An Analytical Study of Creeping Flow of a Second-Order Fluid through a Small Diameter Leaky Tube with Linearly Diminishing Absorption

<div>Behavior of axial velocity <svg height="13.5711pt" id="M139" style="vertical-align:-4.935201pt" version="1.1" viewbox="-0.0498162 -8.6359 13.5016 13.5711" width="13.5016pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M715 650H476L470 622C550 619 562 610 562 570C562 536 553 481 535 384L523 321C485 121 408 37 283 37C178 37 99 109 134 297L178 532C193 612 199 616 278 622L284 650H29L23 622C105 616 109 609 94 532L48 291C23 160 51 83 98 40C143 -1 202 -16 260 -16C321 -16 387 3 439 49C509 111 542 204 563 312L577 384C595 479 608 533 619 569C629 603 637 620 709 622L715 650Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,8.606,3.132)"><path d="M443 689C443 696 439 701 427 701C388 701 338 667 299 636C236 640 219 678 219 695C219 710 226 721 233 730L208 744C164 729 134 695 134 672C134 635 185 597 258 594C148 500 24 351 24 186C24 82 71 43 140 21C159 15 179 9 202 4C244 -5 260 -26 260 -49C260 -96 218 -141 197 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133 369L158 548Z"></path></g></svg> and for different values of linear absorption parameter <span class="nowrap"><svg height="8.8423pt" id="M141" style="vertical-align:-0.2064009pt" version="1.1" viewbox="-0.0498162 -8.6359 6.25863 8.8423" width="6.25863pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M449 634C442 637 425 643 405 650C376 660 341 666 307 666C181 666 98 590 98 485C98 400 170 343 215 310L246 288C307 243 343 204 343 147C343 67 291 18 219 18C104 18 61 124 51 202L23 199C28 124 27 71 27 47C47 22 122 -16 204 -16C324 -16 428 60 428 174C428 256 379 309 307 360L276 382C223 419 179 455 179 516C179 576 221 632 293 632C379 632 410 564 418 487L448 490C446 536 446 592 449 634Z"></path></g></svg>.</span> (a) <span class="nowrap"><svg height="11.7782pt" id="M142" style="vertical-align:-3.42938pt" version="1.1" viewbox="-0.0498162 -8.34882 27.8238 11.7782" width="27.8238pt" 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Journal of Mathematics

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Figure 2

Figure 2: An Analytical Study of Creeping Flow of a Second-Order Fluid through a Small Diameter Leaky Tube with Linearly Diminishing Absorption 