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MHD stagnation point flow of micro nanofluid towards a shrinking sheet with convective and zero mass flux conditions

Rauf A., Shehzad S. A., Hayat T., Meraj M. A., Alsaedi A.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2017

Vol. 65, nr 2

155--162

In this article the stagnation point flow of electrically conducting micro nanofluid towards a shrinking sheet, considering a chemical reaction of first order is investigated. Involvement of magnetic field occurs in the momentum equation, whereas the energy and concentrations equations incorporated the influence of thermophoresis and Brownian motion. Convective boundary condition on temperature and zero mass flux condition on concentration are implemented. Partial differential equations are converted into the ordinary ones using suitable variables. The numerical technique is utilized to discuss the results for velocity, microrotation, temperature, and concentration fields.

On reflectionless equi-transmitting matrices

Kurasov P., Ogik R., Rauf A.

Opuscula Mathematica

2014

Vol. 34, no. 3

483--501

Reflectionless equi-transmitting unitary matrices are studied in connection to matching conditions in quantum graphs. All possible such matrices of size 6 are described explicitly. It is shown that such matrices form 30 six-parameter families intersected along 12 five-parameter families closely connected to conference matrices.