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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.)

Respuesta :

xero099

Answer:

[tex]L = 0.319\,m[/tex]

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:

[tex]\dot Q = h\cdot \pi\cdot D\cdot L\cdot (\bar T-T_{\infty})[/tex]

The required length is:

[tex]L = \frac{\dot Q}{h\cdot \pi\cdot D\cdot (\bar T-T_{\infty})}[/tex]

But,

[tex]\dot Q = \dot m \cdot c_{w}\cdot (T_{o}-T_{i})[/tex]

[tex]\dot Q = \left(0.015\,\frac{kg}{s}\right)\cdot \left(4180\,\frac{J}{kg\cdot ^{\circ}C} \right)\cdot (85^{\circ}C-15^{\circ}C)[/tex]

[tex]\dot Q = 4389\,W[/tex]

[tex]\bar T = \frac{15^{\circ}C + 85^{\circ}C}{2}[/tex]

[tex]\bar T = 50^{\circ}C[/tex]

[tex]L = \frac{4389\,W}{\left(2500\,\frac{W}{m^{2}} \right)\cdot \pi \cdot (0.05\,m)\cdot (50^{\circ}C-15^{\circ}C)}[/tex]

[tex]L = 0.319\,m[/tex]

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