Thermal Properties and Thermodynamics

A refrigerator operates between 120 kPa in an ideal vapour compression cycle with y R - 134a as the refrigerant enters the compressor as saturated vapour and leaves the condenser as saturated liquid. The mass flow rate of the refrigerant is 0.5 kg/s. Properties for R - 134a are as follows: || |---| | Saturated R - 134a| ||||||| |---|---|---|---|---|---| | P (kPa)| T (^oC)| h_f (kJ/kg)| H_g (kJ/kg)| S_f (kJ/kg. k)| S_g (kJ/kg. K)| | 120| - 22.32| 22.5| 237| 0.093| 0.95| | 800| 31.31| 95.5| 267.3| 0.354| 0.918| || |---| | Superheated R - 134a| ||||| |---|---|---|---| | P (kPa)| T (^oC)| h (kJ/kg)| S (kJ/kg)| | 800| 40| 276.45| 0.95|

The power required for the compressor (in kW) is

The non-dimensional fluid temperature profile near the surface of a convectively cooled flat plate is given by ^{$\frac{T_w-T}{T_w-T_w}$} = ^{$a+b\frac{y}{L}+c\bigg(\frac{y}{L}\bigg)^2$}, where y is measured perpendicular to the plate, L is the plate length, and a, b and c are arbitrary constants. T_W and _{^$T_\omega$} are wall and ambient temperatures, respectively. If the thermal conductivity of the fluid is k and the wall heat flux is q², the Nusselt number ^{$Nu=\frac{q''}{T_w-T_\infty}\frac{L}{K}$} is equal to

The contents of a well-insulated tank are heated by a resistor of 23 W in which 10 A current is flowing. Consider the tank along with its contents as a thermodynamic system. The work done by the system and the heat transfer tothe system are positive. The rates of heat (Q), work (W) and change in internal energy (DU) during the process (in kW) are

A spherical steel ball of 12 mm diameter is initially at 1000 K. It is slowly cooled in a surrounding of 300 K. The heat transfer coefficient between the steel ball and the surrounding is 5 W/m²K. The thermal conductivity of steel is 20 W/mK. The temperature difference between the centre and the surface of the steel ball is

A coolant fluid at 30°C flows over a heated flat plate maintained at a constant temperature of 100°C. The boundary layer temperature distribution at a given location on the plate may be approximated as T = 30 + 70exp (y) where y (in m) is the distance normal to the plate and T is in °C. If thermal conductivity of the fluid is 1.0 W/mK, the local convective heat transfer coefficient (in W/m²K) at that location will be

An irreversible heat engine extracts heat from a high temperature source at a rate of 100 kW and rejects heat to a sink at a rate of 50 kW. The entire work output of the heat engine is used to drive a reversible heat pump operating between a set of independent isothermal heat reservoirs at 17°C and 75°C. The rate (in kW) at which the heat pump delivers heat to its high temperature sink is

In a parallel flow heat exchanger operating under steady state, the heat capacity rates (product of specific heat at constant pressure and mass flow rate) of the hot and cold fluid are equal. The hot fluid, flowing at 1 kg/s with Cp = 4 kJ/kgK, enters the heat exchanger at 102°C while the cold fluid has an inlet temperature of 15°C. The overall heat transfer coefficient for the heat exchanger is estimated to be 1 kW/m²K and the corresponding heat transfer surface area is 5m². Neglect heat transfer between the heat exchanger and the ambient. The heat exchanger is characterized by the following relation: 2$\epsilon$= 1 - exp (-2NTU) The exit temperature (in °C) for the cold fluid is

Consider steady-state heat conduction across the thickness in a plane composite wall (as shown in the figure) exposed to convection conditions on both sides.

Given: h_i = 20W / m² k; h₀ = 55 W / m²K; $T_{\infty, 0}$= 2⁰C; k₁ = 20W / mk; k₂ = 500 W / mk; L₁ = 0.30 m and L₂ = 0.15 m. Assuming negligible contact resistance between the wall surfaces, the interface temperature, T (in °C), of the two walls will be

Radiative heat transfer is intended between the inner surfaces of two very large isothermal parallel metal plates. While the upper plate (designated as plate 1) is a black surface and is the warmer one being maintained at 727؛C, the lower plate (plate 2) is a diffuse and gray surface with an emissivity of 0.7 and is kept at 227؛C. Assume that the surfaces are sufficiently large to form a two-surface enclosure and steady state conditions to exist. Stefan Boltzmann constant is given as 5.67×10^-8 W/m²K⁴.

The irradiation (in kW/m²) for the upper plate (plate 1) is

Radiative heat transfer is intended between the inner surfaces of two very large isothermal parallel metal plates. While the upper plate (designated as plate 1) is a black surface and is the warmer one being maintained at 727؛C. The lower plate (plate 2) is a diffuse and gray surface with an emissivity of 0.7 and is kept at 227؛C. Assume that the surfaces are sufficiently large to form a two-surface enclosure and steady state conditions to exist. Stefan Boltzmann constant is given as 5.67×10^-8W/m²K⁴.

If plate 1 is also a diffuse and gray surface with an emissivity value of 0.8, the net radiation heat exchange (in kW/m²) between plate 1 and plate 2 is

For flow of fluid over a heated plate, the following fluid properties are known viscosity = 0.001; specific heat at constant pressure = 1 kJ/kg. k; Thermal conductivity = 1 W/m.k The hydrodynamic boundary layer thickness at a specified location on the plate is 1 mm. The thermal boundary layer thickness at the same location is

For the three dimensional object shown in the figure below, five faces are insulated. The sixth face (PQRS), which is not insulated, interacts thermally with the ambient, with a convective heat transfer coefficient of 10 W/m².k The ambient temperature is 30^oC. Heat is uniformly generated inside the object at the rate of 100 W/m³. Assuming the face PQRS to be at uniform temperature, its steady state temperature is

A hollow enclosure is formed between two infinitely long concentric cylinders of radii 1 m and 2 m, respectively. Radiative heat exchange takes place between the inner surface of the larger cylinder (surface-2) and the outer surface of the smaller cylinder (surface-1). The radiating surfaces are diffuse and the medium in the enclosure is non-participating. The fraction of the thermal radiation leaving the larger surface and striking itself is