Analytic Approximate Solutions for Unsteady Two-Dimensional and Axisymmetric Squeezing Flows between Parallel Plates

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</svg>) for
the axisymmetric and two-dimensional
cases, when <svg height="12.4375" id="M115" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 58.487499 12.4375" width="58.487499" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg>. From <svg height="14.2125" id="M116" style="vertical-align:-1.59703pt" version="1.1" viewbox="0 0 63.150002 14.2125" width="63.150002" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg> the series solution for <svg height="12.4375" id="M117" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 58.487499 12.4375" width="58.487499" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.162)"><path d="M499 88q-41 -46 -83.5 -73t-68.5 -27q-41 0 -19 98l52 225q10 43 8 59.5t-16 16.5q-37 0 -112 -65t-117 -135q-14 -42 -38 -179q-36 -7 -75 -20l-7 8l112 522h-84l11 39h81l7 33q8 40 2.5 49t-35.5 9h-35l5 25q36 3 71.5 13t56.5 18t25 8q11 0 3 -38l-25 -117h165
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</svg> converges in the whole region <svg height="12.1125" id="M118" style="vertical-align:-0.546pt" version="1.1" viewbox="0 0 71.5 12.1125" width="71.5" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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t30 -51.5t49 -42.5t67 -16q56 0 88 32.5t32 87.5q0 51 -31.5 82t-98.5 67q-80 44 -110 73q-55 53 -55 124q0 75 56 126.5t150 51.5q53 0 126 -23z" id="x53"></path></g><g transform="matrix(.017,-0,0,-.017,40.418,11.363)"><path d="M531 71l-474 214v50l474 215v-56l-416 -184l416 -183v-56zM531 -40h-474v50h474v-50z" id="x2264"></path></g><g transform="matrix(.017,-0,0,-.017,55.121,11.363)"><path d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z" id="x31"></path></g><g transform="matrix(.017,-0,0,-.017,63.281,11.363)"><path d="M241 635q53 0 94 -28.5t63.5 -76t33.5 -102.5t11 -116q0 -58 -11 -112.5t-34 -103.5t-63.5 -78.5t-94.5 -29.5t-95 28t-64.5 75t-34.5 102.5t-11 118.5q0 58 11.5 112.5t34.5 103t64.5 78t95.5 29.5zM238 602q-32 0 -55.5 -25t-35.5 -68t-17.5 -91t-5.5 -105
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</svg>.</table>

Mathematical Problems in Engineering

fig7

Figure 7

Figure 7: Analytic Approximate Solutions for Unsteady Two-Dimensional and Axisymmetric Squeezing Flows between Parallel Plates 