Entropy Generation Analysis of Power-Law Non-Newtonian Fluid Flow Caused by Micropatterned Moving Surface

<table>Local Nusselt number as function of <svg height="11.175" id="M151" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 13.3125 11.175" width="13.3125" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg> for various values of <svg height="17.4" id="M152" style="vertical-align:-3.21404pt" version="1.1" viewbox="0 0 20.137501 17.4" width="20.137501" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.162)"><path d="M619 670q0 -13 -9 -26t-18 -19q-13 -10 -25 2q-36 38 -66 38q-31 0 -54.5 -50t-45.5 -185h120l-20 -31l-107 -12q-23 -138 -57 -293q-27 -122 -55 -184.5t-75 -109.5q-60 -61 -114 -61q-25 0 -47.5 15t-22.5 31q0 17 31 44q11 8 20 -1q10 -11 31 -19t35 -8q26 0 47 19
q34 34 71 253l54 315h-90l-3 12l31 30h70q28 138 90 204q35 37 75 57.5t70 20.5q26 0 45 -14t19 -28z" id="x1D453"></path></g>
<g transform="matrix(.012,-0,0,-.012,10.975,17.2)"><path d="M689 332q0 -81 -40 -161.5t-103.5 -131.5t-127.5 -51q-32 0 -58.5 16t-40.5 46q-70 -62 -139 -62q-45 0 -77.5 30t-32.5 86q0 8 7 52q11 77 45 187q6 19 6 34q0 6 -7 6q-24 0 -78 -64l-20 23q32 48 73 77t78 29q32 0 32 -43q0 -30 -12 -73q-27 -95 -38 -152
q-8 -44 -8 -58q0 -77 68 -77q31 0 60 33.5t39 77.5l62 260l75 16l5 -6l-63 -246q-8 -29 -8 -58q0 -77 68 -77q66 0 116 75.5t50 194.5q0 43 -12 57q-11 12 -11 24q0 19 15 35.5t34 16.5q18 0 30.5 -34.5t12.5 -81.5z" id="x1D464"></path></g>
</svg> when <svg height="11.125" id="M153" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 48.275002 11.125" width="48.275002" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,10.862)"><path d="M495 86q-46 -47 -87 -72.5t-63 -25.5q-43 0 -16 107l49 210q7 34 8 50.5t-3 21t-13 4.5q-35 0 -109.5 -72.5t-115.5 -140.5q-21 -75 -38 -159q-50 -10 -76 -21l-6 8l84 340q8 35 -4 35q-17 0 -67 -46l-15 26q44 44 85.5 70.5t64.5 26.5q35 0 10 -103l-24 -98h2
q42 56 97 103.5t96 71.5q46 26 74 26q9 0 16 -2.5t14 -11.5t9.5 -24.5t-1 -44t-13.5 -68.5q-30 -117 -47 -200q-4 -19 -3.5 -25t6.5 -6q21 0 70 48z" id="x1D45B"></path></g><g transform="matrix(.017,-0,0,-.017,13.305,10.862)"><path d="M535 323h-483v50h483v-50zM535 138h-483v50h483v-50z" id="x3D"></path></g><g transform="matrix(.017,-0,0,-.017,28.008,10.862)"><path d="M241 635q53 0 94 -28.5t63.5 -76t33.5 -102.5t11 -116q0 -58 -11 -112.5t-34 -103.5t-63.5 -78.5t-94.5 -29.5t-95 28t-64.5 75t-34.5 102.5t-11 118.5q0 58 11.5 112.5t34.5 103t64.5 78t95.5 29.5zM238 602q-32 0 -55.5 -25t-35.5 -68t-17.5 -91t-5.5 -105
q0 -76 10 -138.5t37 -107.5t69 -45q32 0 55.5 25t35.5 68.5t17.5 91.5t5.5 105t-5.5 105.5t-18 92t-36 68t-56.5 24.5z" id="x30"></path></g><g transform="matrix(.017,-0,0,-.017,36.168,10.862)"><path d="M113 -12q-24 0 -39.5 16t-15.5 42q0 24 16 40.5t40 16.5t40 -16.5t16 -40.5q0 -26 -16 -42t-41 -16z" id="x2E"></path></g><g transform="matrix(.017,-0,0,-.017,40.044,10.862)"><path d="M249 635q70 0 116 -43t46 -105q0 -46 -28 -80q-22 -25 -80 -64q62 -35 97 -75t35 -99q0 -81 -63 -131t-135 -50q-83 0 -137.5 45.5t-54.5 123.5q0 52 45 95q29 28 89 64q-109 62 -109 155q0 66 50.5 115t128.5 49zM238 603q-42 0 -67.5 -31t-25.5 -72q0 -50 32.5 -79.5
t98.5 -62.5q61 48 61 124q0 59 -29.5 90t-69.5 31zM248 20q46 0 76.5 33.5t30.5 89.5q0 50 -39 85.5t-110 71.5q-81 -54 -81 -137q0 -67 35.5 -105t87.5 -38z" id="x38"></path></g>
</svg>, <svg height="11.125" id="M154" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 46.112499 11.125" width="46.112499" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,10.862)"><path d="M352 391q0 -31 -27 -44q-14 -7 -24 6q-39 48 -84 48q-23 0 -39.5 -15t-16.5 -40q0 -43 73 -90q49 -32 70 -58t21 -57q0 -58 -62 -105.5t-129 -47.5q-40 0 -75.5 25t-35.5 52q0 28 32 46q7 4 15 3t11 -6q19 -31 48.5 -50.5t54.5 -19.5q34 0 54 19.5t20 42.5q0 43 -65 81
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q0 -76 10 -138.5t37 -107.5t69 -45q32 0 55.5 25t35.5 68.5t17.5 91.5t5.5 105t-5.5 105.5t-18 92t-36 68t-56.5 24.5z" id="x30"></path></g><g transform="matrix(.017,-0,0,-.017,34.009,10.862)"><path d="M113 -12q-24 0 -39.5 16t-15.5 42q0 24 16 40.5t40 16.5t40 -16.5t16 -40.5q0 -26 -16 -42t-41 -16z" id="x2E"></path></g><g transform="matrix(.017,-0,0,-.017,37.885,10.862)"><path d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z" id="x31"></path></g>
</svg>, <svg height="17.9125" id="M155" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 52.450001 17.9125" width="52.450001" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,17.65)"><path d="M480 416q0 -21 -18 -41q-9 -11 -17 -7q-20 9 -42 9q-62 0 -140 -78q23 -69 88 -192q17 -31 27 -42t20 -11q16 0 62 46l17 -20q-64 -92 -119 -92q-35 0 -70 66q-41 73 -84 187q-36 -30 -62 -61q-27 -115 -35 -172q-41 -8 -78 -20l-6 6l140 612q7 28 0.5 34t-37.5 7l-34 1
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<g transform="matrix(.012,-0,0,-.012,8.612,9.488)"><path d="M227 744l-123 -338l-31 15l73 368q12 3 41.5 -8t36.5 -20z" id="x2032"></path></g>
<g transform="matrix(.017,-0,0,-.017,17.488,17.65)"><path d="M535 323h-483v50h483v-50zM535 138h-483v50h483v-50z" id="x3D"></path></g><g transform="matrix(.017,-0,0,-.017,32.174,17.65)"><path d="M241 635q53 0 94 -28.5t63.5 -76t33.5 -102.5t11 -116q0 -58 -11 -112.5t-34 -103.5t-63.5 -78.5t-94.5 -29.5t-95 28t-64.5 75t-34.5 102.5t-11 118.5q0 58 11.5 112.5t34.5 103t64.5 78t95.5 29.5zM238 602q-32 0 -55.5 -25t-35.5 -68t-17.5 -91t-5.5 -105
q0 -76 10 -138.5t37 -107.5t69 -45q32 0 55.5 25t35.5 68.5t17.5 91.5t5.5 105t-5.5 105.5t-18 92t-36 68t-56.5 24.5z" id="x30"></path></g><g transform="matrix(.017,-0,0,-.017,40.334,17.65)"><path d="M113 -12q-24 0 -39.5 16t-15.5 42q0 24 16 40.5t40 16.5t40 -16.5t16 -40.5q0 -26 -16 -42t-41 -16z" id="x2E"></path></g><g transform="matrix(.017,-0,0,-.017,44.21,17.65)"><path d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z" id="x31"></path></g>
</svg>, <svg height="11.375" id="M156" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 43.424999 11.375" width="43.424999" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.112)"><path d="M46 650h247q112 0 169 -41q64 -49 64 -141q0 -91 -56.5 -143t-138.5 -62q-23 -3 -45 -1l-74 19v-157q0 -63 15.5 -77t83.5 -19v-28h-271v28q60 5 74 20t14 77v400q0 65 -12.5 79t-69.5 18v28zM212 559v-245q31 -12 73 -12q59 0 102 38t43 124q0 77 -42.5 115.5
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</svg>, and <svg height="11.375" id="M157" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 56.674999 11.375" width="56.674999" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.112)"><path d="M517 162l29 -4q-18 -100 -35 -158h-482v28q68 5 83.5 20t15.5 77v398q0 66 -13 80t-73 19v28h446q0 -8 8 -144l-29 -4q-11 51 -32 85q-11 17 -35 23t-78 6h-76q-23 0 -28 -5t-5 -27v-228h94q67 0 83 12t25 63h29v-191h-29q-10 54 -26 65.5t-81 11.5h-95v-189
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</svg>.</table>

Mathematical Problems in Engineering

fig8

Figure 8

Figure 8: Entropy Generation Analysis of Power-Law Non-Newtonian Fluid Flow Caused by Micropatterned Moving Surface 