(1) Incident solar insolation distribution

The solar insolation distribution incident on the target (target structure size 3 m × 3 m) was measured using an indirect method based on a CCD camera and a target. Fig. 3 shows the measured insolation flux distribution along the *y* direction of the target and a Gaussian curve at 11:30 am on September 28, 2018. According to experimental test results, the solar insolation distribution incident on the surface of the volumetric receiver is as follows [11,12]:

where, *A*_{hel} is concentrator field aperture area, and *η*_{hel} is efficiency of the concentrator field.

The solar insolation distribution incident on the water is:

**Fig. 3** Measured solar insolation distribution incident on the target

The solar insolation distribution finally incident on the porous ceramic absorber panel is [13]:

(2) Surface convective heat transfer coefficient on the glass window

The surface convective heat transfer coefficient between the glass window and the water can be cal- culated from the appropriate Nusselt number relation as:

The glass window is assumed to be a vertical flat plate. When the pump is not running, the natural convection heat transfer coefficient between the glass window and the water is calculated using the equation recommended by Churchill and Chu ^{}[14]^{} which is applicable for all Rayleigh numbers:

The Rayleigh number is:

When the pump is running, the forced convection heat transfer coefficient between the window and the water can be calculated using [15]:

The Reynolds number is defined as:

In Section 2.2 we assume that the water flow inside the receiver can be modeled as plug flow. According to this assumption, the speed of the water inside the receiver be calculated as:

When the receiver circulation pump is running, natural convection can still affect the heat transfer which can be evaluated based on the ratio of the Grashof and Reynolds numbers. When *Gr*_{w} /*Re*_{w}^{2} <0.1, the effect of natural convection can be ignored. When 0.1≤*Gr*_{w} /*Re*_{w}^{2} ≤10, the flow is in the mixed convection regime. When *Gr*_{w} /*Re*_{w}^{2} >10, the effect of forced convection can be neglected.

The Grashof number is defined as:

In the mixed convection condition, the Nusselt number can be calculated as [16]:

The surface convective heat transfer coefficient between the window and the environment can also be calculated using Eqs. (28–34).

(3) Volumetric heat transfer coefficient

The volumetric heat transfer coefficients can be calculated by:

Since the volumetric heat transfer coefficient is generally quite large, the temperature difference between the silicon carbide porous ceramic heat absorbing plate and the water can be assumed to be quite small. Thus, when the receiver circulation pump is running, the effect of natural convection on the convective heat transfer between the porous ceramic absorber panel and the water can be neglected. The volumetric heat transfer coefficient can then be calculated as [17,18]:

when 75<*Re*_{d} <350, *h*_{sf} is obtained by linear interpolation of Eqs. (28) and (29). *Re*_{d} is defined as:

When the receiver circulation pump stops working, the volumetric convective heat transfer coefficient between the porous ceramic absorber panel and the water can be calculated as [19]:

Where *Ra*_{d} is defined as:

(4) Water thermophysical properties

The water properties, including the density, specific heat, thermal conductivity, and viscosity, were fit as continuous curves as functions of temperature (0–100°C) from the data in Ref. [15]: