Use of Finite Element Method for Free Convection of Nanofluids between a Rectangular Enclosure and a Sinusoidal Cylinder Using Buongiorno’s Two-Phase Model

<table class="table-group" id="tab2"><tr><td><table class="table"><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr class="thead"><td class="align_left">Mesh size</td><td class="align_center">Domain elements</td><td class="align_center"><span style="width: 24.1663ptpx;"><svg height="11.8174pt" id="M102" style="vertical-align:-3.1815pt" version="1.1" viewbox="-0.0498162 -8.6359 24.1663 11.8174" width="24.1663pt" 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="M699 659C666 654 622 640 595 610C579 591 569 572 562 530L552 472C530 342 504 307 403 302V529C403 604 411 617 483 622V650H238V622C310 617 318 604 318 529V302C232 308 194 347 172 471L161 531C153 573 145 592 131 609C103 643 59 654 25 659L15 632C62 611 63 583 73 524L85 452C97 383 116 347 155 316C199 282 255 269 318 267V122C318 46 310 33 233 28V0H489V28C412 33 403 46 403 122V267C470 269 518 283 559 315C599 346 618 378 632 450L646 519C658 580 665 608 709 632L699 659Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,8.32,3.132)"><path d="M810 0V30C751 35 744 40 744 106V296C744 396 694 451 614 451C583 451 558 438 537 425C512 409 485 391 454 368C434 420 390 451 342 451C309 451 285 439 260 424C228 405 206 387 185 372V453C141 434 90 421 43 413V386C102 378 105 373 105 309V106C105 41 96 35 29 30V0H243V30C194 35 185 41 185 106V335C216 360 256 389 297 389C357 389 384 348 384 275V106C384 41 374 35 312 30V0H530V30C475 35 465 41 465 104V294C465 313 464 324 463 336C502 367 539 389 576 389C637 389 663 346 663 274V109C663 41 653 35 593 30V0H810Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,15.909,3.132)"><path d="M138 535C169 535 191 560 191 589C191 620 168 644 139 644S85 620 85 589C85 560 110 535 138 535ZM257 0V30C192 35 185 43 185 109V453C142 435 94 422 40 414V386C101 378 104 372 104 311V109C104 41 97 35 33 30V0H257Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,18.412,3.132)"><path d="M532 0V30C473 38 467 38 467 107V298C467 395 416 451 336 451C307 451 279 439 251 420C226 404 205 389 185 374V453C142 434 94 422 43 413V386C98 378 104 373 104 309V107C104 41 100 38 31 30V0H251V30C191 35 185 40 185 107V337C216 364 255 389 295 389C360 389 386 347 386 276V110C386 44 380 35 321 30V0H532Z"></path></g></svg></span></td><td class="align_center"><span style="width: 17.9373ptpx;"><svg height="12.1044pt" id="M103" style="vertical-align:-0.2062998pt" version="1.1" viewbox="-0.0498162 -11.8981 17.9373 12.1044" width="17.9373pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><rect height="0.65243" width="17.8376" x="0" y="-11.1958"></rect><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M822 650H589L583 622C660 617 677 607 674 561C672 534 664 481 647 390L600 137H596L273 650H126L120 622C176 620 194 615 207 594C221 571 225 557 214 504L161 257C141 166 129 112 121 85C108 42 83 30 29 28L23 0H260L266 28C193 33 173 42 176 89C178 122 186 172 202 255L256 527H259L583 -8H612L690 390C708 481 720 535 728 558C744 603 756 619 816 622L822 650Z"></path></g><g transform="matrix(.013,0,0,-0.013,10.78,0)"><path d="M515 96L502 119C471 88 431 62 423 62C416 62 411 70 417 101C440 223 469 341 497 448H486L412 422L380 277C330 188 210 57 152 57C137 57 126 69 139 124L195 366C210 431 205 448 182 448C155 448 89 413 23 350L36 326C73 354 103 376 112 376C118 376 118 365 113 340L61 118C54 90 52 68 52 51C52 0 75 -12 98 -12S151 -3 181 17C242 58 305 119 362 193H364L345 104C323 3 339 -12 359 -12C390 -12 464 35 515 96Z"></path></g></svg></span></td><td class="align_center">CPU time (s)</td></tr><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr><td class="align_left">M1</td><td class="align_center">6329</td><td class="align_center">-3.3058</td><td class="align_center">6.7280</td><td class="align_center">37</td></tr><tr><td class="align_left">M2</td><td class="align_center">9063</td><td class="align_center">-3.2863</td><td class="align_center">6.7210</td><td class="align_center">60</td></tr><tr><td class="align_left">M3</td><td class="align_center">14127</td><td class="align_center">-3.2716</td><td class="align_center">6.7026</td><td class="align_center">169</td></tr><tr><td class="align_left">M4</td><td class="align_center">31000</td><td class="align_center">-3.2673</td><td class="align_center">6.7249</td><td class="align_center">214</td></tr><tr><td class="align_left">M5</td><td class="align_center">38498</td><td class="align_center">-3.2673</td><td class="align_center">6.7229</td><td class="align_center">351</td></tr><tr class="table-tr"><td colspan="5"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

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Advances in Mathematical Physics

tab2

Table 2

Table 2: Use of Finite Element Method for Free Convection of Nanofluids between a Rectangular Enclosure and a Sinusoidal Cylinder Using Buongiorno’s Two-Phase Model 

Table 2 | Use of Finite Element Method for Free Convection of Nanofluids between a Rectangular Enclosure and a Sinusoidal Cylinder Using Buongiorno’s Two-Phase Model 