# zbMATH — the first resource for mathematics

##### Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
Hydromagnetic flow of fluid with variable viscosity in a uniform tube with peristalsis. (English) Zbl 1032.92011

Summary: We formulate the problem under an infinitely long wavelength approximation, a negligible Reynolds number and a small magnetic Reynolds number. We decide on a perturbation method of solution. The viscosity parameter $\alpha \ll 1$ is chosen as a perturbation parameter. The governing equations are developed up to first-order in the viscosity parameter $\left(\alpha \right)$. The zero-order system yields the classical Poiseuille flow when the Hartmann number $M$ tends to zero.

For the first-order system, we simplify a complicated group of products of Bessel functions by approximating the polynomials. The results show that the increasing magnetic field increases the pressure rise. In addition, the pressure rise increases as the viscosity parameter decreases at zero flow rate. Moreover, it is independent of the Hartmann number and viscosity parameter at certain values of the flow rate. We make comparisons with other studies.

##### MSC:
 92C35 Physiological flows 92C05 Biophysics 92C50 Medical applications of mathematical biology