Analytical Formulation for Temperature Evolution in Flat Wheel-Rail Sliding Surfaces

<div>Pure sliding of a wheel onto rail, wheel flat on wheel tread, and sliding surface on rail. Heat generated during sliding (<span class="nowrap"><svg height="10.786562pt" id="M35" style="vertical-align:-2.150657pt" version="1.1" viewbox="-0.049816 -8.635905 9.520831 10.786562" width="9.520831pt" 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 368C699 549 574 666 407 666C186 666 23 488 23 277C23 113 129 -3 288 -13L307 -26C431 -111 501 -139 533 -147C559 -154 613 -163 658 -164L666 -141C597 -111 507 -66 430 -11L416 -1C580 42 699 190 699 368ZM601 371C601 227 518 54 381 22L354 40L278 24C175 47 120 145 120 269C120 451 235 631 398 631C540 631 601 521 601 371Z"></path></g></svg>)</span> enters equally into wheel and rail. Due to temperature difference between wheel and rail, a secondary heat (<span class="nowrap"><svg height="13.586775pt" id="M36" style="vertical-align:-2.150657pt" version="1.1" viewbox="-0.049816 -11.436118 13.316366 13.586775" width="13.316366pt" 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 368C699 549 574 666 407 666C186 666 23 488 23 277C23 113 129 -3 288 -13L307 -26C431 -111 501 -139 533 -147C559 -154 613 -163 658 -164L666 -141C597 -111 507 -66 430 -11L416 -1C580 42 699 190 699 368ZM601 371C601 227 518 54 381 22L354 40L278 24C175 47 120 145 120 269C120 451 235 631 398 631C540 631 601 521 601 371Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,9.421,-5.741)"><path d="M310 541L304 571C290 586 211 619 185 610L80 76L131 52L310 541Z"></path></g></svg>)</span> transfers from wheel into rail.</div>

Mathematical Problems in Engineering

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Figure 1

Figure 1: Analytical Formulation for Temperature Evolution in Flat Wheel-Rail Sliding Surfaces 