperature cases.     

Dynamics of a two-layer beam with layer slip

A possible type of structural damping in mechanical systems when there is a distinct dependence of the oscillation decrement on the amplitude is investigated, using the example of the solution of a model problem on the oscillations of a two-layer beam. It is assumed that layer slip only occurs along the beam axis and that the layers together in the transverse direction. The interaction between the layers is of an elastic-friction form. The equations of motion of the beam in Timoshenko's form are numerically integrated using Godunov's difference scheme.