# Effects of thermal conductivity and geometry of materials on the temperature variation in packed bed solar air heater

- First Online:

- Received:
- Accepted:

DOI: 10.1007/s10973-011-2182-5

- Cite this article as:
- Singh, O.K. & Panwar, N.L. J Therm Anal Calorim (2013) 111: 839. doi:10.1007/s10973-011-2182-5

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## Abstract

The efficiency of energy collection of a flat plate type of solar air heater is low because of the large thermal losses and low heat transfer coefficient between the absorber plate and the air flowing in the duct. Packed beds have been successfully employed for the enhancement of the heat transfer coefficients in solar air heaters and such air heaters can be used for drying agricultural produce and space heating as well. This article deals with the theoretical investigation on the effects of thermal conductivity of material and geometry of a screen on the temperature variation in woven wire screen packed bed solar air heater. Theoretical results have been compared with the experimental results reported earlier by other researchers and found to match reasonably well with them. It has been found that the thermal performance depends upon a little on the thermal conductivity of screen material. Instead, it depends more on the geometry and an extinction coefficients of the matrix. A low value of extinction coefficient is desirable for maximum absorption of solar radiations and minimum thermal losses. The numerical method of analysis used here is based on finite difference approximation. The finite difference equations have been solved through a computer program in C^{++}.

### Keywords

Packed bed solar air heaterThermal conductivityExtinction coefficientScreen geometryFinite difference approximation### List of symbols

### Variables

*A*_{c}Gross collector area (m

^{2})*A*_{f}Frontal area of duct =

*B·D*(m^{2})*A*_{p}Packing surface area (m

^{2})*B*Width of the absorber plate/packed bed (m)

*C*_{g},*C*_{p},*C*_{s}Specific heats of air, packed material and cover glass, respectively (J kg

^{−1}K^{−1})*C*_{c}Circumference associated with collector gross area (m)

*D*Depth of packed bed or air channel (m)

*d*_{p}Diameter of packed material (m)

*G*Mass flux or mass flow rate per unit area (kg m

^{−2 }s^{−1})*H*_{0}= I = Insolation (kg m

^{−2 }s^{−1})*H*_{1}Irradiation at the top surface of the matrix (W m

^{−2})*H*_{2}Irradiation at the bottom plate (W m

^{−2})*h*_{g}Convective heat transfer coefficient between cover glass and surrounding (W m

^{−2 }K^{−1})*h*_{rca}Radiative heat transfer coefficient between cover glass and ambient air (W m

^{−2 }K^{−1})*h*_{p}Convective heat transfer coefficient between packed material and air (W m

^{−2 }K^{−1})*h*_{w}Heat transfer coefficient of wall (W m

^{−2 }K^{−1})*h*_{pc}Convective heat transfer coefficient between absorber and cover glass (W m

^{−2 }K^{−1})*h*_{rpc}Radiative heat transfer coefficient between absorber and cover glass (W m

^{−2 }K^{−1})*h*_{rs}Radiative heat transfer coefficient solid to solid (W m

^{−2 }K^{−1})*h*_{rv}Radiative heat transfer coefficient void to void (W m

^{−2}K^{−1})*k*_{e}Effective thermal conductivity of packed bed with flowing air (W m

^{−1 }K^{−1})*k*_{e}^{0}Effective thermal conductivity of packed bed with motionless fluid (W m

^{−1}K^{−1})*k*_{g}Thermal conductivity of air (W m

^{−1 }K^{−1})*k*_{p}Thermal conductivity of packed material (W m

^{−1 }K^{−1})*L*Collector length (m)

*L**Characteristic length = 4

*A*_{c}/*C*_{c}(m)*m*Mass flow rate of air (kg s

^{−1})*Q*_{ry}Radiative heat flux at any depth ‘

*y*’ of the matrix (W m^{−2})*R*_{0}Radiosity at the top surface of the cover glass (W m

^{−2})*R*_{1}Radiosity at the top surface of the matrix (W m

^{−2})*R*_{2}Radiosity at the bottom plate (W m

^{−2})*r*_{s}Reflectivity of the cover glass

*T*_{a}Temperature of ambient air (K)

*T*_{g}Temperature of air flowing through the duct (K)

*T*_{p}Temperature of packed material (K)

*T*_{s}Temperature of cover glass (K)

*T*_{b}Average temperature of the packing and air = (

*T*_{p }+*T*_{g})/2 (K)*T*_{pm}Average temperature of top surface of packed bed (K)

*T*_{sky}Sky temperature (K)

- Δ
*t* Time increment (s)

*u*Velocity of air (m s

^{−1})*u*_{∞}Wind speed (m s

^{−1})*V*Total volume of bed (m

^{3})*V*_{p}Volume of packed solid (s

^{3})*x*Distance in

*x*direction (m)- Δ
*x* Distance increment in

*x*direction (m)*y*Distance in

*y*direction (m)- Δ
*y* Distance increment in

*y*direction (m)- E.F
*.* Enhancement factor

### Greek letters

- β
_{p} Extinction coefficient of matrix (m

^{−1})- ε
Emissivity of absorber matrix

- ε
_{w} Emissivity of bottom plate

- ε
_{s} Emissivity of cover glass

- ε
_{p} Void fraction or porosity of packed bed

- ρ
Reflectivity

- ρ
_{g}, ρ_{p}, ρ_{s} Densities of air, packed material and cover glass respectively (kg m

^{−3})- σ
Stefan–Boltzmann constant = 5.67 × 10

^{−8}(W m^{−2 }K^{−4})- τ
_{s} Transmissivity of cover system

- η
Efficiency