A $15$ cm $\backslash$times $20$ cm hot surface at $85\backslash$deg C is to be cooled by attaching $4$ cm long aluminum $($k $=237$ W$/$m$-\backslash$deg C$)$ fins of $2$ mm $\backslash$times $2$ mm square cross section. The temperature of surrounding medium is $25\backslash$deg C and the heat transfer coefficient on the surfaces can be taken to be $20$ W$/$m$2-\backslash$deg C$.$ If it is desired to triple the rate of heat transfer from the bare hot surface, determine the number of fins that needs to be attached. plot the number of fins as a function of the increase in the heat loss by fins relative to no fin case $($i$.$e$.,$ overall effectiveness of the fins$)$ in the range of $1\mathrm{.}5$ to $5.$ Discuss the results

Organize the solution according to this process

Known: State briefly what is known.

$2.$ Find: Understand the intent$/$objective of the problem. State concisely what is to be determined.

$3.$ Schematic and Given Data: Clearly define the system being analyzed. Here, you introduce the identifiers which label your states, your control mass or control volume, and your nomenclature. Draw a sketch of the system to be considered. Label the sketch with relevant information from the problem statement. Note down all property values which are given, or you look up and find which may be relevant to solving the problem.

$4.$ Engineering Model: form a record of how you model the problem, list all simplifying assumptions and idealizations made to reduce it to one that is manageable.

$5.$ Analysis: Using your assumptions and idealizations, reduce the appropriate governing equations and relationships to forms that will produce the desired results. Document your work by providing text leading the reader through the analysis.

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