An Analytical Solution for Transient Heat Conduction in a Composite Slab with Time-Dependent Heat Transfer Coefficient

<table class="fixed-width table-group" id="tab1"><tr><td><table class="table"><colgroup><col style="width:9.09em"/><col style="width:5.61em"/><col style="width:5.44em"/></colgroup><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr class="thead"><td class="align_left">Fourier number <svg height="11.5564pt" id="M121" style="vertical-align:-2.26807pt" version="1.1" viewbox="-0.0498162 -9.28833 15.4319 11.5564" width="15.4319pt" 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="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z" id="g113-41"></path></g><g transform="matrix(.013,0,0,-0.013,4.498,0)"><path d="M471 456L444 459C426 433 414 430 388 430C324 430 270 434 216 434C103 434 51 374 23 338L43 317C96 366 146 380 221 375L154 109C149 86 147 68 147 52C147 4 168 -12 197 -12C240 -12 291 25 334 71L320 96C295 75 268 58 252 58C238 58 227 79 238 138C251 211 272 296 292 372C310 372 332 368 350 368C391 368 421 369 434 371C444 388 455 413 471 456Z" id="g113-241"></path></g><g transform="matrix(.013,0,0,-0.013,10.78,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z" id="g113-42"></path></g></svg></td><td class="align_center">1</td><td class="align_center">4</td></tr><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr><td class="align_left">Error</td><td class="align_center">2.08 × 10<sup>−3</sup></td><td class="align_center">1.39 × 10<sup>−4</sup></td></tr><tr class="table-tr"><td colspan="3"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Mathematical Problems in Engineering

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Table 1

Table 1: An Analytical Solution for Transient Heat Conduction in a Composite Slab with Time-Dependent Heat Transfer Coefficient 