Here is an efficiency analysis of solar cookers based on the 1st Law of Thermodynamics and the 2nd Law of Thermodynamics, explaining also how to calculate the cooking power of any device.

Based on the 1st Law of Thermodynamics [1][edit | edit source]

[math]\displaystyle{ \text{Energy input} = \text{Energy output} + \text{Energy losses} }[/math]

Energy input to the solar cooker can be calculated as follows:

[math]\displaystyle{ E_i = I_t \times A_{sc} }[/math]

Where:
Ei is the energy input in W
It = total solar energy incident upon plane of the solar air being heated in W/m2
Asc is the surface area of the solar cooker in m2

Energy output from the solar cooker can be found as shown below:

[math]\displaystyle{ E_o = { { m_w c_{pw} ( T_{wf} - T_{wi}) } \over t } }[/math]

Where:
Eo is the energy output in W
mw is the mass of water in kg
cpw = specific heat of water in J/kgK
Asc is the surface area of the solar cooker in m2
Twi is the initial temperature of the water in K
Twf is the final temperature of the water in K
t is the time in seconds

Energy efficiency of the solar cooker can be found as shown below:

[math]\displaystyle{ \eta = { \text{Energy output} \over \text{Energy input} } = { E_o \over E_i} = { {[m_w c_{pw}(T_{wf} - T_{wi})] / t } \over {I_t \times A_{sc} } } }[/math]

Based on the 2nd Law of Thermodynamics [2][edit | edit source]

[math]\displaystyle{ \text{Exergy input} = \text{Exergy output} + \text{Irreversibility} }[/math]

Exergy input to the solar cooker can be calculated as follows:

[math]\displaystyle{ \Xi_i = I_b [1 - (T_o / T_s) (4/3) ] }[/math]

Where:
Exergy input in W/m2
cpw = specific heat of water in J/kgK
To is the outside temperature in K
Ts is the surface temperature of the sun in K

Exergy efficiency of the solar cooker can be calculated as follows:

[math]\displaystyle{ \Psi = { \text{Exergy output} \over \text{Exergy input} } = { \dot{\Xi_o} \over \dot{\Xi_i} } = { {m_w c_{pw} [(T_{wf} - T_{wi}] - T_o \ln (T_{wf} / T_{wi})]/t } \over {I_b[1-(T_o/T_s)(4/3)]A_{sc}} } }[/math]

Where:
Asc is the incident area of the solar cooker

The ability of a solar cooker to collect sunlight is directly related to the projected area of the collector perpendicular to the incident radiation.

Cooking power[edit | edit source]

The primary reference measurement used by ASAE S580[3] is the cooking power, which can be calculated as follows over 10 minute intervals:

[math]\displaystyle{ P = { { M C (T_2 - T_1) } \over 600} }[/math]

Where:
M is the mass of water in kg
C is the specific heat of water in J/kgK
T1 is the water temperature at the start of each interval in K
T2 is the water temperature at the end of each interval in K

This temperature change is detected over 10 minute intervals, thus the equation above is divided by 600 s.

References[edit | edit source]

  1. Ozturk, H. "Second Law Analysis for Solar Cookers", http://www.informaworld.com/smpp/1138067100-85020668/content~db=all~content=a713635696, Accessed April 8, 2010
  2. Ozturk, H. "Second Law Analysis for Solar Cookers", http://www.informaworld.com/smpp/1138067100-85020668/content~db=all~content=a713635696, Accessed April 8, 2010
  3. ASABE Technical Library. "Testing and Reporting Solar Cooker Performance",http://asae.frymulti.com/abstract.asp?aid=24465&t=2, Accessed April 8, 2010
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Authors Rohanm
Published 2022
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