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The energy transferred from the anterior chamber of the eye through the cornea varies considerably depending on whether a contact lens is worn. Treat the eye as a spherical system and assume the system to be at steady state. The convection coefficient h, is unchanged with and without the contact lens in place. The cornea and the lens cover one-third of the spherical surface area. Anterior chamber k2 Conea Contact lens Values of the parameters representing this situa- tion are as follows: η 10.2 mm r 16.5 mm T 37°C k-0.35 W/m.K h,-12 W/m2 K (a) Construct the thermal circuits, labeling all potentials r2-12.7 mm T-21°C k2-0.80 W/m-K and flows for the systems excluding the contact lens and including the contact lens. Write resistance ele- ments in terms of appropriate parameters. (b) Determine the rate of heat loss from the anterior chamber with and without the contact lens in place.
The energy transferred from the anterior chamber of the eye through the cornea varies considerably depending on whether a contact lens is worn. Treat the eye as a spherical system and assume the system to be at steady state. The convection coefficient h, is unchanged with and without the contact lens in place. The cornea and the lens cover one-third of the spherical surface area. Anterior chamber k2 Conea Contact lens Values of the parameters representing this situa- tion are as follows: η 10.2 mm r 16.5 mm T 37°C k-0.35 W/m.K h,-12 W/m2 K (a) Construct the thermal circuits, labeling all potentials r2-12.7 mm T-21°C k2-0.80 W/m-K and flows for the systems excluding the contact lens and including the contact lens. Write resistance ele- ments in terms of appropriate parameters. (b) Determine the rate of heat loss from the anterior chamber with and without the contact lens in place.
Final answer:The thermal analysis involves constructing thermal circuits for scenarios with and without a contact lens, calculating conductive and convective resistances to then determine the rate of heat loss. The presence of a contact lens alters the overall thermal resistance due to its different thermal conductivity, affecting heat loss from the anterior chamber.Explanation:Thermal Analysis of the Eye With and Without a Contact LensThe question inquires about heat loss from the anterior chamber of the eye, comparing scenarios with and without a contact lens. The parameters provided include the thermal conductivity of the cornea (k), the thermal conductivity of the contact lens (k2), the convection coefficient (h), among others. The eye is approximated as a spherical system at steady state to simplify the analysis.Thermal Circuit ConstructionFor both scenarios, the thermal circuit consists of conductive resistances represented by the cornea (and contact lens, if present) and a convective resistance at the cornea's exterior interface. The total thermal resistance can be calculated using the formulas for conductive and convective resistance,R_cond = L/(kA)andR_conv = 1/(hA)respectively, where L is thickness, k is thermal conductivity, A is the area, and h is the convection coefficient.Heat Loss CalculationTo determine the rate of heat loss, apply Fourier’s law of thermal conduction,q = (T1 - T2) / R_total, where q is the heat flux, T1 and T2 are temperatures, and R_total is the total thermal resistance. In constructing the total resistance, account for the additional layer and altered thermal conductivity when the contact lens is present.In essence, the presence of a contact lens modifies the conductive resistance across the eye's surface, thereby affecting the rate of heat transfer from the anterior chamber to the environment. Since thermal conductivity of the contact lens material differs from that of the corneal tissue, the inclusion of the lens changes the system’s overall thermal resistance and, consequently, the heat loss rate....