A solar collector and storage tank, shown in Figure (a) below, is to be optimized toachieve minimum first cost. During the day the temperature of water in the storage vessel iselevated from 25 °C (the minimum useful temperature) to tmax, as shown in Figure (b). Thecollector receives 260 W/m² of solar energy, but there is heat loss from the collector to ambientair by convection. The convection coefficient is 2 W/(m²*K), and the average temperaturedifference during the 10-hour day is (25 + tmax)/2 minus the ambient temperature of 10 °C.The energy above the minimum useful temperature of 25 °C that is to be stored in thevessel during the day is 200,000 kJ. The density of water is 1000 kg/m³, and its specific heat is4.19 kJ/(kg*K). The cost of the solar collector in dollars is 20A, where A is the area in squaremeters, and the cost of the storage vessel in dollars is 101.5C, where V is the volume in cubicmeters.StoragetankCollector(a)Temperature, Ctmax25°C, lowest useful temperature i10°C ambientTime(b)Using A and V as the variables, set up the objective functiocost. Set it up so that there is one constraint equation.10 h = 36,000 sand constraint to optimize the first

Given:water temperature = T = 250CSolar Energy: 260 W/m2convection coefficient = h = 2…

Answered: Using A and V as the variables, set up…

Using A and V as the variables, set up the objective function and constraint to optimize the first cost. Set it up so that there is one constraint equation.

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter5: Analysis Of Convection Heat Transfer

Section: Chapter Questions

Problem 5.3DP

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