METHODS: The governing equations are modelled by a sudden coincidence of the axes of a disk and the fluid at infinity rotating with uniform angular velocity, together with initial and boundary conditions. Some suitable non-dimensional variables are introduced. The Laplace transform method is used to obtain the exact solutions of the corresponding non-dimensional momentum and energy equations with conditions. Solutions of the velocity for cosine and sine oscillations as well as for temperature fields are obtained and displayed graphically for different values of time (t ), the Grashof number (Gr), the Prandtl number ([Formula: see text]), and the phase angle ([Formula: see text]). Skin friction and the Nusselt number are also evaluated.
RESULTS: The exact solutions are obtained and in limiting cases, the present solutions are found to be identical to the published results. Further, the obtained exact solutions also validated by comparing with results obtained by using Gaver-Stehfest algorithm.
CONCLUSION: The interested physical property such as velocity, temperature, skin friction and Nusselt number are affected by the embedded parameters time (t), the Grashof number (Gr), the Prandtl number ([Formula: see text]), and the phase angle ([Formula: see text]).
MATERIALS AND METHODS: Data were used from the Well-being of the Singapore Elderly (WiSE) study, a nationally representative, cross-sectional survey among Singapore residents aged 60 years and above. Caregiver dependence was ascertained by asking the informant (the person who knows the older person best) a series of open-ended questions about the older person's care needs.
RESULTS: The older adult sample comprised 57.1% females and the majority were aged 60 to 74 years (74.8%), while 19.5% were 75 to 84 years, and 5.7% were 85 years and above. The prevalence of caregiver dependence was 17.2% among older adults. Significant sociodemographic risk factors of caregiver dependence included older age (75 to 84 years, and 85 years and above, P <0.001), Malay and Indian ethnicity (P <0.001), those who have never been married (P = 0.048) or have no education (P = 0.035), as well as being homemakers or retired (P <0.001). After adjusting for sociodemographic variables and all health conditions in multiple logistic regression analyses, dementia (P <0.001), depression (P = 0.011), stroke (P = 0.002), eyesight problems (P = 0.003), persistent cough (P = 0.016), paralysis (P <0.001), asthma (P = 0.016) and cancer (P = 0.026) were significantly associated with caregiver dependence.
CONCLUSION: Various sociodemographic and health-related conditions were significantly associated with caregiver dependence. Dependent older adults will put greater demands on health and social services, resulting in greater healthcare expenditures. Hence, effective planning, services and support are crucial to meet the needs of dependent older adults and their caregivers.