Transient Natural Convection in Porous Square Cavity Heated and Cooled on Adjacent Walls

<table>Variations of the local <svg height="15.4" id="M119" style="vertical-align:-3.39066pt" version="1.1" viewbox="0 0 28.5375 15.4" width="28.5375" 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="M719 650v-28q-43 -2 -62 -15t-22 -44q-6 -47 -6 -169v-403h-31l-426 524h-2v-251q0 -111 6 -169q4 -37 24 -50.5t72 -16.5v-28h-237v28q45 2 64.5 16t23.5 49q6 62 6 171v220q0 54 -3 68.5t-17 32.5q-16 19 -34.5 26.5t-54.5 10.5v28h147l418 -502h3v246q0 117 -7 166
q-4 34 -24.5 47t-73.5 15v28h236z" id="x4E"></path></g><g transform="matrix(.017,-0,0,-.017,12.693,11.112)"><path d="M518 50v-26q-32 -4 -77 -16l-37 -11t-33 -9l-6 6v71q-56 -42 -74 -52q-43 -25 -77 -25q-55 0 -89.5 36.5t-34.5 112.5v196q0 38 -6.5 48.5t-26.5 15.5l-28 6v23q19 1 72 7q59 9 71 11q-3 -31 -3 -145v-135q0 -113 88 -113q59 0 108 48v234q0 38 -8 49t-34 15l-36 6v23
q44 2 90 8q37 4 67 10v-334q0 -37 8.5 -47t38.5 -12z" id="x75"></path></g>
<g transform="matrix(.012,-0,0,-.012,21.712,15.187)"><path d="M499 88q-41 -46 -83.5 -73t-68.5 -27q-41 0 -19 98l52 225q10 43 8 59.5t-16 16.5q-37 0 -112 -65t-117 -135q-14 -42 -38 -179q-36 -7 -75 -20l-7 8l127 594q8 40 2.5 49t-35.5 9h-35l5 25q36 3 71.5 13t56.5 18t25 8q11 0 3 -38l-88 -417h2q77 102 195 167q44 24 79 24
q61 0 30 -130l-52 -220q-8 -33 4 -33q8 0 31 14.5t43 33.5z" id="x210E"></path></g>
</svg> and local <svg height="15.4" id="M120" style="vertical-align:-3.39066pt" version="1.1" viewbox="0 0 27.237499 15.4" width="27.237499" 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)"><use xlink:href="#x4E"></use></g><g transform="matrix(.017,-0,0,-.017,12.693,11.112)"><use xlink:href="#x75"></use></g>
<g transform="matrix(.012,-0,0,-.012,21.712,15.187)"><path d="M383 397q0 -32 -35 -49q-12 -6 -23 8q-37 45 -84 45t-90 -71q-40 -65 -40 -167q0 -57 22 -86t59 -29q38 0 81.5 24.5t69.5 51.5l16 -21q-44 -53 -104 -84t-109 -31q-56 0 -89.5 41t-33.5 117q0 61 30 124t79 105q33 28 81 50.5t86 22.5q34 0 59 -15.5t25 -35.5z" id="x1D450"></path></g>
</svg> on the hot and cold wall, respectively, for different <svg height="11.375" id="M121" style="vertical-align:-0.16379pt" version="1.1" viewbox="0 0 18.450001 11.375" width="18.450001" 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="M631 18l-4 -26q-24 0 -35 1q-57 3 -92.5 23t-69.5 68q-21 30 -101 160q-13 22 -30.5 31t-54.5 9h-32v-159q0 -63 14 -77.5t74 -19.5v-28h-262v28q62 5 76 19.5t14 77.5v402q0 62 -13 76t-73 19v28h248q109 0 159 -34q67 -42 67 -131q0 -115 -127 -172q27 -52 89 -144
q49 -71 81 -104q31 -36 72 -47zM212 316h48q73 0 108 29q55 42 55 124q0 76 -42 112t-104 36q-41 0 -54 -10q-11 -7 -11 -44v-247z" id="x52"></path></g><g transform="matrix(.017,-0,0,-.017,10.908,11.112)"><path d="M433 39l-85 -51q-27 0 -47 20q-16 16 -24 44q-5 -3 -24 -16.5t-27 -18.5t-23 -13.5t-25 -12t-19 -3.5q-52 0 -86 36.5t-34 85.5q0 71 81 99q128 43 155 65v17q0 54 -23 83.5t-62 29.5q-28 0 -45 -19t-29 -66q-7 -23 -29 -23q-15 0 -29 13t-14 30t31 40q25 19 68.5 40.5
t81.5 29.5q49 0 82 -27q45 -39 45 -123v-185q0 -60 35 -60q18 0 36 11zM275 84v156q-12 -6 -49 -23t-41 -19q-31 -14 -46 -31t-15 -43q0 -35 22.5 -55.5t48.5 -20.5q19 0 42 10.5t38 25.5z" id="x61"></path></g>
</svg> at steady-state condition.</table>

Mathematical Problems in Engineering

fig6

Figure 6

Figure 6: Transient Natural Convection in Porous Square Cavity Heated and Cooled on Adjacent Walls 