Implementation of a rational drying process for fish conservation

Abstract

Fishing is a traditional activity that is widespread in West Africa. One of the greatest problems for fishermen and a cause of lack of food accessibility is the difficulty in conserving fish. Drying is a widely used technique in sub-Saharan Africa for preservation of fish. However, drying is a complex process, making the construction and calibration of efficient drying devices challenging. This paper presents the construction and calibration of five mobile fish dryers in Mali and, for one of them, development of a method for its use. The performances achieved far exceeded those of traditional solar dryers as drying was faster and the fish were not contaminated by being exposed to flies. Furthermore, construction and user manuals were written for the local fishermen which were well understood as the fishermen were able to disassemble and reassemble the dryers when they were required to be moved.

Appendix

Notations

c_p,a :

heat capacity of air (at 60°C, c_p,a is approximately equal to 1,000 J/kg/K)

D_h :

hydraulic diameter of the dryer (m)

e:

thickness of the plastic (10⁻³ m)

F_s :

solar flux (W/m²)

g:

acceleration of gravity (m/s²)

Gr:

Grasshof number (-)

h:

height of the dryer, see Fig. 1a (0.43 m)

h_n :

heat transfer coefficient between the covering plastic and the ambient air (W/m²/K)

h_f(v):

heat transfer coefficient between the air in the dryer and the covering plastic, as a function of the air velocity in the dryer (W/m²/K)

l:

width of the dryer, see Fig. 1a (1.25 m)

L_c :

see Fig. 1a (m)

L_k :

massic latent heat of water vaporization (at 60°C, L_k is approximately equal to 2,250 kJ/kg)

L_m :

molar latent heat of water vaporization (at 60°C, L_m is approximately equal to 40,500 J/mol.)

M_f :

initial mass of fish in the dryer (kg)

MM_a :

molar mass of air (29 10⁻³ kg/mol.)

MM_w :

molar mass of water (18 10⁻³ kg/mol.)

Nu_f :

Nusselt number for forced convection (-)

Nu_n :

Nusselt number for natural convection (-)

p_atm :

atmospheric pressure (101,325 kg/m/s²)

p_sat(T):

saturation pressure of water at temperature T (kg/m/s²)

p₀ :

saturation pressure of water at temperature T₀ (12,349 kg/m/s²)

Pr:

Prandtl number (-)

R_g :

perfect gas constant (8.314 J/mol./K)

R_w :

global rate of water evaporation in the dryer (kg of water/s)

Re:

Reynolds number (-)

t_s :

drying time (s)

T₀ :

reference temperature (50°C)

T_atm :

atmospheric temperature (K)

T_s(z):

temperature of the air at position z in the dryer (K)

T_p,i(z):

temperature of the inner side of the covering plastic, at position z in the dryer (K)

T_p,e(z):

temperature of the outer side of the covering plastic, at position z in the dryer (K)

U(v):

global heat transfer coefficient between the air in the dryer and the atmosphere, as a function of the air velocity in the dryer (W/m²/K)

v:

velocity of the air in the dryer (m/s)

x:

length of the dryer, see Fig. 1a (10.5 m)

x_c :

length of the heating zone in the dryer, see Fig. 1a (3 m)

x_d :

length of the drying zone in the dryer, see Fig. 1a (7.5 m)

Y(z):

humidity of the air at position z in the dryer (kg of water / kg of dried air)

Y₀ :

humidity of the ambient air (kg of water / kg of dried air)

Y_sat(T):

saturation humidity of air at temperature T (kg of water / kg of dried air)

z:

position in the dryer. z = 0 at the entrance in the dryer. z = x at the outlet of the dryer (m)

Greek letters

β:

air dilation coefficient (1/K)

ε_a :

emissivity of air (0.9)

ε_p :

emissivity of plastic (0.9)

λ_a :

thermal conductivity of air (at 60°C, λ_a is approximately equal to 2.8 10⁻² W/m/K)

λ_p :

thermal conductivity of plastic (0.17 W/m/K)

μ_a :

dynamic viscosity of the air (at 60°C, μ_a is approximately equal to 2 10⁻⁵ kg/m/s)

ρ_a :

volumetric mass of air (kg/m³)

σ:

Stefan-Boltzmann constant (5.67 10⁻⁸ W/m²/K⁴)

Ω:

area of the triangular section of the dryer perpendicular to the air flow (m²)

Assumptions

• The air is considered as a perfect gas.

• As the amount of water in the air in a well operated dryer remains limited (see below), it is assumed that the flow rate of air throughout the dryer is conserved and can be considered as being the flow rate of dried air.

• In the calculations below, the physico-chemical properties of air (ρ_a, c_p,a, λ_a, β, μ_a) are always evaluated at 60°C.

Preliminary calculations

The following relations can be written:

$$ \Omega = \frac{{hl}}{2} $$

(1)

$$ {D_h} = \frac{{4\frac{{lh}}{2}}}{{2{L_c} + l}} $$

(2)

L_c can be approximated as follows:

$$ {L_c} = \sqrt {{\frac{{{l^2}}}{4} + {h^2}}} $$

(3)

Therefore, Ω = 0.25 m², L _c = 0.76 m, D _h = 0.39 m.

As the air is considered as a perfect gas:

$$ {\rho_a} = \frac{{{p_{atm}}M{M_a}}}{{{R_g}T}} $$

(4)

$$ \beta = \frac{1}{T} $$

(5)

Therefore, at T = 60°C, ρ _a = 1.1 kg/m³ and β = 3.0 10⁻³ 1/K.

U(v) can be expressed as follows:

$$ \frac{1}{{U(v)}} = \frac{1}{{{h_f}(v)}} + \frac{e}{{{\lambda_p}}} + \frac{1}{{{h_n}}} $$

(6)

It can be easily demonstrated that:

$$ {T_{p,e}}(z) = T(z) - \left( {\frac{1}{{{h_f}(v)}} + \frac{e}{{{\lambda_p}}}} \right)U(v)\left( {T(z) - {T_{atm}}} \right) $$

(7)

Three dimensionless numbers are classically used to compute h_f(v):

$$ N{u_f} = \frac{{{h_f}(v){D_h}}}{{{\lambda_a}}} $$

(8)

$$ {\rm Re} = \frac{{v\,{D_h}{\rho_a}}}{{{\mu_a}}} $$

(9)

$$ \Pr = \frac{{{c_{p,a}}{\mu_a}}}{{{\lambda_a}}} $$

(10)

If 10.10³ < Re < 120.10³ and 0.7 < Pr < 120 (it can be checked, a posteriori, that this condition is fulfilled for the dryer):

$$ N{u_f} = 0.023\,{{\rm Re}^{0.8}}{\Pr^{0.3}} $$

(11)

Therefore, at T = 60°C, h_f(v) = 4.2 v^0.8 W/K/m².

Three dimensionless numbers are classically used to compute h_n:

$$ N{u_n} = \frac{{{h_n}{L_c}}}{{{\lambda_a}}} $$

(12)

$$ Gr = \frac{{\rho_a^2\beta g\Delta TL_c^3}}{{\mu_a^2}} $$

(13)

$$ \Pr = \frac{{{c_{p,a}}{\mu_a}}}{{{\lambda_a}}} $$

(14)

where ΔT is the temperature difference causing the natural convection (assumed here to be approximately equal to 20°C).

If 8 10⁶ < Gr Pr < 10¹¹ (it can be checked that this condition is fulfilled for the dryer):

$$ N{u_f} = 0.15\,{\left( {{\rm Re} \,Gr} \right)^{0.33}} $$

(15)

Therefore, at T = 60°C, h _n = 4.2 W/K/m².

The saturation pressure at a temperature T is evaluated using Clapeyron’s law:

$$ {p_{sat}}(T) = {p_0}\exp \left( { - \frac{{{L_m}}}{{{R_g}}}\left( {\frac{1}{T} - \frac{1}{{{T_0}}}} \right)} \right) $$

(16)

It can be easily shown that:

$$ {Y_{sat}}(T) = \frac{{\frac{{{p_{sat}}(T)}}{{{p_{atm}}}}\frac{{M{M_w}}}{{M{M_a}}}}}{{1 - \frac{{{p_{sat}}(T)}}{{{p_{atm}}}}\frac{{M{M_w}}}{{M{M_a}}}}} $$

(17)

Methodology

The operation of the dryer is characterized by three parameters: v, the velocity of the air delivered by the ventilator (that can be adjusted), t_s, the drying time (the time of the operation), and M_f, the mass of fish placed in the dryer. M_f approximates to 50 kg for most fish and corresponds to the maximum number of fish that can be placed in the dryer without touching each other.

It is assumed that a good drying of the fish is achieved if:

• the temperature at the end of the heating zone is close to 60°C,

• a mass reduction of 70% is obtained at the end of the operation,

• the temperature at the end of the drying zone is not higher than 75°C (to avoid the fish being cooked),

• the relative humidity of the air at the end of the drying zone is not greater than 25% (to avoid a significant heterogeneity of the humidity in the dryer and therefore a significant heterogeneity of the drying rate, that would lead to a product of uneven quality).

An energy balance on a slice [z, z + Δz] of the heating zone in the dryer yields the following equation:

$$ {\rho_a}{c_{p,a}}v\Omega \frac{{dT}}{{dz}} = l{F_s} + l{\varepsilon_a}\sigma T_{atm}^4 - 2{L_c}U(v)\left[ {T(z) - {T_{atm}}} \right] - 2{L_c}\sigma {\left[ {{T_{p,e}}(z)} \right]^4} $$

(18)

This equation can be numerically solved with Mathematica® for any value of v, if T_atm and F_s are given. In Fig. 4, T_s(z) is presented for different values of v, with F _s = 700 W/m² and T _atm = 40°C.

Fig. 4

Temperature of the air at position z in the heating zone of the dryer for different air velocities

It can be observed in Fig. 4 that, for F _s = 700 W/m² and T _atm = 40°C, a temperature of 60°C is achieved at the end of the heating zone if v = 0.3 m/s.

If the drying kinetic is limited by the rate at which energy is brought to the fish, the energy consumed by the evaporation process is exactly equal to the radiative energy flux (solar + atmospheric) caught by the dryer minus the energy lost by the dryer (by radiation and heat conduction/convection). Therefore, the temperature in the drying zone is homogeneous (and written T_s) and the global rate of water evaporation in the dryer, R_w, can be calculated solving the following equation:

$$ {x_d}l{F_s} + {x_d}l{\varepsilon_a}\sigma T_{atm}^4 = 2{L_c}{x_d}U(v)\left[ {{T_s} - {T_{atm}}} \right] + 2{L_c}{x_d}\sigma {\left[ {{T_s} - \left( {\frac{1}{{{h_f}(v)}} + \frac{e}{{{\lambda_p}}}} \right)U(v)\left( {{T_s} - {T_{atm}}} \right)} \right]^4} + {R_w}{L_k} $$

(19)

If F _s = 700 W/m², T _atm = 40°C and v = 0.3 m/s, R _w = 1.9 g/s is calculated. Hence, if 50 kg of fish are placed initially in the dryer, the time needed to obtain a mass reduction of 70% is approximately 6 h and 15 min.

A mass balance on the vapour in the air in the dryer may be written as follows:

$$ {\rho_a}v\Omega {Y_0} + {R_w} = {\rho_a}v\Omega Y(x) $$

(20)

If F _s = 700 W/m², T _atm = 40°C and v = 0.3 m/s, Y(x) = 37 g of water per kg of air is calculated. Hence, the relative humidity of the air at the end of the drying zone is equal to 23% (T _s = 61°C was used).

Therefore, if the drying kinetic is limited by the rate at which energy is brought to the fish, v = 0.3 m/s, t _s = 6 h and 15 min and M _f = 50 kg are operating conditions that will lead to a drying of good quality, if F _s = 700 W/m² and T _atm = 40°C.