A study on heat transfer in a second‐grade fluid through a porous medium with the modified differential transform method

This study investigates the boundary‐layer flow and heat transfer characteristics in a second‐grade fluid through a porous medium. The similarity transformation for the governing equations gives a system of nonlinear ordinary differential equations which are analytically solved by the differential transform method (DTM) and the DTM‐Padé. The DTM‐Padé is a combination of the DTM and the Padé approximant. The convergence analysis elucidates that the DTM does not give accurate results for large values of independent variables. Hence the DTM is not applicable for the solution of boundary‐layer flow problems having boundary conditions at infinity. Comparison between the solutions obtained by the DTM and the DTM‐Padé with numerical solution (fourth‐order Runge–Kutta with shooting method) illustrates that the DTM‐Padé is the most effective method for solving the problems that have boundary conditions at infinity. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21030     

HALL EFFECTS ON UNSTEADY FLOW DUE TO NON-COAXIALLY ROTATING DISK AND A FLUID AT INFINITY

An investigation is made on the unsteady magnetohydrodynamic (MHD) flow caused by the non-coaxial rotation of a disk and a fluid at infinity being permeated by a transverse magnetic field. The disk is porous and nonconducting and executes oscillations in its own plane. The Laplace transform method is used to obtain the exact solution of the velocity field. The structure of the steady and unsteady flow fields is investigated. It is shown that the ultimate steady-state blowing solution is established in the presence of Hall current also for resonant frequency, which was not possible in the hydrodynamic case. The combined effects of Hall current, rotation, and suction or blowing are examined. The physical significance of mathematical results is given with various limiting cases.     

Online ice crystal size measurements during sorbet freezing by means of the focused beam reflectance measurement (FBRM) technology. Influence of operating conditions

In ice cream and sorbet manufacturing small ice crystals are desired to deliver a product with a smooth texture and good palatability. This research studied the influence of the operating conditions on the ice crystal size and the draw temperature of the sorbet during the freezing process. The evolution of ice crystal size was tracked with the focused beam reflectance measurement (FBRM) technique, which uses an in situ sensor that makes it possible to monitor online the chord length distribution (CLD) of ice crystals in sorbets containing up to 40% of ice. The refrigerant fluid temperature had the most significant influence on the mean ice crystal chord length, followed by the dasher speed, whereas the mix flow rate had no significant influence. A decrease in the refrigerant fluid temperature led to a reduction in ice crystal size, due to the growth of more small ice crystals left behind on the scraped wall from previous scrapings. Increasing the dasher speed slightly reduced the mean ice crystal chord length, due to the production of new small ice nuclei by secondary nucleation. For a given refrigerant fluid temperature and dasher speed, low mix flow rates resulted in lower draw temperatures, due to the fact that the product remains in contact with the freezer wall longer. High dasher speeds warmed the product slightly, due to the dissipation of frictional energy in the product, the effect of which was in part moderated by the improvement in the heat transfer coefficient between the product and the freezer wall.     

Group theory transformation for Soret and Dufour effects on free convective heat and mass transfer with thermophoresis and chemical reaction over a porous stretching surface in the presence of heat source/sink

The group theoretic method is applied for solving the problem of combined effect of thermal diffusion and diffusion thermo on free convective heat and mass transfer over a porous stretching surface in the presence of thermophoresis particle deposition with variable stream conditions. The application of one-parameter groups reduces the number of independent variables by one and consequently, the system of governing partial differential equations with the boundary conditions reduces to a system of ordinary differential equations with appropriate boundary conditions. The equations along with the boundary conditions are solved numerically by using Runge Kutta Gill integration scheme with shooting technique. Impact of Soret and Dufour effects in the presence of thermophoresis particle deposition with chemical reaction plays an important role on the flow field. The results thus obtained are presented graphically and discussed.     

INFLUENCE OF HEAT TRANSFER IN THE SQUEEZING FLOW BETWEEN PARALLEL DISKS

This article addresses the squeezing flow and heat transfer between parallel disks when one disk is impermeable and the other is porous. Appropriate similarity transformations are invoked to convert the partial differential equations into ordinary ones. Expressions for velocity and temperature fields have been obtained by homotopy analysis method (HAM). The effects of embedding parameters such as squeeze number (S), Hartman number (M), Prandtl number (Pr), and Eckert number (Ec) are analyzed through graphs for the velocity and temperature profiles and tables for skin friction coefficient and local Nusselt number. It is observed that the series solutions are convergent only at third-order of approximation. The obtained results for velocity are also compared with the homotopy perturbation method (Domairry and Aziz, 2009).     

INFLUENCE OF AN INDUCED MAGNETIC FIELD ON PERISTALTIC TRANSPORT IN AN ASYMMETRIC CHANNEL

In this study, we investigate the effects of an induced magnetic field on the peristaltic transport of a Phan-Thien-Tanner (PTT) fluid in an asymmetric channel. Asymmetry in the flow is induced because of wave trains with different amplitudes and phases. Development of mathematical analysis is made under long wavelength and low Reynolds number approximations. Explicit expressions of stream function, pressure gradient, magnetic force function, axial induced magnetic field, and current density are derived. Computation of pressure rise is based upon numerical integration. The obtained expressions are carefully analyzed through physical interpretation.     

Influence of thermal radiation on the boundary layer flow due to an exponentially stretching sheet

The effect of radiation on the boundary layer flow and heat transfer of a viscous fluid over an exponentially stretching sheet is studied. The homotopy analysis method (HAM) is employed to determine the convergent series expressions of velocity and temperature. The physical interpretation to these expressions is assigned through graphs. It is found that the effects of Prandtl and radiation numbers on the temperature are opposite.