Effects of Chemical Reactions on Unsteady Free Convective and Mass Transfer Flow from a Vertical Cone with Heat Generation/Absorption in the Presence of VWT/VWC

<table>(a) Transient velocity profiles at <svg height="11.375" id="M112" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 53.200001 11.375" width="53.200001" 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="M775 650l-6 -28q-60 -6 -81.5 -16t-61.5 -54l-175 -191l125 -243q30 -58 48.5 -71t82.5 -19l-5 -28h-275l7 28l35 4q31 4 37 12t-6 34l-108 216q-140 -165 -177 -219q-16 -22 -10.5 -30.5t41.5 -13.5l22 -3l-7 -28h-244l8 28q52 4 75 15.5t67 52.5q48 46 206 231
l-110 215q-26 51 -44 63t-72 17l6 28h250l-6 -28l-27 -4q-30 -5 -35 -10t3 -27q17 -43 95 -190q70 78 154 185q15 21 10 29.5t-33 12.5l-30 4l5 28h236z" id="x1D44B"></path></g><g transform="matrix(.017,-0,0,-.017,18.234,11.112)"><path d="M535 323h-483v50h483v-50zM535 138h-483v50h483v-50z" id="x3D"></path></g><g transform="matrix(.017,-0,0,-.017,32.938,11.112)"><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><g transform="matrix(.017,-0,0,-.017,41.097,11.112)"><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,-.017,44.973,11.112)"><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>
</svg> for different values of <svg height="7.9499998" id="M113" style="vertical-align:-0.10033pt" version="1.1" viewbox="0 0 13.5375 7.9499998" width="13.5375" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,7.675)"><path d="M766 88q-40 -45 -83.5 -72.5t-63.5 -27.5q-39 0 -16 103l49 224q15 68 -10 68q-36 0 -112.5 -78.5t-105.5 -133.5q-27 -101 -38 -165q-35 -4 -77 -18l-6 6q42 153 70 288q12 55 10 78t-19 23q-38 0 -114 -80.5t-101 -131.5q-24 -68 -41 -165q-36 -3 -76 -18l-8 6
q56 202 87 347q7 33 -3 33q-8 0 -31.5 -17.5t-41.5 -35.5l-12 28q42 45 84 72t63 27q44 0 10 -124l-20 -75h2q92 121 193 178q36 21 64 21q62 0 28 -159l-8 -37h2q50 67 103.5 112t94.5 65q39 19 62 19q60 0 23 -156l-45 -189q-9 -39 2 -39q17 0 71 49z" id="x1D45A"></path></g>
</svg>. (b) Transient temperature profiles at <svg height="11.375" id="M114" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 53.200001 11.375" width="53.200001" 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="M775 650l-6 -28q-60 -6 -81.5 -16t-61.5 -54l-175 -191l125 -243q30 -58 48.5 -71t82.5 -19l-5 -28h-275l7 28l35 4q31 4 37 12t-6 34l-108 216q-140 -165 -177 -219q-16 -22 -10.5 -30.5t41.5 -13.5l22 -3l-7 -28h-244l8 28q52 4 75 15.5t67 52.5q48 46 206 231
l-110 215q-26 51 -44 63t-72 17l6 28h250l-6 -28l-27 -4q-30 -5 -35 -10t3 -27q17 -43 95 -190q70 78 154 185q15 21 10 29.5t-33 12.5l-30 4l5 28h236z" id="x1D44B"></path></g><g transform="matrix(.017,-0,0,-.017,18.234,11.112)"><path d="M535 323h-483v50h483v-50zM535 138h-483v50h483v-50z" id="x3D"></path></g><g transform="matrix(.017,-0,0,-.017,32.938,11.112)"><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><g transform="matrix(.017,-0,0,-.017,41.097,11.112)"><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,-.017,44.973,11.112)"><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>
</svg> for different values of <svg height="7.9499998" id="M115" style="vertical-align:-0.10033pt" version="1.1" viewbox="0 0 13.5375 7.9499998" width="13.5375" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,7.675)"><path d="M766 88q-40 -45 -83.5 -72.5t-63.5 -27.5q-39 0 -16 103l49 224q15 68 -10 68q-36 0 -112.5 -78.5t-105.5 -133.5q-27 -101 -38 -165q-35 -4 -77 -18l-6 6q42 153 70 288q12 55 10 78t-19 23q-38 0 -114 -80.5t-101 -131.5q-24 -68 -41 -165q-36 -3 -76 -18l-8 6
q56 202 87 347q7 33 -3 33q-8 0 -31.5 -17.5t-41.5 -35.5l-12 28q42 45 84 72t63 27q44 0 10 -124l-20 -75h2q92 121 193 178q36 21 64 21q62 0 28 -159l-8 -37h2q50 67 103.5 112t94.5 65q39 19 62 19q60 0 23 -156l-45 -189q-9 -39 2 -39q17 0 71 49z" id="x1D45A"></path></g>
</svg>. (c) Transient concentration profiles at <svg height="11.375" id="M116" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 53.200001 11.375" width="53.200001" 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="M775 650l-6 -28q-60 -6 -81.5 -16t-61.5 -54l-175 -191l125 -243q30 -58 48.5 -71t82.5 -19l-5 -28h-275l7 28l35 4q31 4 37 12t-6 34l-108 216q-140 -165 -177 -219q-16 -22 -10.5 -30.5t41.5 -13.5l22 -3l-7 -28h-244l8 28q52 4 75 15.5t67 52.5q48 46 206 231
l-110 215q-26 51 -44 63t-72 17l6 28h250l-6 -28l-27 -4q-30 -5 -35 -10t3 -27q17 -43 95 -190q70 78 154 185q15 21 10 29.5t-33 12.5l-30 4l5 28h236z" id="x1D44B"></path></g><g transform="matrix(.017,-0,0,-.017,18.234,11.112)"><path d="M535 323h-483v50h483v-50zM535 138h-483v50h483v-50z" id="x3D"></path></g><g transform="matrix(.017,-0,0,-.017,32.938,11.112)"><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><g transform="matrix(.017,-0,0,-.017,41.097,11.112)"><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,-.017,44.973,11.112)"><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>
</svg> for different values of <svg height="7.9499998" id="M117" style="vertical-align:-0.10033pt" version="1.1" viewbox="0 0 13.5375 7.9499998" width="13.5375" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,7.675)"><path d="M766 88q-40 -45 -83.5 -72.5t-63.5 -27.5q-39 0 -16 103l49 224q15 68 -10 68q-36 0 -112.5 -78.5t-105.5 -133.5q-27 -101 -38 -165q-35 -4 -77 -18l-6 6q42 153 70 288q12 55 10 78t-19 23q-38 0 -114 -80.5t-101 -131.5q-24 -68 -41 -165q-36 -3 -76 -18l-8 6
q56 202 87 347q7 33 -3 33q-8 0 -31.5 -17.5t-41.5 -35.5l-12 28q42 45 84 72t63 27q44 0 10 -124l-20 -75h2q92 121 193 178q36 21 64 21q62 0 28 -159l-8 -37h2q50 67 103.5 112t94.5 65q39 19 62 19q60 0 23 -156l-45 -189q-9 -39 2 -39q17 0 71 49z" id="x1D45A"></path></g>
</svg>.</table>

Mathematical Problems in Engineering

fig4

Figure 4

Figure 4: Effects of Chemical Reactions on Unsteady Free Convective and Mass Transfer Flow from a Vertical Cone with Heat Generation/Absorption in the Presence of VWT/VWC 

Figure 4 | Effects of Chemical Reactions on Unsteady Free Convective and Mass Transfer Flow from a Vertical Cone with Heat Generation/Absorption in the Presence of VWT/VWC 