Numerical and Optimization-Based Study on Split Hemispherical Shaped Fins for Augmenting Heat Transfer Rate

This paper deals with the numerical investigation of split hemispherical fins mounted staggered over a base plate. The thermal and flow analyses have been carried out to evaluate the Nusselt number (Nu), pressure drop <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"> <a:mfenced open="(" close=")"> <a:mrow> <a:mi>Δ</a:mi> <a:mi>P</a:mi> </a:mrow> </a:mfenced> </a:math> , and hydrothermal performance factor (HTPF) with air as a medium and Reynolds number ( <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" id="M2"> <e:mi mathvariant="normal">Re</e:mi> <e:mo>=</e:mo> <e:mo>/</e:mo> <e:mn>3000</e:mn> </e:math> to 15000). The cylindrical fin (CF) and hemispherical fin (HF, of radius <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" id="M3"> <h:mi>R</h:mi> </h:math> ) of the same volume and height have been formed and placed in the computational domain. Results reveal that the Nu for CF compared to HF is 1.3-1.4 times higher, with approximately 1.5 times higher <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" id="M4"> <j:mi>Δ</j:mi> <j:mi>P</j:mi> </j:math> for the given Re range. The value of HTPF for HF is greater than unity (/1.13-1.20) for all the considered Re values. Secondly, the HF gets split into longitudinal and transverse flow directions for better solid-fluid interaction. The geometrical parameters are transverse offset TO (/= <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" id="M5"> <l:mn>0</l:mn> <l:mo>−</l:mo> <l:mi>R</l:mi> <l:mo>/</l:mo> <l:mn>8</l:mn> </l:math> ), longitudinal offset LO (/= <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" id="M6"> <n:mn>0</n:mn> <n:mo>−</n:mo> <n:mi>R</n:mi> <n:mo>/</n:mo> <n:mn>8</n:mn> </n:math> ), and Re. Results show that the highest value of Nu (/=384.10) and HTPF (/=1.33) have been obtained at <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" id="M7"> <p:mtext>TO</p:mtext> <p:mo>=</p:mo> <p:mi>R</p:mi> <p:mo>/</p:mo> <p:mn>10</p:mn> </p:math> (at LO =0) and <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" id="M8"> <r:mtext>TO</r:mtext> <r:mo>=</r:mo> <r:mi>R</r:mi> <r:mo>/</r:mo> <r:mn>10</r:mn> </r:math> (at <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" id="M9"> <t:mtext>LO</t:mtext> <t:mo>=</t:mo> <t:mi>R</t:mi> <t:mo>/</t:mo> <t:mn>10</t:mn> </t:math> ) for the highest Re (/=15000). At last, the cuckoo search algorithm (CSA) coupled with the response surface method (RSM) has been performed to fetch the optimum value of Nu based upon dimensionless TO <v:math xmlns:v="http://www.w3.org/1998/Math/MathML" id="M10"> <v:msup> <v:mrow/> <v:mrow> <v:mo>∗</v:mo> </v:mrow> </v:msup> </v:math> , dimensionless LO <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" id="M11"> <x:msup> <x:mrow/> <x:mrow> <x:mo>∗</x:mo> </x:mrow> </x:msup> </x:math> , and Re. The optimum value (obtained at <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" id="M12"> <z:msup> <z:mrow> <z:mtext>TO</z:mtext> </z:mrow> <z:mrow> <z:mo>∗</z:mo> </z:mrow> </z:msup> <z:mo>=</z:mo> <z:mn>0.1</z:mn> </z:math> , <bb:math xmlns:bb="http://www.w3.org/1998/Math/MathML" id="M13"> <bb:mtext>L</bb:mtext> <bb:msup> <bb:mrow> <bb:mtext>O</bb:mtext> </bb:mrow> <bb:mrow> <bb:mo>∗</bb:mo> </bb:mrow> </bb:msup> <bb:mo>=</bb:mo> <bb:mn>0</bb:mn> </bb:math> , and <db:math xmlns:db="http://www.w3.org/1998/Math/MathML" id="M14"> <db:mi mathvariant="normal">Re</db:mi> <db:mo>=</db:mo> <db:mn>15000</db:mn> </db:math> ) of Nu (=/392.16) from CSA is promising, with the numerically obtained Nu value (=/384.1059) with an error of 2.05%.