Consider the convective heat transfer from a spherical reactor of diameter D and temperature Ts to a fluid at temperature Ta, with a convective heat transfer coefficient h. Denoting (T s T a ) as ?, h is given by Also, a constraint arises from strength considerations and is given by D? = 75 We wish to minimize the heat transfer from the sphere. Set up the objective function in terms of D and ? and with one constraint. Employing Lagrange multipliers for this constrained optimization, obtain the optimal values of D and ?. Also, obtain the sensitivity coefficient and explain its physical

Consider the convective heat transfer from a spherical reactor of diameter D and temperature Ts to a fluid at temperature Ta, with a convective heat transfer coefficient h. Denoting (T s T a ) as ?, h is given by Also, a constraint arises from strength considerations and is given by D? = 75 We wish to minimize the heat transfer from the sphere. Set up the objective function in terms of D and ? and with one constraint. Employing Lagrange multipliers for this constrained optimization, obtain the optimal values of D and ?. Also, obtain the sensitivity coefficient and explain its physical meaning in this problem. How will you use it in the final selection of the values of D and ??

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