Magnetohydrodynamic flow and heat transfer about a rotating disk with suction and injection at the disk surface

Abstract

This paper studies the effects of an axial magnetic field on the flow and heat transfer about a porous rotating disk. Using modern quasi-Newton and globally convergent homotopy methods, numerical solutions are obtained for a wide range of magnetic field strengths and injection and suction velocities. Results are presented graphically in terms of three nondimensional parameters. There is excellent agreement with previous work and asymptotic formulas.

Thermal radiation effects on the time-dependent MHD permeable flow having variable viscosity

“…These are compared with those steady state calculations of [27]. Numerical values of H(N) and Àq 0 (0) are tabulated in Table 2 between the steady state results corresponding to system (6)e(9) for M ¼ 0.5 and Pr ¼ 1.0 and those of Kumar et al [9]. Excellent agreements can be observed from Tables for the considered parameters, pointing to the fact that our numerical procedure is free of numerical errors.…”

“…It should be noticed that, a discontinuity is present between initial values and boundary conditions in (8) and (9). Unlike to the finite-difference techniques as employed in [7,24] which are not so powerful in dealing with such singularities, a better algorithm based on the fully implicit time-stepping method was proposed in [22].…”

“…Hossain et al [7] and Maleque and Sattar [8] investigated the influence of variable properties on the physical quantities of the rotating disk problem by obtaining a self-similar solution of the Navier-Stokes equations along with the energy equation. Kumar et al [9] and Turkyilmazoglu [10] covered the effects of a uniform external magnetic field on the steady flow over a rotating disk. For the flow and heat transfer characteristics over rotor-rotator and rotating disk systems, one can refer to the books [11e13].…”

Globally convergent homotopy algorithms for nonlinear systems of equations

“…While predicting the best algorithm for a given problem is risky, some general rules of thumb are: the ODE-based algorithm is the most robust but the most expensive; if the zero curve y has very sharp turns (it doesn't for this problem) then the ODE-based algorithm is the best: if the Jacob(an matrices are very expensive to evaluate (they aren't for this problem) then the quasi-Newton augmented Jacob(an scheme is best: otherwise the normal flow algorithm is best. The values H(~) are from [16], and r can be inferred from n, k, and the breakpoint sequence ~, listed above. The integrals in (1441 were computed by 10-point Gauss(an quadrature over each subinterval, and are thus essentially exact.…”

A class of exact solutions for the incompressible viscous magnetohydrodynamic flow over a porous rotating disk

“…Because the vertically applied magnetic field can strongly influence the character of the flow and temperature fields, a number of researches were also devoted to this subject, amongst them are the analytical and numerical investigations of Refs. [36][37][38][39][40][41][42][43].…”