Question

1. A solar concentrator produces a heat flux of 2500 W/m2 on the projected area of a tube of diameter 50 mm. Water flows through the tube at a rate of 0.015 kg/s. If the water temperature at the inlet is 15°C, what length of pipe is required to produce water at a temperature of 85°C?

(Water at 50 degree C has: rho = 990 kg m^-3, k = 0.64 Wm^-1 K^-1, c = 4180 Jkg^-1 K^-1.)

Answer 1

`L = 0.319\,m`

Step-by-step explanation:

Let suppose that temperature of air is 15°C. The heating process of the solar concentrator is modelled after the First Law of Thermodynamics:

`\dot Q = h\cdot \pi\cdot D\cdot L\cdot (\bar T-T_(\infty))`

The required length is:

`L = (\dot Q)/(h\cdot \pi\cdot D\cdot (\bar T-T_(\infty)))`

But,

`\dot Q = \dot m \cdot c_(w)\cdot (T_(o)-T_(i))`

`\dot Q = \left(0.015\,(kg)/(s)\right)\cdot \left(4180\,(J)/(kg\cdot ^(\circ)C) \right)\cdot (85^(\circ)C-15^(\circ)C)`

`\dot Q = 4389\,W`

`\bar T = (15^(\circ)C + 85^(\circ)C)/(2)`

`\bar T = 50^(\circ)C`

`L = (4389\,W)/(\left(2500\,(W)/(m^(2)) \right)\cdot \pi \cdot (0.05\,m)\cdot (50^(\circ)C-15^(\circ)C))`

`L = 0.319\,m`