Forced Convection with Laminar Pulsating Flow in a Saturated Porous Channel or Tube

Abstract

A perturbation approach is used to obtain analytical expressions for the velocity, temperature distribution, and transient Nusselt number for the problem of forced convection, in a parallel-plates channel or a circular tube occupied by a saturated porous medium modeled by the Brinkman equation, produced by an applied pressure gradient that fluctuates with small amplitude harmonically in time about a non-zero mean. It is shown that the fluctuating part of this Nusselt number alters in magnitude and phase as the dimensionless frequency increases. The magnitude increases from zero, goes through a peak, and then decreases to zero. The height of the peak decreases as the modified Prandtl number increases. The phase (relative to that of the steady component) decreases from π/2 to −π/2. The height of the peak at first increases, goes through a maximum, and then decreases as the Darcy number decreases.

Forced Convection with Laminar Pulsating Counterflow in a Saturated Porous Circular Tube

“…In particular, we confirmed the results shown in Fig. 6 of Kuznetsov and Nield (2006) and in Fig. 3b of Kuznetsov and Nield (2008).…”

“…We tested our Mathematica code using the results for special cases available in Kuznetsov and Nield (2006) (for a single layer, ξ = 1) and Kuznetsov and Nield (2008) (for the nonpulsating case). In particular, we confirmed the results shown in Fig.…”

“…All of these studies are concerned with a time-independent applied pressure gradient, and consequently Nield and Kuznetsov (2007) and Kuznetsov and Nield (2006) broke new ground in discussing an applied pressure gradient that varies harmonically with time about a non-zero mean. Pulsating flow is of practical importance in biology (because of heart beating; see, for example, Han et al 2005), automotive industry (simulation of exhaust from I.C.…”

Heat Transfer Characteristics of Reciprocating Flows in Channels Partially Filled with Porous Medium

“…Due to the importance of pulsating flows especially in biological applications (such as blood flow in vessels), fundamental studies of unidirectional pulsating flows have been conducted in empty channels as well as channels saturated with a porous medium. (Kuznetsov and Nield 2006;Nield and Kuznetsov 2007).…”

The Starting Flow in Ducts Filled with a Darcy–Brinkman Medium

“…Al-Nimr and Alkam (2000) considered the starting flow in a circular (and annular) duct, but their solutions are in error. Only recently Kuznetkov and Nield (2006) successfully solved the oscillatory flow in a parallel plate channel and in a circular tube. In the present paper we present the solutions to the transient starting flow in a porous channel, a circular duct, and a rectangular duct.…”