A simplified model can be applied to describe the steady-state temperature distribution through the core region, muscle region and skin region of the human body. The core region temperature \(T_{c}\), is the mean operating temperature of the internal organs. The muscle temperature, \(T_{m}\) is the operating temperature of the muscle layer of the human body. Muscle is a shell tissue and can be either resting or actively working. The skin temperature, \(T_{s}\), is the operating temperature of the surface region of the body consisting of a subcutaneous fat layer, the dermal layer and finally epidermal layer. If the metabolic heat rate of a common man is \(45 \mathrm{~W} / \mathrm{m}^{2}\) and the skin temperature is \(32.6^{\circ} \mathrm{C}\), calculate the core region temperature if the thermal conductivity of the core, muscle and skin are \(0.48 \mathrm{~W} / \mathrm{m}^{\circ} \mathrm{C}\) and the thickness of the layers are \(4 \mathrm{~cm}, 2 \mathrm{~cm}\) and \(1 \mathrm{~cm}\) respectively. Also calculate the muscle temperature.