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  ____       ___               __   __   _____    
 |  _ \\    / _ \\      ___    \ \\/ // |  __ \\  
 | |_| ||  / //\ \\    /   ||   \ ` //  | |  \ || 
 | .  //  |  ___  ||  | [] ||    | ||   | |__/ || 
 |_|\_\\  |_||  |_||   \__ ||    |_||   |_____//  
 `-` --`  `-`   `-`     -|_||    `-`'    -----`   
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Text this: Mathematical modeling of closed-End pulsating heat pipes pperating with a bottom heat mode