It is proposed to um a roof-mounted solar water-heating system to supplement ene

Question

It is proposed to um a roof-mounted solar water-heating system to supplement energy input into a certain industrial process. The south-facing solar collector is to be used to heat indirectly the water in a storage tank of capacity 5000 imperial gallons (22.700 litres). Water can be pumped through the collector by a range of available water pumps. On a typical summer day. there are 5.6 hours of sunshine which causes an average temperature difference of 16.5 degree C between the inflow and outflow of the collector. If the anticipated efficiency of the system is 42.6%. what rate of water pump flow in m^3 is needed to cause a temperature ruse of 12 degree C in t he storage tank? If this pump is used and the temperature of the storage tank becomes 14.5 degree C, what is the efficiency of the collector system?

Explanation / Answer

(a)

let rate of water pump flow = F cubic meter per sec

volume of water transferred = F * 5.6 * 3600 cubic metres

Mass of water transferred = F * 5.6 * 3600 grams

quantity of heat collected = H = F * 5.6 * 3600 * 16.5 calories

given Efficiency = E = 0.426 temp. rise = T =12 degrees C

Total capacity of tank = 22700 lit = 22700 kg

T = H * E / 22700

this gives

F = 5.767 cubic meter per second

(b)

According to the given question,

At 0.426 efficiency, the temperature rise in storage tank = 12 degrees C

Let's say at 'X' efficiency the temp rise in storage tank = 14.5 degrees C

X = 0.426 * 14.5 / 12 = 0.51475

i.e., 51.475 % is the collector system efficiency

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