Numerical Study of Heat Transfer in Trefoil Buried Cable with Fluidized Thermal Backfill and Laying Parameter Optimization

<div>Variations of <svg height="12.584pt" id="M30" style="vertical-align:-3.29567pt" version="1.1" viewbox="-0.0498162 -9.28833 18.404 12.584" width="18.404pt" 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="M480 416C480 431 465 448 438 448C388 448 312 383 252 330C217 299 188 273 155 237H153L257 680C262 700 263 712 253 712C240 712 183 684 97 674L92 648L126 647C166 646 172 645 163 606L23 -6L29 -12C51 -5 77 2 107 8C115 62 130 128 142 180C153 193 179 220 204 241C231 170 259 106 288 54C317 0 336 -12 358 -12C381 -12 423 2 477 80L460 100C434 74 408 54 398 54C385 54 374 65 351 107C326 154 282 241 263 299C296 332 351 377 403 377C424 377 436 372 445 368C449 366 456 368 462 375C472 386 480 402 480 416Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.474,3.132)"><path d="M731 650H485V618C556 614 580 601 585 558C588 530 592 485 592 390V153H589L173 650H22V618C69 614 92 606 112 582C131 558 132 555 132 483V266C132 175 129 128 125 96C120 49 95 36 36 33V0H281V33C212 36 188 50 183 98C180 129 177 175 177 266V510H179L603 -9H638V390C638 483 640 530 644 561C649 602 674 615 731 618V650Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,13.335,3.132)"><path d="M416 501L399 642C356 655 314 665 271 665C140 665 63 582 63 486C63 372 163 325 229 290C304 250 359 217 359 142C359 70 316 25 240 25C138 25 94 125 78 186L44 178C52 123 64 45 72 21C81 16 96 8 121 0S179 -15 220 -15C353 -15 445 68 445 176C445 289 350 335 270 375C191 414 143 449 143 520C143 572 177 627 253 627C340 627 366 556 382 495L416 501Z"></path></g></svg> and <svg height="12.4698pt" id="M31" style="vertical-align:-3.18147pt" version="1.1" viewbox="-0.0498162 -9.28833 23.2268 12.4698" width="23.2268pt" 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="M480 416C480 431 465 448 438 448C388 448 312 383 252 330C217 299 188 273 155 237H153L257 680C262 700 263 712 253 712C240 712 183 684 97 674L92 648L126 647C166 646 172 645 163 606L23 -6L29 -12C51 -5 77 2 107 8C115 62 130 128 142 180C153 193 179 220 204 241C231 170 259 106 288 54C317 0 336 -12 358 -12C381 -12 423 2 477 80L460 100C434 74 408 54 398 54C385 54 374 65 351 107C326 154 282 241 263 299C296 332 351 377 403 377C424 377 436 372 445 368C449 366 456 368 462 375C472 386 480 402 480 416Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.474,3.132)"><path d="M502 500C497 551 492 613 491 650H43V617C122 612 130 606 130 521V129C130 45 122 38 41 33V0H319V33C227 38 217 45 217 129V305H319C411 305 413 295 427 225H461V421H427C414 357 411 348 319 348H217V580C217 609 219 612 250 612H330C401 612 423 605 439 578C452 557 458 539 467 496L502 500Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,11.388,3.132)"><path d="M601 496C596 555 591 627 591 675H567C551 656 544 650 516 650H120C91 650 79 651 64 675H41C38 619 34 555 29 492H63C75 537 83 566 96 582C110 604 128 612 207 612H272V126C272 46 264 38 170 33V0H464V33C368 38 359 48 359 126V612H430C502 612 520 605 535 582C547 566 556 541 567 492L601 496Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,17.103,3.132)"><path d="M384 354C435 370 515 408 515 502C515 549 494 593 459 616C426 639 384 650 308 650H45V618C127 613 130 606 130 524V127C130 45 125 38 37 33V0H262C342 0 409 12 461 40C521 73 558 124 558 192C558 295 481 336 384 352V354ZM217 365V556C217 587 221 597 229 604C238 611 261 615 288 615C382 615 421 558 421 490C421 406 374 365 266 365H217ZM217 327H264C384 327 457 284 457 183C457 80 383 38 301 38C235 38 217 55 217 127V327Z"></path></g></svg> with temperature.</div>

Mathematical Problems in Engineering

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Figure 3

Figure 3: Numerical Study of Heat Transfer in Trefoil Buried Cable with Fluidized Thermal Backfill and Laying Parameter Optimization 